Gregory (method)

In counting votes under a single transferable vote system, if a candidate has more than the minimum number of votes needed to be elected (see Droop quota ), a procedure is needed to allocate the surplus votes to other candidates.  The may be done by taking a number of ballots equal to the surplus at random from the ballots of the successful candidate and assigning votes to the next available preference shown on the ballot (that is, to candidates who have not already been elected or excluded).

In 1880, J B Gregory contended that this process of random seelction could produce varying results depending on the choice of the randomly selected ballots used for making the transfers to other candidates.  He suggested that all the relevant ballots should be recounted, assigned to other candidates according to the preferences of the voters, but at a reduced value called the transfer value.  The transfer value is calculated by dividing the surplus votes by the total number of relevant votes.

There are three variations of the Gregory method which differ as to the definition of ‘relevant votes’ for calculating the transfer value.  Gregory’s original suggestion was that only the ballots that last contributed to the creation of the surplus votes should be counted (the Gregory last parcel method).  Some Australian elections use a second method, the Inclusive Gregory method, where relevant votes are defined as all the votes that contributed to a candidate’s surplus.  The BC-STV system recommended by the Citizen’s Assembly uses the Weighted Inclusive Gregory method under which all votes are counted and assigned to other candidates still in the count according to the voters’ preferences, but the ballots are given separate transfer values depending on their origin (that is, whether they are first preferences, or transfers from one or more other candidates).

The Citizens’ Assembly decided that the Weighted Inclusive Gregory method was most in keeping with the goals of proportional representation by the single transferable vote, was fairer to the voters than the other options, and did not add significantly to task of counting (or recounting) ballots.