OpenSTV implements voting methods where votes consist of rankings of one or more candidates. The terms instant runoff voting, the single transferable vote, and ranked-choice voting (among others) are often used to describe these voting methods.
Instant runoff voting (IRV) is a voting method where ranked ballots are used to simulate a series of runoff elections. IRV is most often used to elect a single candidate but could also be used to elect more than one candidate with a kind of proportional representation.
The single transferable vote (STV) is a voting method where ranked ballots are used to provide proportional representation by transferring surplus votes from winning candidates and transferring votes from losing candidates. When STV is used to elect a single candidate, it is equivalent to IRV.
Ranked-choice voting (RCV) is a relatively new term to describe elections using the single transferable vote or instant runoff voting. San Francisco uses ranked-choice voting to describe its instant runoff voting elections, and Minneapolis uses ranked-choice voting to describe both its instant runoff voting and single transferable vote elections.
OpenSTV also implements a number of other methods based on ranked ballots, including Condorcet voting.
In a traditional first-past-the-post election, the winner of the election may receive far less than a majority of the votes. To ensure that the winner of the election has broad support among the voters, some governments hold a second election, called a runoff election, where the winner of the first election has less than a majority of the vote.
Instant runoff voting provides the benefits of runoff voting but with only one election. Each voter ranks the candidates in order of preference. The votes are first distributed to the candidates according to their first choices. If no candidate has a majority of the votes, then the candidate with the fewest number of votes is eliminated and those ballots are transferred to their next choices. This step is repeated until either a candidate has a majority or only two candidates remain.
Instant runoff voting is also known as ranked-choice voting in the United States and as the alternative vote in the United Kingdom and Australia. Historically, instant runoff voting has also been known as majority preferential voting, English preferential voting, the Hare system, the Ware system. Instant runoff voting is currently used in several cities in the United States (Minneaoplis, MN; Berkeley, Oakland, San Francisco, and San Leandro, CA; and Takoma Park, MD), Australia, and Ireland.
OpenSTV allows you to implement instant runoff voting for your own elections. To learn more about how to do this, please use the links above.
San Francisco enacted instant runoff voting in 2002, and uses the name ranked choice voting. San Francisco's first election with ranked choice voting was in 2004 and it has been used annually since then. San Francisco's charter governing ranked choice voting elections is shown below.
SEC. 13.102. - INSTANT RUNOFF ELECTIONS.
(a) For the purposes of this section: (1) a candidate shall be deemed "continuing" if the candidate has not been eliminated; (2) a ballot shall be deemed "continuing" if it is not exhausted; and (3) a ballot shall be deemed "exhausted," and not counted in further stages of the tabulation, if all of the choices have been eliminated or there are no more choices indicated on the ballot. If a ranked-choice ballot gives equal rank to two or more candidates, the ballot shall be declared exhausted when such multiple rankings are reached. If a voter casts a ranked-choice ballot but skips a rank, the voter's vote shall be transferred to that voter's next ranked choice.
(b) The Mayor, Sheriff, District Attorney, City Attorney, Treasurer, Assessor-Recorder, Public Defender, and members of the Board of Supervisors shall be elected using a ranked-choice, or "instant runoff," ballot. The ballot shall allow voters to rank a number of choices in order of preference equal to the total number of candidates for each office; provided, however, if the voting system, vote tabulation system or similar or related equipment used by the City and County cannot feasibly accommodate choices equal to the total number of candidates running for each office, then the Director of Elections may limit the number of choices a voter may rank to no fewer than three. The ballot shall in no way interfere with a voter's ability to cast a vote for a write-in candidate.
(c) If a candidate receives a majority of the first choices, that candidate shall be declared elected. If no candidate receives a majority, the candidate who received the fewest first choices shall be eliminated and each vote cast for that candidate shall be transferred to the next ranked candidate on that voter's ballot. If, after this transfer of votes, any candidate has a majority of the votes from the continuing ballots, that candidate shall be declared elected.
(d) If no candidate receives a majority of votes from the continuing ballots after a candidate has been eliminated and his or her votes have been transferred to the next-ranked candidate, the continuing candidate with the fewest votes from the continuing ballots shall be eliminated. All votes cast for that candidate shall be transferred to the next-ranked continuing candidate on each voter's ballot. This process of eliminating candidates and transferring their votes to the next-ranked continuing candidates shall be repeated until a candidate receives a majority of the votes from the continuing ballots.
(e) If the total number of votes of the two or more candidates credited with the lowest number of votes is less than the number of votes credited to the candidate with the next highest number of votes, those candidates with the lowest number of votes shall be eliminated simultaneously and their votes transferred to the next-ranked continuing candidate on each ballot in a single counting operation.
(f) A tie between two or more candidates shall be resolved in accordance with State law.
(g) The Department of Elections shall conduct a voter education campaign to familiarize voters with the ranked-choice or, "instant runoff," method of voting.
(h) Any voting system, vote tabulation system, or similar or related equipment acquired by the City and County shall have the capability to accommodate this system of ranked-choice, or "instant runoff," balloting.
(i) Ranked choice, or "instant runoff," balloting shall be used for the general municipal election in November 2002 and all subsequent elections. If the Director of Elections certifies to the Board of Supervisors and the Mayor no later than July 1, 2002 that the Department will not be ready to implement ranked-choice balloting in November 2002, then the City shall begin using ranked-choice, or "instant runoff," balloting at the November 2003 general municipal election.
If ranked-choice, or "instant runoff," balloting is not used in November of 2002, and no candidate for any elective office of the City and County, except the Board of Education and the Governing Board of the Community College District, receives a majority of the votes cast at an election for such office, the two candidates receiving the most votes shall qualify to have their names placed on the ballot for a runoff election held on the second Tuesday in December of 2002.
A commonly used threshold is defined as
number of votes
threshold = --------------------- + 1
number of seats + 1
and then dropping any fraction. This is the smallest threshold such that any candidate receiving this number of votes is guaranteed to be elected.
Methods for transferring surplus votes can be classified into two main groups: random transfer of votes and fractional transfer of votes. Methods for transferring votes from eliminated candidates do not vary greatly.
Here are some examples of variations in STV counting rules.
There are a variety of methods for computing the winning threshold. I prefer to define them in words rather than through formulas.
Within these two types there are two options. A threshold can be static or dynamic. A static threshold is determined once at the beginning and is the same until the end. A dynamic threshold is recomputed every round and decreases as the number of exhausted votes increases. The threshold can also be a whole number or a fraction. Thus, there eight variations for determining the threshold.
The above descriptions of the Droop and Hare thresholds is an ideal which is not always perfectly realized. How well a threshold conforms to the ideal is how "tight" the threshold is. For example, a fractional threshold is slightly tighter than a whole threshold since there is greater precision.
If voters are required to rank all the candidates, then there will be no exhausted votes and the static and dynamic thresholds will be identical. If voters are not required to rank all the candidates, then there will be exhausted votes and the dynamic threshold will be tighter than the static threshold.
The ERS97 rules implement a threshold that is a variation of the Droop threshold. For a static threshold, Droop and ERS97 are identical. For a dynamic threshold, ERS97 is tighter than Droop. For a given candidate, his surplus votes are transferred only once. Thus, when the threshold decreases, these votes that are above the new threshold do not help elect any candidate. The ERS97 threshold takes into account these nontransferable surplus votes when computing the threshold and this results in a threshold that is smaller (tighter) than the Droop threshold.
The basic algorithm above requires that all surplus votes be transferred before the last place candidate is eliminated. However, if the last place candidate can't win, even if he received all the surplus votes, then he can safely be eliminated before transferring the surplus votes. Thus, we can delay the transfer of surplus until after this losing candidate is eliminated.
There are two reasons for doing this. First, eliminating last place candidates is much simpler than transferring surplus votes. Thus, we should delay transferring surplus as long as we can. Second, it will help minimize the number of times that a given vote will be transferred. If we transfer surplus immediately, then part of it could transfer to a candidate who will be eliminated in the next round. These votes would be transferred twice. If we delay the transfer of surplus until after this candidate is eliminated, then the same vote would be transferred just once.
One could eliminate candidates in batches rather than one by one. There are two rationales for this. The first is practicality. If there are many candidates, each with very few votes, then it would be tedious to eliminate them one by one. The second is efficiency. If it is known that several candidates can't win, then it makes sense to eliminate them all right away.
