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Variants of the Gregory Fractional Transfer


The simple but realistic example below, which appears at Pages 22-23 of the PRSA's Submission No. 142 to the federal Joint Standing Committee on Electoral Matters in 2014, will help illuminate the great differences that may arise from the adoption of one particular transfer value definition instead of another, and thereby emphasize the importance of immediately abandoning the current deeply-flawed definition: there were many instances during the 2013 Senate scrutinies where small numbers of votes determined who was excluded at a particular count.

Suppose that the quota is 450,000 and that candidate Perez begins with 400,000 first preferences and later receives 1,000,000 ballot papers with transfer value 0.1, taking her progress total to 500,000 and requiring a surplus of 50,000 votes to be distributed.
Under the Senate transfer value definition as at March 2014, each of the 1,400,000 ballot papers involved would move on at value 50,000/1,400,000 or 1/28 (taken to eight decimal places): in other words, those giving a first preference to Perez would have over 96% of their voteís value used in helping her get elected, whereas those who have already contributed to the election of others would see just over 64% of their voteís remaining value used in electing her.

The alternative Weighted Inclusive Gregory method applies the surplus factor 50,000/500,000 or 0.1 to each previous transfer value, meaning that everyone contributing to Perezís election has 90% of their ballot paperís remaining value used in the process, and 10% available for transfer to continuing candidates: the first preferences for Perez would therefore be transferred at value 0.1 while the value of the other ballot papers would reduce to 0.01 when moving to their next available preference.

Some of these salient differences in the distribution of the surplus of 50,000 votes, and their implications are summarized in the table below:

Transfer value
Percentage of previous value used
Division of Surplus
Percentage of Surplus
Senate definition as at March 2014
(Unweighted Inclusive Gregory Method)

First preferences 0.03571428 96.4%
Other votes at 0.1 0.03571428 64.3%
Weighted Inclusive Gregory Method

First preferences 0.10000000
Other votes at 0.1 0.01000000

The difference of more than 25,000 votes in the apportionment of the surplus could well be critical to what happens at further counts in the scrutiny were the next available preference different on the two parcels of votes that Perez received. The scale of that type of potential distortion and its impact on the composition of the surplus highlights why the current unsatisfactory definition should not be used again.

A thorough review of underlying principles and the research literature was undertaken for the Western Australian Electoral Commission by Dr Narelle Miragliotta following controversy over transfer values in the Mining and Pastoral region (including one that increased as a surplus was being distributed) after the 2001 Legislative Council elections in Western Australia. Her comprehensive report Determining The Result: Transferring Surplus Votes in the Western Australian Legislative Council assessing the options commonly under consideration was released in 2002, and was reflected in a change to WA's Electoral Act 1907 in 2006.
When voters are given some real latitude in the marking of preferences, it is vital that adequate resources be applied to make as many as possible aware that marking more preferences can only increase the chances of making their vote fully effective. There also needs to be a slight refinement of the Western Australian surplus fraction concept to successfully apply the Weighted Inclusive Gregory methodology and simultaneously keep exhausted votes to a minimum.
First, the total transferable vote weight for continuing candidates, the aggregate amount by which their progress totals would increase if all the ballot papers were transferred at their current value, needs to be established: if, in the normal run of events, it exceeds the surplus, the previous transfer values are now all multiplied by the surplus divided by the total transferable vote weight, when the surplus is transferred to continuing candidates; otherwise, all of the previous transfer values remain unchanged and some exhaustion of votes is unavoidable as the transfer is made.
Ballot papers for candidates that cannot be elected and are being excluded are always transferred at their prevailing unused value to others that remain as continuing candidates. Where they are not transferable, exhaustion of the remaining value of the ballot papers involved is unavoidable.

As recently as 2008, a submission to the Joint Standing Committee on Electoral Matters of the Federal Parliament by the Australian Electoral Commission defended the Senate's Unweighted Inclusive Gregory method, and did not support its replacement with the Weighted Inclusive Gregory method.