Fractional transfer

The simplest methods of transferring surpluses under STV involve an element of randomness; partially random systems are used in the Republic of Ireland (except Senate elections) and Malta, among other places.

An alternative is to give each ballot a fractional weighting, to give the effect of subtracting a quota's worth of votes from the winning candidates. Specifically, if the quota is Q, a candidate with V votes is assigned a retention fraction of:

The weight of each ballot is multiplied by the retention fraction of it's top-ranked candidate (or, if equal rankings are allowed, the average of the top-ranked candidates).