The first method is to eliminate all candidates who have fewer votes than a flat cutoff. This would take place immediately after all surplus votes have been transferred to allow all candidates to take advantage of surplus votes to avoid being eliminated in this fashion. This will be useful when there are many candidates with very few (or even no) first place votes. With many such candidates, it would take many rounds to eliminate them one by one. The batch elimination simplifies the count by eliminating all candidates with very few votes in one round. Note that this will possibly eliminate candidates who have a chance of winning. However, this is not a problem as long as the cutoff is chosen wisely.
The second method is the same as the first, except that the cutoff is chosen as a percentage, say 0.5%, of the total number of votes cast. This method is suggested in the STV rules in Behind the Ballot Box.
The third method is to eliminate all candidates immediately who have no chance of winning. This can happen before surplus votes are transferred and at any time throughout the count. To test if a given candidate can win, it is assumed that she will receive all surplus votes and all transfers from eliminated candidates. Under this assumption, a candidate can win if it is possible that she can beat all candidates between her and the last seat. If it is known that a candidate can't win then she should be eliminated immediately. It is possible that at a given round, that several candidates can't possibly win and they should all be eliminated in a batch.
With random transfer of surplus votes, a number of ballots corresponding to the candidate's surplus are transferred to their next choices. One could choose the last ballots the candidate received, the first ballots the candidate received, or choose some other method. It is important to note is that changing the order of the ballots can change the outcome of the election. In reality, this will only happen in a close election. However, many people find this aspect disturbing.
One could choose a stack or a queue model for transferring ballots. It is useful to visualize the candidates' ballots in separate piles. With a stack model, one would take the ballots off the top of one pile and place them on the top of another pile. With a queue model, one would take the ballots off the top of one pile and place them on the bottom of another pile. With a stack model, one ballot could be transferred many times, while with the queue model, a ballot would probably transferred only once. This implementation uses the queue model.
Another consideration is whether to allow secondary surpluses. A primary surplus arises only after counting the first choices. A secondary surplus could arise after the transfer of a surplus or the transfer of votes from an eliminated candidate. This implementation allows secondary surpluses.
Fractional transfer methods are designed so that the result of the election remains the same when the order of the ballots is changed. The basic idea is that, when transferring a candidate's surplus votes, all of the ballots are transferred but at a fractional value. The fraction is set so that the total value of all the transferred ballots equals the candidate's surplus.
With fractional transfers of votes, secondary surpluses must be allowed. Since the point of fractional transfers is to ensure that the method is independent of the order of the ballots, all the ballots transferred in a given round must be treated identically.
Since floating-point arithmetic, some implementations round all calculations to a number of decimal places. This implementation does all computations in floating point.
The City of Cambridge, Massachusetts has used the single transferable vote to elect its city council and school committee since 1941. The statute providing the counting rules is Chapter 54A of Massachusetts General Laws, the relevant portions of which are included below. Note that § 16(b) allows Cambridge to use any method for transfering surplus votes that was in use in 1938, and Cambridge has chosen to use the Cincinnati method.
The City of Cambridge describes the Cincinnati method as follows: The ballots of the candidate who has a surplus are numbered sequentially in the order in which they have been counted (that is, in the sequence dictated by the random draw of precincts) and then every nth ballot is drawn and transferred to a continuing candidate until the original candidate is credited with ballots equaling no more than quota. n is nearest whole number computed by the formula
n = Candidate's Total Ballots
Surplus Ballots.
A ballot selected by this method that does not show a preference for a continuing candidate is skipped and remains with the original candidate. If not enough ballots are removed when ballots n, 2n, 3n, .... have been transferred, the sequence starts again with n+1, 2n+1, 3n+1, ....
For more information, see http://www.cambridgema.gov/election/Proportional_Representation.cfm.
Since candidates with fewer than 50 votes are eliminated, this method should not be used with a small number of ballots. OpenSTV's implementation of Cambridge STV has been validated against official Cambridge results from 1999 to present.
OpenSTV provides the option of saving the winning candidates' ballots to separate files. The Cambridge rules use these ballots to elect a replacement candidate in the event of a vacancy.
Massachusetts General Laws, Chapter 54A
ELECTION OF CERTAIN CITY AND TOWN OFFICERS BY PROPORTIONAL REPRESENTATION OR PREFERENTIAL VOTING
§ 9. Rules for counting ballots, and determining results. Ballots cast under proportional representation shall be counted and the results determined under the supervision of the director of the count appointed pursuant to section six, according to the following rules:-
(a) The ballots in each ballot receptacle shall be examined for validity and those which are found to be blank or otherwise invalid shall be separated from the valid ballots. The number of valid ballots from each precinct and the total number of valid ballots shall be recorded. If a ballot does not clearly show which candidate the voter prefers to all others, or if it contains any word, mark or other sign apparently intended to identify the voter, it shall be set aside as invalid. Every ballot not thus invalid shall be counted according to the intent of the voter, so far as that can be clearly ascertained, whether marked according to the directions printed on it or not. No ballot shall be held invalid because the names of candidates thereon for whom the voter did not mark a choice have been stricken out, unless such striking out constitutes an identifying mark. A single cross on a ballot on which no figure 1 appears shall be considered equivalent to the figure 1. If a ballot contains both figures and crosses, the order of the choice shown by the figures shall be taken as the voter's intention in so far as the order is clearly indicated. If the consecutive numerical order of the figures on a ballot is broken by the omission of one or more figures, the smallest number marked shall be taken to indicate the voter's first choice, the next smallest his second, and so on, without regard to the figure or figures omitted.
(b) Each candidate shall be credited with one vote for every valid ballot that is sorted to him as first choice, or otherwise credited to him as hereinafter provided, and no ballot shall ever be credited to more than one candidate at the same time.
(c) A "quota" is the smallest number of votes which any candidate must receive in order to be assured of election without more candidates being elected than there are offices to be filled. It shall be determined by dividing the total number of valid ballots by one more than the total number of candidates to be elected and adding one to the result, disregarding fractions. Whenever at any stage of the counting the number of ballots credited to a candidate becomes equal to the quota, he shall be declared elected, and no ballots in excess of the quota shall be credited to him except as provided in rule (f) or (1) of this section.
(d) The ballots shall be sorted according to the first choices marked on them, the ballots from each polling place being handled together, and those from different polling places being handled in the order of polling places determined under the provisions of section eight.
(e) If a candidate is elected while the ballots are being sorted according to first choices, any subsequent ballots which show him as first choice shall each be credited to the second choice marked on it, or, if the second choice also has been elected, to the next choice marked on it for a candidate not yet elected.
(f) If during the first sorting of ballots, ballots are found which are marked for a candidate already elected as first choice, but show no clear choice for any unelected candidate, such ballots shall at the end of the sorting be given to the candidate of their first choice, and in their place an equal number, as nearly as possible, of the last ballots sorted to that candidate which show a clear choice for unelected candidates, all as determined by the director of the count, shall be taken and re-sorted to unelected candidates as if they were then being sorted for the first time.
(g) When all the ballots have been thus sorted and credited to the first available choices marked on them, every candidate who is credited with fewer ballots than the number of signatures required for his nomination shall be declared defeated.
(h) All the ballots of the candidates thus defeated shall be transferred, each to the candidate indicated on it as next choice among the continuing candidates. A "continuing candidate" is a candidate not as yet either elected or defeated. Any ballot taken for transfer which does not clearly indicate any candidate as next choice among the continuing candidates shall be set aside as "exhausted".
(i) When all the ballots of the candidates thus defeated have been transferred, the one candidate who is then lowest on the poll shall be declared defeated and all his ballots transferred in the same way.
(j) Thereupon the candidate who is then lowest shall be declared defeated and all his ballots similarly transferred; and in like manner candidates shall be declared defeated one at a time and all their ballots transferred.
(k) If, when a candidate is to be declared defeated, two or more candidates are tied at the bottom of the poll, that one of the tied candidates shall be declared defeated who was credited with fewest ballots immediately prior to the last transfer of ballots. If two or more of the tied candidates were tied at that stage of the count, also, the second tie shall be decided by referring similarly to the standing of candidates immediately prior to the last transfer of ballots before that. This principle shall be applied successively as many times as may be necessary, a tie shown at any stage of the count being decided by referring to the standing of the tied candidates immediately prior to the last preceding transfer of ballots. Any tie not otherwise provided for shall be decided by lot.
In interpreting this and other rules contained in this section the transfer of all ballots from candidates defeated together under rule (g) of this section, and the transfer of all ballots from each candidate defeated thereafter shall each constitute a single separate transfer.
(l) Whenever candidates to the number to be elected have received the quota, any transfer of ballots in progress when the last quota was reached shall be completed, but immediately thereafter all continuing candidates shall be declared defeated and the election shall be at an end. Whenever all ballots of all defeated candidates have been transferred, and it is impossible to defeat another candidate without reducing the continuing candidates below the number still to be elected, all the continuing candidates shall be declared elected and the election shall be at an end.
