There are a variety of methods for computing the winning threshold. I prefer to define them in words rather than through formulas.
- Droop -- The smallest number such that any candidate receiving this number of votes is guaranteed to be elected.
- Hare -- The largest number such that all winners can receive this number of votes.
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.