(m) A record of the count shall be kept in such form as to show, after each sorting or transfer of ballots, the number thereby credited to each candidate, the number thereby set aside as exhausted, the total for each candidate, the total set aside as exhausted, and the total number of valid ballots found by adding the totals of all candidates and the total set aside as exhausted.
(n) Every ballot that is transferred from one candidate to another shall be stamped or marked so that its entire course from candidate to candidate can be conveniently traced.
(o) If at any time after the first sorting of the ballots a ballot is found to have been credited to the wrong candidate, it may be transferred, as part of the transfer that is in progress, to the continuing candidate, if any, to whom it should have been credited at the time the error was made, or, if it should previously have become exhausted, may be set aside as exhausted as part of the transfer that is in progress; provided, that if the number of misplaced ballots found is sufficient to make it possible that any candidate has been wrongly defeated, so much of the sorting and transferring as may be required to correct the error shall be done over again before the count proceeds.
If in correcting an error any ballots are re-sorted or re-transferred, every ballot shall be made to take the same course that it took in the original count unless the correction of an error requires its taking a different course. The principles of the rules of this section shall apply also to any recount which may be made after the original count has been completed.
(p) The director of the count and his assistants shall proceed with reasonable expedition in the counting of the ballots, but may take recesses at the discretion of the director. The city or town clerk shall make proper provision for the safekeeping of the ballots while the counting is not in progress.
(q) The candidates, their witnesses, alternate witnesses and representatives accredited under section seven, representatives of the press, and, as far as may be consistent with good order and with convenience in the counting and transferring of the ballots, the public shall be afforded every facility for being present and witnessing the counting and transferring of the ballots.
(r) Each of the candidates entitled to appoint witnesses of the central count as provided in section seven shall be entitled to appoint a member of a board of review of the central count. Such appointment shall be made within the time and in the manner prescribed for the appointment of such witnesses of the central count. In the central counting place a board of review so constituted shall be given facilities for examining all the ballots in the quota of each elected candidate in order to make sure that all the ballots of such quota are rightfully credited to the candidate toward whose election they have been counted, that the number of ballots therein is actually equal to the quota prescribed in this section, and that"exhausted" ballots have been properly so designated. Any errors discovered by such a board of review shall be reported to the director of the count.
(s) When the election with respect to any particular body or office is at an end the director of the count shall publicly announce the result of the vote for such body or office. The provisions of section one hundred and seven of chapter fifty-four relative to presiding officers and other election officers at polling places shall, so far as apt, apply to the director of the count and his assistants with respect to all ballots, records, copies of records, envelopes and ballot boxes, transmitted to the central counting place under section eight and to all other papers, records and apparatus used in counting the votes at the central counting place, except that ballots cast for a particular body or office, as well as those spoiled and returned and those not given out, shall be enclosed, and the envelopes sealed and delivered or transmitted to the city or town clerk as soon as may be after the public announcement of the result of the vote for such body or office.
(t) No canvass or count of the vote shall be made on the Lord's day.
§ 10. Ballots; preservation; examination. The ballots cast at each election by proportional representation or preferential voting shall be preserved by the city or town clerk until the term of office of the members of the body or of the officer elected thereby has expired, and shall be available for examination continuously throughout the business day, under supervision of the city or town clerk, on written application signed by not less than one hundred voters of the city or town and the payment of a fee of twenty-five dollars for each day on which such inspection is held. Such application shall name not more than three representatives of the applicants to make such examination.
§ 11. Publication of statements regarding ballots cast. Within thirty days after an election to elect members of a body by proportional representation or an officer by preferential voting, the city or town clerk shall cause the ballots cast for such body or office to be examined and shall publish a statement showing-
(a) The number of first-choice ballots cast for each candidate at each polling place.
(b) The number of ballots from each polling place finally counted for each of the elected candidates.
(c) The number of the exhausted ballots from each polling place which showed one or more choices for elected candidates and the number which did not show any such choice.
(d) The number of blank ballots cast for each body or office at each polling place.
(e) The number of ballots otherwise invalid cast for each body or office at each polling place.
(f) The number of first choices, second choices, third choices, and so on, used in the election of each of the elected candidates.
(g) Such other information in regard to the ballots as the city or town clerk may deem of interest.
A copy of such statement shall be kept on file in the office of the city or town clerk open to public inspection.
§ 12. Recount of ballots. Partial or complete recounts of the ballots cast for any body or office in an election by proportional representation or by preferential voting shall take place in the manner provided in sections one hundred and thirty-four to one hundred and thirty-seven, inclusive, of said chapter fifty-four, except that any petition shall be submitted on or before five o'clock in the afternoon of the third day following the public announcement by the director of the count of the result of the vote for such body or office and shall be on a form approved and furnished by the city or town clerk and be signed in a town by ten or more voters of such town, in a city, except Boston, by fifty or more voters of such city and in Boston by two hundred and fifty or more voters of said Boston and except that any such recount in any city or in any town divided into precincts shall be conducted for the entire city or town instead of for specified precincts. If a partial or complete recount of the ballots cast in such an election shall in fact take place, it shall be conducted according to the rules prescribed for the original count as nearly as is practicable.
§ 13. Vacancies in bodies elected by proportional representation; filling. When a vacancy occurs in an elective body whose members were elected by proportional representation, such vacancy shall be filled for the remainder of the unexpired term by a public recount of the ballots credited at the end of the original count to the candidate elected thereby whose place has become vacant. Except for the following special rules, the provisions governing the original count shall be in effect:
(a) All choices marked for candidates theretofore elected or who have become ineligible or have withdrawn shall be disregarded:
(b) The ballots shall be sorted each to the earliest choice marked on it for any of the eligible candidates.
(c) If any candidate has to his credit more than half of the ballots which show any preference among the eligible candidates he shall be declared elected to the vacant place.
(d) If no candidate receives more than half of such ballots, the candidates lowest on the poll shall be declared defeated one after another and after each candidate is defeated his ballots shall be transferred among the continuing candidates.
(e) The process hereinbefore provided shall be continued until one candidate is credited with more ballots than all the other undefeated candidates together, when he shall be declared elected to the vacant place.
If a vacancy in an elective body occurs for which no regularly nominated candidate remains it shall be filled for the unexpired term by a majority vote of the remaining members; and if but a single member remains or if a majority vote of the remaining members is not obtained within thirty days after the vacancy occurs, it shall be filled by a special election, in the case of a single vacancy, by preferential voting or, in case two or more vacancies exist at the same time, by proportional representation.
§ 14. Ballots; rules for counting where election by preferential voting. Ballots cast under preferential voting shall be counted in the central counting place under the supervision of the director of the count, in accordance with the following rules:-
(a) The ballots shall first be sorted according to the first choices marked on them, and the total number of valid ballots thus sorted to each candidate shall be ascertained. The validity of ballots shall be determined according to the principles laid down for the count of ballots in an election by proportional representation in rule (a) of section nine.
(b) If any candidate is found to have been marked as first choice on more than half of the valid ballots he shall be declared elected.
(c) If no candidate is so elected after the count of first choices, every candidate who is credited with fewer ballots than the number of signatures required for his nomination shall be declared defeated.
(d) All the ballots of the candidates so defeated shall be transferred, each to the candidate indicated on it as next choice among the undefeated candidates. Any ballot taken for transfer which does not clearly indicate any candidate as next choice among the undefeated candidates shall be set aside as "exhausted".
(e) If, after this or any subsequent transfer of ballots, one candidate is credited with more than half of the valid ballots which have not become exhausted, he shall be declared elected.
(f) If no candidate is so elected after the transfer of the ballots of candidates defeated under rule (c), the one candidate who is then lowest on the poll shall be declared defeated and all his ballots transferred in the same way.
(g) Thereupon, if no candidate is yet elected, the candidate who is then lowest shall be declared defeated and all his ballots similarly transferred. Thus candidates shall be deemed defeated one at a time, and all their ballots transferred until some candidate has received the necessary majority of the ballots which have not become exhausted and is accordingly declared elected.
(h) Ties shall be decided, a record of the count kept, errors corrected, recesses taken, and candidates and others permitted to be present according to the principles prescribed for elections by proportional representation in rules (k), (m), (o), (p) and (q) of section nine.
§ 15. Vacancies in single elective offices; filling. All provisions of law from time to time applicable in the case of a vacancy in an elective office shall continue to apply after the filling of such office by preferential voting, except that any election to fill such vacancy shall also be by preferential voting.
§ 16. Mechanical or other voting devices; methods of counting first choices.
(a) In conducting any election by proportional representation or preferential voting, mechanical or other devices may be used, subject, however, to the provisions of sections thirty-two to thirty-nine, inclusive, of chapter fifty-four, if the city council or the town passes a vote providing expressly that such devices shall be used in such election; and said sections, so far as apt, shall be applicable in all respects in case of such devices so used. In case such devices are to be used in any city or town, the city or town clerk may modify the form of ballot, the rotation of names thereon, the directions to voters and other details in respect to the election process; provided, that no change shall be made which will alter or impair the principles of voting or counting the ballots governing elections by proportional representation or preferential voting, as the case may be, but the voter may be limited to not less than fifteen choices for any particular body or office.
(b) In any city or town where elections by proportional representation are to be held, any method of counting the voters' first choices and treating any such choices in excess of the quota, provided for under any system of proportional representation which on January first, nineteen hundred and thirty-eight was in effect for the purpose of municipal elections in any city of the United States, may be substituted for the method of counting such choices set forth in this chapter, if the registrars of voters determine that such substitution is advisable; provided, that they issue regulations embodying the method so substituted and provided, further, that such regulations shall not be effective with respect to any election unless at least thirty days prior thereto copies of such regulations are available for delivery to such of the voters as may request them.
Scotland enacted these rules for local elections in 2007. This is a straightforward implementation of STV and recommended to organizations using STV for the first time.
The complete set of rules can be found at http://www.opsi.gov.uk/legislation/scotland/ssi2007/ssi_20070042_en.pdf. The relevant portions of the these rules are included below.
OpenSTV's implementation of the Scottish STV rules has been validated against the eSTV program.
SCOTTISH STATUTORY INSTRUMENTS
2007 No. 42
REPRESENTATION OF THE PEOPLE
The Scottish Local Government Elections Order 2007
Citation, commencement and extent
1.—(1) This Order may be cited as the Scottish Local Government Elections Order 2007.
(2) This Order shall come into force on 17th February 2007 except for the purposes of any election to be held on or before 2nd May 2007.
(3) This Order shall extend to Scotland only.
Interpretation
2. In this Order, unless the context otherwise requires—
"anonymous entry" in relation to a register of electors, shall be construed in accordance with section 9B of the 1983 Act and "the record of anonymous entries" means the record prepared in pursuance of regulations made by virtue of paragraph 8A of Schedule 2 to the 1983 Act;
"ballot paper account" has the meaning given in rule 39(3);
"companion" has the meaning given in rule 34(1);
"corresponding number list" means the list prepared in accordance with rule 15;
"completed corresponding number list" has the meaning given in rule 39(1);
"continuing candidate" means any candidate not deemed to be elected as a councillor and not excluded from the list of candidates under rule 50;
"council" means a council constituted by section 2 of the Local Government etc. (Scotland) Act 1994(b);
"count" means all the operations involved in counting and crediting votes, including the ascertainment of the quota, the transfer of ballot papers and the exclusion of candidates;
"election court" means the court constituted under the 1983 Act for the trial of a petition questioning an election;
"election petition" means a petition presented in pursuance of Part III of the 1983 Act as that Act is applied by this Order;
"election" means an election under the Local Governance (Scotland) Act 2004 and, for the purposes of articles 1(2) and 6(2), an election under the Local Government etc. (Scotland) Act 1994;
"elector" means a person who is registered in the register (or, in the case of a person who has an anonymous entry in the register, in the record of anonymous entries) to be used at the election as a local government elector for the local government area in which the election is held and includes a person shown in the register as below voting age if (but only if) it appears from the register that such person will be of voting age on the day fixed for the poll;
"electoral registration officer" has the same meaning as in the 1983 Act;
"electronic counting system" means such computer hardware and software, other equipment, data and services as may be necessary in order to—
(a) maintain a list of the areas in relation to which an election is being held by reference to ward barcodes on ballot papers issued to voters in relation to that area;
(b) read electronically the votes marked and the unique identifying number on each ballot paper returned;
(c) calculate the number of votes cast for each candidate at the election otherwise than on any spoilt, tendered or rejected ballot paper; and
(d) ensure the retention of a record of the votes given for each candidate, without identifying the elector by whom, or on whose behalf, the votes were cast;
"list of proxies" has the meaning given by paragraph 5(3) of Schedule 4 to the Representation of the People Act 2000;
"local authority" means a council constituted by section 2 of the Local Government etc. (Scotland) Act 1994;
"local government area" is to be construed in accordance with section 1 (local government areas) of the Local Government etc. (Scotland) Act 1994;
"next available preference" means a preference which is the second or, as the case may be, subsequent preference in consecutive order for a continuing candidate (any preferences for any candidate who is deemed to be elected or is excluded from the list of candidates under rule 50 being ignored);
"non-transferable paper" means a ballot paper on which there is no next available preference;
"proper officer" has the same meaning as in section 235(3) of the Local Government (Scotland) Act 1973(a);
"postal voters list" means the list of persons kept in pursuance of paragraph 5(2) (persons whose applications to vote by post have been granted) of Schedule 4 to the Representation of the People Act 2000(b);
"proxy postal voters list" means the list of persons kept in pursuance of paragraph 7(8) (persons whose applications to vote by post as proxy have been granted) of Schedule 4 to the Representation of the People Act 2000;
"qualifying address" in relation to a person registered in the register of electors, is the address in respect of which that person is entitled to be so registered;
"quota" has the meaning given in rule 46;
"registered political party" means a party registered under Part II of the Political Parties, Elections and Referendums Act 2000(c);
"returning officer" means, in relation to an election, the returning officer appointed for the election under section 41(1) (duty of local authority to appoint returning officer for each local authority election) of the 1983 Act;
"special lists" means the lists kept under paragraph 5 of schedule 4 to the Representation of the People Act 2000(d);
"spoilt ballot paper" has the meaning given in rule 36;
"stage of the count" means—
(a) the determination of the number of votes for each candidate as first preference;
(b) the transfer of transferable papers from a candidate deemed to be elected who has a surplus; or
(c) the exclusion of a candidate at any given time;
"surplus" means the number of votes, if any, by which the total number of votes credited to a candidate deemed to be elected as a councillor exceeds the quota;
"tendered ballot paper" has the meaning given in rule 35(1);
"tendered votes list" has the meaning given in rule 35(8);
"transferable paper" means a ballot paper on which a next available preference is given;
"transfer value" means the value of a vote on a ballot paper calculated in accordance with rule 48;
"unique identifying mark" means the mark (for example, a bar code, letter, number or numerical sequence) on a ballot paper which is unique to that ballot paper and which identifies that ballot paper as a ballot paper to be issued by the returning officer; and
"voter" means a person voting at an election and includes a person voting as proxy and "vote" (whether noun or verb) shall be construed accordingly except that any reference to an elector voting or an elector's vote shall include a reference to an elector voting by proxy or an elector's vote given by proxy.
* * *
SCHEDULE 1
PART III — CONTESTED ELECTIONS
* * *
Counting of votes
* * *
First stage
45.—(1) The returning officer shall sort the valid ballot papers into parcels according to the candidates for whom first preference votes are given.
(2) The returning officer shall then—
(a) count the number of ballot papers in each parcel;
(b) credit the candidate receiving the first preference vote with one vote for each ballot paper; and
(c) record those numbers.
(3) The returning officer shall also ascertain and record the total number of valid ballot papers.
The quota
46.—(1) The returning officer shall divide the total number of valid ballot papers for the electoral ward by a number exceeding by one the number of councillors to be elected at the election for that electoral ward.
(2) The result of the division under paragraph (1) (ignoring any decimal places), increased by one, is the number of votes needed to secure the return of a candidate as a councillor (in these rules referred to as the "quota").
Return of councillors
47.—(1) Where, at any stage of the count, the number of votes for a candidate equals or exceeds the quota, the candidate is deemed to be elected.
(2) A candidate is returned as a councillor when declared to be elected in accordance with rule 55(a).
Transfer of ballot papers
48.—(1) Where, at the end of any stage of the count, the number of votes credited to any candidate exceeds the quota and, subject to rules 49 and 52, one or more vacancies remain to be filled, the returning officer shall sort the ballot papers received by that candidate into further parcels so that they are grouped—
(a) according to the next available preference given on those papers; and
(b) where no such preference is given, as a parcel of non-transferable papers.
(2) The returning officer shall, in accordance with this rule and rule 49, transfer each parcel of ballot papers referred to in paragraph (1)(a) to the continuing candidate for whom the next available preference is given on those papers and shall credit such continuing candidates with an additional number of votes calculated in accordance with paragraph (3).
(3) The vote on each ballot paper transferred under paragraph (2) shall have a value ("the transfer value") calculated as follows—
A divided by B
Where
A = the value which is calculated by multiplying the surplus of the transferring candidate by the value of the ballot paper when received by that candidate; and
B = the total number of votes credited to that candidate,
the calculation being made to five decimal places (any remainder being ignored).
(4) For the purposes of paragraph (3)—
(a) "transferring candidate" means the candidate from whom the ballot paper is being transferred; and
(b) "the value of the ballot paper" means—
(i) for a ballot paper on which a first preference vote is given for the transferring candidate, one; and
(ii) in all other cases, the transfer value of the ballot paper when received by the transferring candidate.
Transfer of ballot papers — supplementary provisions
49.—(1) If, at the end of any stage of the count, the number of votes credited to two or more candidates exceeds the quota the returning officer shall—
(a) first sort the ballot papers of the candidate with the highest surplus; and
(b) then transfer the transferable papers of that candidate.
(2) If the surpluses determined in respect of two or more candidates are equal, the transferable papers of the candidate who had the highest number of votes at the end of the most recent preceding stage at which they had unequal numbers of votes shall be transferred first.
(3) If the numbers of votes credited to two or more candidates were equal at all stages of the count, the returning officer shall decide, by lot, which candidate's transferable papers are to be transferred first.
Exclusion of candidates
50.—(1) If, one or more vacancies remain to be filled and—
(a) the returning officer has transferred all ballot papers which are required by rule 48 or this rule to be transferred; or
(b) there are no ballot papers to be transferred under rule 48 or this rule, the returning officer shall exclude from the election at that stage the candidate with the then lowest number of votes.
(2) The returning officer shall sort the ballot papers for the candidate excluded under paragraph (1) into parcels so that they are grouped—
(a) according to the next available preference given on those papers; and
(b) where no such preference is given, as a parcel of non-transferable papers.
(3) The returning officer shall, in accordance with this article, transfer each parcel of ballot papers referred to in paragraph (2)(a) to the continuing candidate for whom the next available preference is given on those papers and shall credit such continuing candidates with an additional number of votes calculated in accordance with paragraph (4).
(4) The vote on each ballot paper transferred under paragraph (3) shall have a transfer value of one unless the vote was transferred to the excluded candidate in which case it shall have the same transfer value as when transferred to the candidate excluded under paragraph (1).
(5) This rule is subject to rule 52.
Exclusion of candidates — supplementary provisions
51.—(1) If, when a candidate has to be excluded under rule 50—
(a) two or more candidates each have the same number of votes; and
(b) no other candidate has fewer votes,
paragraph (2) applies.
(2) Where this paragraph applies—
(a) regard shall be had to the total number of votes credited to those candidates at the end of the most recently preceding stage of the count at which they had an unequal number of votes and the candidate with the lowest number of votes at that stage shall be excluded; and
(b) where the number of votes credited to those candidates was equal at all stages, the returning officer shall decide, by lot, which of those candidates is to be excluded.
Filling of last vacancies
52.—(1) Where the number of continuing candidates is equal to the number of vacancies remaining unfilled, the continuing candidates are deemed to be elected.
(2) Where the last vacancies can be filled under this rule, no further transfer shall be made.
The Green Party of California (GPCA) adopted these rules in 2000. The rules are described in the GPCA bylaws. The rules are based on the description of STV found in Electoral System Design: The New International IDEA Handbook, except that GPCA uses a fractional threshold, and does not elect candidates that do not reach the a full (static) threshold.
Neither IDEA nor the GPCA bylaws specify a method of breaking ties. This implementation breaks all ties randomly. See Jonathan Lundell's paper Random tie-breaking in STV for the rationale.
The Electoral Reform Society of Great Britian and Ireland has issued its recommended rules for implementing the single transferable vote. The most recent version of its rules issued in 1997 and is commonly referred to as the ERS97 rules. These rules are similar to those used in Northern Ireland and Malta.
The complete set of rules can be found at http://www.cix.co.uk/~rosenstiel/stvrules/. The most relevant portions are copied below.
OpenSTV's implementation of the ERS97 rules has been validated against the eSTV program, which can be found at http://www.estv.co.uk/.
4. GENERAL DESCRIPTION OF THE COUNT
4.1 The count is divided into a number of stages. At the first stage the voting papers are counted to determine the total vote. They are then sorted according to their first preferences, and any papers which are invalid are removed. The total number of valid votes is then found and the quota calculated. Any candidates who have at least a quota of first preference votes are deemed elected at this stage.
4.2 Each subsequent stage of the count is concerned either with the transfer of surplus votes of a candidate whose vote exceeds the quota, or with the exclusion of one or more candidates with the fewest votes.
4.3 This procedure continues until either sufficient candidates have reached the quota to fill all the seats, or there is the same number of candidates left as unfilled seats.
4.4 These rules refer to the various forms published by the Electoral Reform Society. The use of these forms is optional, but where they are used, the various options should be made easier, particularly for those not experienced in conducting STV counts.
4.5 In the rules below, words in bold type indicate that there is a definition in the glossary (section 6).
5. DETAILED INSTRUCTIONS FOR THE COUNT In a public election, it is necessary to include certain formalities, such as unsealing and opening the ballot boxes at the start, checking the number of papers in each and ascertaining that the candidates and their agents are content at the conclusion of each stage. For simplicity these have been omitted from these instructions.
5.1 First stage
5.1.1 Count all the voting papers to determine the total number of votes cast.
5.1.2 Sort the voting papers into first preferences, setting aside any invalid papers. Count the number of invalid papers, and subtract this from the total vote to get the total valid vote.
5.1.3 Check the sorting, and count the papers for each candidate into bundles, inserting a counting slip (green) in each bundle marked with the name of the candidate, the number of papers, and 'first stage'. For very small elections, the use of counting slips may be dispensed with.
5.1.4 Check the counting. Enter on each candidate's vote record form (yellow) the total number of first preference votes.
5.1.5 Copy the candidates' votes from the vote record forms onto a result sheet (white), and check that their total is the same as the total valid vote.
5.1.6 Calculate the quota by dividing the total valid vote by one more than the number of places to be filled. Take the division to two decimal places. If the result is exact that is the quota. Otherwise ignore the remainder, and add 0.01.
5.1.7 Considering each candidate in turn in descending order of their votes, deem elected any candidate whose vote equals or exceeds (a) the quota, or (b) (on very rare occasions, where this is less than the quota), the total active vote, divided by one more than the number of places not yet filled, up to the number of places to be filled, subject to paragraph 5.6.2.
5.1.8 That completes the first stage of the count. Now proceed to section 5.2 below.
5.2 Subsequent stages
5.2.1 Each subsequent stage will involve either the distribution of a surplus, or, if there is no surplus to distribute, the exclusion of one or more candidates.
5.2.2 If one or more candidates have surpluses, the largest of these should now be transferred. However the transfer of a surplus or surpluses is deferred and reconsidered at the next stage, if the total of such surpluses does not exceed either:
(a) The difference between the votes of the two candidates who have the fewest votes, or
(b) The difference between the total of the votes of two or more candidates with the fewest votes who could be excluded under rule 5.2.5, and the vote of the candidate next above.
5.2.3 If one or more candidates have surpluses which have not been deferred, transfer the largest surplus. If the surpluses of two or more candidates are equal, and they have the largest surplus, transfer the surplus of the candidate who had the greatest vote at the first stage or at the earliest point in the count, after the transfer of a batch of papers, where they had unequal votes. If the votes of such candidates have been equal at all such points, the Returning Officer shall decide which surplus to transfer by lot.
5.2.4 The transfer of a surplus constitutes a stage in the count. Details of how to do this are in section 5.3. If, after completing the transfer, there are still any untransferred surpluses, and not all the places have been filled, proceed as in paragraph 5.2.2
5.2.5 If, after all surpluses have been transferred or deferred, one or more places remain to be filled, the candidate or candidates with the fewest votes must be excluded. Exclude as many candidates together as possible, provided that:
(a) Sufficient candidates remain to fill all the remaining places
(b) The total votes of these candidates, together with the total of any deferred surpluses, does not exceed the vote of the candidate next above.
If the votes of two or more candidates are equal, and those candidates have the fewest votes, exclude the candidate who had the fewest votes at the first stage or at the earliest point in the count, after the transfer of a batch of papers, where they had unequal votes. If the votes of such candidates have been equal at all such points the Returning Officer shall decide which candidate to exclude by lot.
5.2.6 Details of how to exclude a candidate are given in section 5.4.
5.2.7 Exclusion of one or more candidates constitutes a stage in the count. If, after completing this, there are any surpluses to transfer, and not all the places have been filled, proceed as in paragraph 5.2.2. Otherwise proceed to exclude further candidates as in paragraph 5.2.5.
5.3 Transfer of a surplus
5.3.1 If a surplus arises at the first stage, select for examination all the papers which the candidate has received.
5.3.2 If a surplus arises at a later stage, because of the transfer of another surplus or the exclusion of a candidate or candidates, select only the last received batch of papers, which gave rise to the surplus.
5.3.3 Examine the selected voting papers and sort them into their next available preferences for continuing candidates. Set aside as non-transferable papers any on which no next available preference is expressed.
5.3.4 Check the sorting, count and bundle the papers now being transferred to each candidate, also any non-transferable papers. Insert a counting slip in each bundle marked with the stage number, the name of the candidate to whom the papers are being transferred, and the number of papers in the bundle.
5.3.5 Count the number of transferable papers and enter the number for each candidate on the vote record forms.
5.3.6 Prepare a surplus form (pink). Copy the number of papers for each candidate from the vote record forms to the surplus form, and check the total.
5.3.7 Calculate the total value of the transferable papers. If this exceeds the surplus, determine the transfer value of each paper by dividing the surplus by the number of transferable papers, to two decimal places, ignoring any remainder. If the total value does not exceed the surplus, the transfer value of each paper is its present value.
5.3.8 Calculate the value to be credited to each candidate by multiplying the transfer value by the number of papers, check the totals, and enter these on the surplus form.
5.3.9 Copy the values to be credited, and the non-transferable difference arising from the neglected remainder, from the surplus form to the vote record forms and to the result sheet.
5.3.10 Add these values to the previous votes for each candidate, and add the non-transferable difference to the previous total of non-transferable votes, entering the figures onto the vote record forms and the result sheet.
5.3.11 Add up the new total number of votes on the result sheet, and check that this still equals the original total valid vote.
5.3.12 Complete the counting slips with the transfer value of each paper, and place the bundles of voting papers for each candidate with those previously received. In a small election, where counting slips are not being used, each ballot paper should be marked with its transfer value.
5.3.13 Considering each continuing candidate in turn in descending order of their votes, deem elected any candidate whose vote now equals or exceeds
(a) the quota, or
(b) the total active vote, divided by one more than the number of places not yet filled, up to the number of places remaining to be filled, subject to paragraph 5.6.2.
5.4 Transfer of the votes of excluded candidates
5.4.1 Take together all the bundles of papers which are currently credited to the candidate or candidates to be excluded, and arrange them in batches in descending order of transfer value. Check that the number and total value of the papers in each batch agrees with the numbers on the vote record forms and the result sheet. Prepare an exclusion form (blue).
5.4.2 First, take the batch of papers with the highest transfer value. Sort them according to the next available preferences for continuing candidates, and set aside as non-transferable papers any on which no next available preference is expressed.
5.4.3 Check the sorting, count and bundle the papers for each candidate and any non-transferable papers. Insert a counting slip in each bundle stating the stage, the name of the candidate to whom the papers are being transferred, the number of papers, and the transfer value of each paper. If counting slips are not being used, the transfer value should be marked on each paper.
5.4.4 Check the counting and enter the number of papers for each candidate and the number of non-transferable papers on the vote record forms.
5.4.5 Copy the number of papers to be transferred to each candidate and the number of non-transferable papers, from the vote record forms onto a column of the exclusion form, and check the total.
5.4.6 Determine the total value of the papers for each candidate and that of the non-transferable papers and check the total.
5.4.7 Copy the total values for each candidate from the exclusion form to the vote record forms, and place the bundles of voting papers for each candidate with those previously received.
5.4.8 If any papers have become non-transferable before any candidate has been deemed elected, recalculate the quota as in paragraph 5.1.6, ignoring the non-transferable vote.
5.4.9 Considering each continuing candidate in turn in descending order of their votes, deem elected any candidate whose vote now equals or exceeds
(a)the quota, or
(b)the total active vote, divided by one more than the number of places not yet filled, up to the number of places remaining to be filled, subject to paragraph 5.6.2.
5.4.10 Ensure that no further papers are given to candidates who are no longer continuing candidates because they have been deemed to be elected after transferring a batch of papers.
5.4.11 As in paragraph 5.4.2 and subsequently, sort and transfer each batch of papers in turn in descending order of transfer value, complete a column of the exclusion form for each batch, and deem candidates to be elected as appropriate.
5.4.12 After all the batches of papers have been transferred, the right hand (totals) column on the exclusion form should be completed and these totals checked against the vote record form(s) of the excluded candidate(s).
5.4.13 Copy the total values to be credited from the exclusion form to the vote record forms and to the result sheet, and add these to the previous totals for each candidate.
5.4.14 Copy the new vote for each candidate from the vote record forms onto the result sheet, and the new non-transferable vote from the exclusion forms onto the result sheet.
5.4.15 Add up the new total vote on the result sheet and check that this agrees with the original total valid vote.
5.5 Completion of the count
5.5.1 If a proposed exclusion of one or more candidates would leave only the same number of continuing candidates as there are places remaining unfilled, all such continuing candidates shall be deemed to be elected.
5.5.2 If, at any point in the count, the number of candidates deemed to be elected is equal to the number of places to be filled, no further transfers of papers are made, and the remaining continuing candidate(s) are formally excluded.
5.5.3 The count is now completed.
5.5.4 Declare elected all those candidates previously deemed to be elected.
5.6 Notes
5.6.1 Calculation of the total active vote may be simplified if the Count Control Form (beige) is used. This form enables the Returning Officer to keep a continuous check on the number of votes which are required for election of a candidate at any point in the count, by deducting the quotas (or actual votes if less) of the candidates deemed elected, and the total of non-transferable votes, from the total valid vote, to give the total active vote.
5.6.2 If, when candidates should be deemed elected under sections 5.1.7, 5.3.13 or 5.4.9, two or more have the same number of votes, and there are not sufficient places left for them all, then the one or more to be deemed elected shall be selected in descending order of votes at the first stage or at the earliest point in the count, after the transfer of a batch of papers, where they had unequal votes. If, however, their votes have been equal at all such points, then none of them shall be deemed elected at that stage.
5.6.3 If a re-count is conducted where a decision has been determined by lot, and the relevant votes are still equal in the recount, the earlier determination shall still hold.
5.6.4 These rules refer to the various forms published by the Electoral Reform Society. The use of these forms is optional, but where they are used, the various options should be made easier.
6. GLOSSARY OF TERMS in alphabetical order
6.1 Batch: a bundle containing all the papers of one value in a transfer.
6.2 Candidate's vote: the value of voting papers credited to a candidate at any point in the count.
6.3 Continuing candidate: a candidate not yet deemed elected or excluded.
6.4 Count Control form (beige): a form designed to be used to keep a continuous note of the total active vote, and hence the vote required for election of a candidate at any point in the count.
6.5 Counting slip (green): a slip inserted with a bundle of voting papers, showing the stage at which the papers are transferred, the name of the candidate to whom they are transferred, the number of papers in the bundle, and the transfer value of each paper.
6.6 Deemed elected: status of a candidate who is elected subject to formal confirmation.
6.7 Exclusion form (blue): a form showing the distribution of batches of papers in descending order of transfer value from one or more excluded candidates to continuing candidates.
6.8 First preference: this is shown by the figure "1" standing alone against only one candidate on a voting paper; or the name or code of a candidate entered on a voting paper as first preference.
6.9 Invalid paper: a voting paper on which no first or only preference is expressed, or on which any first preference is void for uncertainty.
6.10 Next available preference: the next subsequent preference in order, passing over earlier preferences for candidates already deemed elected or excluded. There is no next available preference where the next sequential preference for a continuing candidate is uncertain.
6.11 Non-transferable difference: the difference between the value of a surplus and the total new value of the papers transferred, which arises from ignoring the remainder when calculating the transfer values to two decimal places.
6.12 Non-transferable paper: a voting paper on which no next available preference for a continuing candidate is expressed, or on which any next available preference is void for uncertainty.
6.13 Non-transferable vote: the value credited as non-transferable at any point in the count.
6.14 Quota: the vote which, if attained by as many candidates as there are places to be filled, leaves at most a quota for all other candidates; the total valid vote divided by one more than the number of places to be filled, or a lesser value calculated as in paragraph
5.4.8.
6.15 Result sheet (white): a sheet showing the vote credited to each and every candidate, and the non-transferable vote at successive stages of the count.
6.16 Stage of the count: the determination of the first preference vote for each candidate (first stage) or the transfer of a surplus or the exclusion of a candidate, or two or more candidates at the same time, and the transfer of their votes.
6.17 Subsequent preferences: shown by the figures "2", "3", etc., standing alone against different candidates on a voting paper; or the names or codes of candidates entered in order on a voting paper as second, third, etc., preferences.
6.18 Surplus: the amount by which a candidate's vote exceeds the quota.
6.19 Surplus form (pink): A form showing the calculation of the transfer value and the distribution of transferable papers from a candidate deemed elected to continuing candidates.
6.20 Total active vote: the sum of the votes credited to all continuing candidates, plus any votes awaiting transfer.
6.21 Total valid vote: the total number of valid voting papers.
6.22 Transfer value: the value, being unity or less, at which a voting paper is transferred from an elected or an excluded candidate to a continuing candidate. Where counting slips are not used, it is recommended that this value be marked on each paper at the time of transfer.
6.23 Transferable paper: a voting paper which, having been allocated to a candidate, bears a next available preference for a continuing candidate.
6.24 Valid voting paper: a voting paper on which a first or an only preference is unambiguously expressed.
6.25 Value: the value of a voting paper is unity, or a lower value at which it was last transferred.
6.26 Vote record form (yellow): a form showing the vote credited to any one candidate, or showing the non-transferable vote, at successive stages of the count.
7. CASUAL VACANCIES
No purpose is served by holding a by-election, since a representative so elected would represent the dominant opinion group in the particular multi-member constituency, and not necessarily the opinion group of the vacating member. There are three possibilities:
7.1 The vacancy may be filled by recounting all the original voting papers for the constituency, passing over all preferences for the vacating representative, and for any other candidate who now withdraws. With the provision that no other previously elected representative should be excluded, the count proceeds until a stage when a new representative has been elected. This representative, together with the surviving representatives, will reflect the original wishes of the electorate. This method requires that the original voting papers should be retained under secure conditions.
7.2 The vacancy may be filled by co-option. A person could be co-opted who reflects, as far as possible, the opinion group of the vacating representative. The party, if any, of the vacating representative might be invited to nominate a candidate for the elected body to co-opt. Alternatively, the last formally excluded candidate could be co-opted.
7.3 The vacancy may be left unfilled. When a large number of representatives has been elected together by the Single Transferable Vote, it may be thought that the surviving representatives can adequately represent the electorate until the next election.
The STV rules used for local elections in Northern Ireland are similar to the ERS97 rules, but significantly simpler.
The Local Elections (Northern Ireland) Order 1985. Statutory Instrument 1985 No. 454. Not available online.
STATUTORY INSTRUMENTS
1985 No. 454
NORTHERN IRELAND
The Local Elections (Northern Ireland) Order 1985
PART IV — Counting Of Votes
Interpretation
41. In this Part of these rules—
"continuing candidate" means any candidate not deemed to be elected and not excluded;
"count" means all the operations involved in the counting of the first preferences recorded for candidates, the transfer of the surpluses of elected candidates, and the transfer of the vote, of excluded candidates;
"deemed to be elected" means deemed to be elected for the purpose of the counting of the votes but without prejudice to the declaration of the result of the poll;
"mark" means a figure a word written in the English language or a mark such as "X";
"non-transferable vote" means a ballot paper—
(a) on which no second or subsequent preference is recorded for a continuing candidate, or
(b) which is excluded by the returning officer under rule 50(4);
"preference" as used in the following contexts has the meaning assigned below:—
(a) "first preference" means the figure "1" or any mark or word which clearly indicates a first (or only) preference;
(b) "next available preference" means a preference which is the second or, as the case may be, subsequent preference recorded in consecutive order for a continuing candidate (any candidate who is deemed to be elected or is excluded thereby being ignored), and
(c) in this context, a "second preference" is shown by the figure "2" or any mark or word which clearly indicates a second preference, a third preference by the figure "3" or any mark or word which clearly indicates a third preference, arid so on;
"quota" means the number calculated in accordance with rule 48;
"surplus" means the number of votes by which the total number of votes for any candidate (whether first preference or transferred votes, or a combination of both) exceeds the quota; but references in these rules to the transfer of the surplus means the transfer (at a transfer value) of all transferable papers from the candidate who has the surplus;
"stage of the count" means—
(a) the determination of the first preference vote for each candidate;
(b) the transfer of a surplus of a candidate deemed to be elected; or
(c) the exclusion of one or more candidates at any given time;
"transferable paper" means a ballot paper on which, following a first preference, a second or subsequent preference is recorded in consecutive numerical order for a continuing candidate;
"transferred vote" means a vote derived from a ballot paper on which a second or subsequent preference is recorded for the candidate to whom that paper has been transferred;
"transfer value" means the value of a transferred vote calculated in accordance with paragraph (4) or (7) of rule 49, as the case may be.
* * *
Rejected ballot papers
46.— (1) Any ballot paper—
(a) which does not bear the official mark; or
(b) on which the figure 1 standing alone is not placed so as to indicate a first preference for some candidate; or
(c) on which the figure 1 standing alone indicating a first preference is set opposite the name of more than one candidate; or
(d) on which anything (other than the printed number on the back) is written or marked by which the voter can be identified; or
(e) which is unmarked or void for uncertainty,
shall be void and not counted, but the ballot paper shall not be void by reason only of carrying the words "one", "two", "three", (and so on) or any other mark instead of a figure if, in the opinion of the returning officer, the word or mark clearly indicates a preference or preferences.
(2) The returning officer shall endorse "rejected" on any ballot paper which under this rule is not to be counted and if an election agent objects to his decision shall add to the endorsement the words "rejection objected to".
(3) The returning officer shall prepare a statement showing the number of ballot papers rejected by him under each of sub-paragraphs (a), (b), (c), (d), and (e) of paragraph (I) and shall, on request, allow any candidate or agent of a candidate to copy such statement.
(4) The decision of the returning officer on any question arising in respect of a ballot paper shall be final but shall be subject to review on an election petition.
First stage
47.— (1) The returning officer shall sort the ballot papers into parcels according to the candidates for whom first preference votes are given.
(2) The returning officer shall then count the number of first preference votes given on ballot papers for each candidate and shall record those numbers.
(3) The returning officer shall also ascertain and record the number of valid ballot papers.
The quota
48.— (1) The returning officer shall divide the number of valid ballot papers by a number exceeding by one the number of members to be elected.
(2) The result, increased by one, of the division under paragraph (1) (any fraction being disregarded) shall be the number of votes sufficient to secure the election of a candidate (in these rules referred to as "the quota").
(3) At any stage of the count a candidate whose total vote equals or exceeds the quota shall be deemed to be elected, except that at an election where there is only one vacancy a candidate shall not be deemed to be elected until the procedure set out in paragraphs (1) to (3) of rule 51 has been complied with.
Transfer of votes
49.— (1) Where the number of first preference votes for any candidate exceeds the quota, the returning officer shall sort all the ballot papers on which first preference votes are given for that candidate into sub-parcels so that they are grouped—
(a) according to the next available preference given on those papers for any continuing candidate, or
(b) where no such preference is given, as the sub-parcel of non-transferable votes.
(2) The returning officer shall count the number of ballot papers in each parcel referred to in paragraph (1)
(3) The returning officer shall, in accordance with this rule and rule 50, transfer each sub-parcel of ballot papers referred to in sub-paragraph (a) of paragraph (1) to the candidate for whom the next available preference is given on those papers.
(4) The vote on each ballot paper transferred under paragraph (3) shall be at a value ("the transfer value") which—
(a) reduces the value of each vote transferred so that the total value of all such votes does not exceed the surplus, and
(b) is calculated by dividing the surplus of the candidate from whom the votes arc being transferred by the total number of the ballot papers on which those votes an given, the calculation being made to two decimal places (ignoring the remainder if any).
(5) Where, at the cad of any stage of the count involving the transfer of ballot papers, the number of votes for any candidate exceeds the quota, the returning officer shall sort the ballot papers in the sub-parcel of transferred votes which was last received by that candidate into separate sub-parcels so that they are grouped—
(a) according to the next available preference given on those papers for any continuing candidate, or
(b) where no such preference is given, as the sub-parcel of non-transferable votes.
(6) The returning officer shall, in accordance with this rule and and rule 50, transfer each sub-parcel of ballot papers referred to in sub-paragraph (a) of paragraph (5) to the candidate for whom the next available preference is given on those papers.
(7) The vote on each ballot paper transferred under paragraph (6) shall be at—
(a) a transfer value calculated as set out in sub-paragraph (b) of paragraph (4), or
(b) at the value at which that vote was received by the candidate from whom it is now being transferred,
whichever is the less.
(8) Each transfer of a surplus constitutes a stage in the count.
(9) Subject to paragraph (10), the returning officer shall proceed to transfer transferable papers until no candidate who is deemed to be elected has a surplus or all of the vacancies have been filled.
(10) Transferable papers shall not be liable to be transferred where any surplus or surpluses which, at a particular stage of the count, have not already been transferred, are
(a) less than the difference between the total vote then credited to the continuing candidate with the lowest recorded vote and the vote of the candidate with the next lowest recorded vote; or
(b) less than the difference between the total votes of the two or more continuing candidates, credited at that stage of the count with the lowest recorded total numbers of votes and the candidate next above such candidates.
(11) This rule shall not apply at an election where there is only one vacancy.
Supplementary provisions on transfer
50.— If at any stage of the count, two or more candidates have surpluses, the transferable papers of the candidate with the largest surplus shall be transferred first, and if—
(a) the surplus determined in respect of two or more candidates are equal, the transferable papers of the candidate who had the highest recorded votes at the earliest preceding stage at which they had unequal votes, shall be transferred first, and
(b) the votes credited to two or more candidates were equal at all stages of the count, the returning officer shall decide between those candidates by lot and the transferable papers of the candidate on whom the lot falls shall be transferred first.
(2) The returning officer shall, on each transfer of transferable papers under rule 49—
(a) record the total transfer value of the votes transferred to each candidate;
(b) add that value to the previous total of votes recorded for each candidate, and record the new total;
(c) record as non-transferable votes the difference between the surplus and the total transfer value of transferred votes and add that difference to the previously recorded total of non-transferable votes, and
(d) compare—
(i) the total number of votes then recorded for all of the candidates, together with total number of non-transferable votes, with
(ii) the recorded total of valid first preference votes.
(3) All ballot papers transferred under rule 49 or 51 shall be clearly marked, either individually or as a sub-parcel, so as to indicate the transfer value recorded at that time to each vote on that paper or, as the case may be, all the papers in that sub-parcel.
(4) Where a ballot paper is so marked that it is unclear to the returning officer at any stage of the count under rule 49 or 51 for which candidate the next preference is recorded, the returning officer shall treat any vote on that ballot paper as a non-transferable vote; and votes on a ballot paper shall be so treated where, for example, the names of two or more candidates (whether continuing candidates or not) are so marked that, in the opinion of the returning officer, the same order of preference is indicated or the numerical sequence is broken.
Exhaustion of candidates
51.—(1) if—
(a) all transferable papers which under the provisions of rule 49 (including that rule as applied by paragraph (11)) and this rule are required to be transferred, have been transferred, and
(b) subject to rule 52 one or more vacancies remain to be filled,
the returning officer shall exclude from the election at that stage the candidate with the then lowest vote (or, where paragraph (12) applies, the candidates with the then lowest votes).
(2) The returning officer shall sort all the ballot papers on which first preference votes are given for the candidate or candidates excluded under paragraph (1) into two sub-parcels so that they are grouped as—
(a) ballot papers on which a next available preference is given, and
(b) ballot papers on which no such preference is given (thereby including ballot papers on which preferences are given only for candidates who are deemed to be elected or are excluded).
(3) The returning officer shall, in accordance with this rule and rule 50, transfer each sub-parcel of ballot papers referred to in sub-paragraph (a) of paragraph (2) to the candidate for whom the next available preference is given on those papers.
(4) The exclusion of a candidate, or of two or more candidates together, constitutes a further stage of the count.
(5) If, subject to rule 52, one or more vacancies still remain to be filled, the returning officer shall then sort the transferable papers, if any, which had been transferred to any candidate excluded under paragraph (1) into sub-parcels according to their transfer values.
(6) The returning officer shall transfer those papers in the sub-parcel of transferable papers with the highest transfer value to the continuing candidates in accordance with the next available preferences given on those papers (thereby passing over candidates who are deemed to be elected or are excluded).
(7) The vote on each transferable paper transferred under paragraph (6) shall be at the value at which that vote was received by the candidate excluded under paragraph (1).
(8) Any papers on which no next available preferences have been expressed shall be set aside as non-transferable votes.
(9) After the returning officer has completed the transfer of the ballot papers in the sub-parcel of ballot papers with the highest transfer value he shall proceed to transfer in the same way the sub-parcel of ballot papers with the next highest value and so on until he has dealt with each sub-parcel of a candidate excluded under paragraph (1).
(10) The returning officer shall after each stage of the count completed under this rule—
(a) record—
(i) the total value of votes, or
(ii) the total transfer value of votes transferred to each candidate;
(b) add that total to the previous total of votes recorded for each candidate and record the new total;
(c) record the value of non-transferable votes and add that value to the previous non-transferable votes total, and
(d) compare—
(i) the total number of votes then recorded for each candidate together with the total number of non-transferable votes, with
(ii) the recorded total of valid first preference votes.
(11) If after a transfer of votes under any prevision of this rule, a candidate has a surplus, that surplus shall be dealt with in accordance with paragraphs (5) to (10) of rule 49 and rule 50.
(12) Where the total of the votes of the two or more lowest candidates, together with any surpluses not transferred is less than the number of votes credited to the next lowest candidate, the returning officer shall in one operation exclude such two or more candidates.
(13) If where a candidate has to be excluded under this rule, two or more candidates each have the same number of votes and are lowest—
(a) regard shall be had to the total number of votes credited to those candidates at the earliest stage of the count at which they had an unequal number of votes and the candidate with the lowest number of votes at that stage shall be excluded; and
(b) where the number of votes credited to those candidates was equal at all stages, the returning officer shall decide between the candidates by lot and the candidate on whom the lot falls shall be excluded.
Filling last vacancies
52.— (1) Where the number of continuing candidates is equal to the number of vacancies remaining unfilled the continuing candidates shall thereupon be deemed to be elected.
(2) Where only one vacancy remains unfilled and the votes of any one continuing candidate are equal to or greater than the total of votes credited to another or other continuing candidates together with any surplus not transferred, the candidate shall thereupon be deemed to be elected.
(3) Where the last vacancies can be filled under this rule, no further transfer
Previous rules are all designed for hand counting. Meek and Warren STV provide the most accurate proportional representation, but the count must be done with a computer and cannot be done by hand. The basic idea is similar to Fractional Transfer STV. There are two main differences: (1) winning candidates also receive vote transfers from eliminated candidates and surplus votes from other winning candidates, and (2) when a candidate is eliminated it is as if the candidate never entered the election. These changes create a feedback loop of vote transfers which requires a computer to implement.
OpenSTV also supports these other methods listed below.
Condorcet elects the candidate who wins all pairwise competitions against the other candidates. Sometimes a cycle will occur where no Condorcet winner exists. In this instance, other techniques are necessary to break the cycle. The set of candidates in the cycle is called the Smith set. Three methods are available for choosing the winner from the cycle: Borda, IRV, and Schwartz Sequential Dropping (SSD).
With SNTV, only the first-place votes are used. In an actual election, the voter would simply pick one candidate instead of ranking the candidates. The candidates receiving the largest number of first-place votes are elected. SNTV provides only limited proportional representation, but it is a useful alternative if it is not possible to have ranked ballots.
With the Borda count, if there eight candidates competing, then a candidate gets seven points for every first ranking, six points for every second ranking, and so on. If a candidate is not ranked on a ballot then he gets no points. When more than one candidate is to be elected, the Borda count provides some degree of proportionality, but not as well as STV methods.
With the Bucklin system, if a candidate receives a majority of first choices, then she is elected. Otherwise, if a candidate is first or second on a majority of ballots, then she is elected. This process is repeated for higher choices as necessary.
Coombs is like IRV, but with one difference. The candidate with the most last rankings is eliminated at each round. If a ballot does not rank all the candidates, then the unlisted candidates share the last ranking equally.
With approval voting, each voter may approve of one or more candidates. The candidate being approved of by the largest number of voters is elected. Each candidate ranked on a ballot counts as an approval, and thus the order of the candidates on the ballot is not relevant.
OpenSTV has created the following ballot files using ballot data published by government sources to allow you to better understand ranked-choice voting. You may use these ballot for any purpose and freely distribute them. For listings below without links, the data has not yet been processed into the OpenSTV file format.