Curiosities in drafting for the weighted inclusive Gregory method of STV
In Australia, 2 jurisdictions make use of the weighted inclusive Gregory method of the single transferable vote (STV). The weighted inclusive Gregory method of STV is one of 2 systems recommended by the Proportional Representation Society of Australia as part of a gold standard electoral system.
Each of the 2 jurisdictions, however, has interesting quirks in the drafting of the legislation giving the specifications for the weighted inclusive Gregory method, which are worth exploring.
Western Australia
In Western Australia, the weighted inclusive Gregory method is used for elections to the Legislative Council. The method is prescribed by Schedule 1 of Electoral Act 1907 (WA).
Clauses 6 and 9 have the effect that a continuing candidate, who is raised up to or above the quota at the conclusion of a transfer, is elected. The application of the rules, then, turns on the definition of what is a ‘transfer’.
Clause 19 provides that each of the following ‘constitutes a separate transfer’:
 ‘a transfer under clause 4, 5 or 9 of all the surplus votes of an elected candidate’
 ‘a transfer in accordance with clause 8(a) of all first preference votes of an excluded candidate’
 ‘a transfer in accordance with clause 8(b) of all the votes of an excluded candidate that were transferred to him from a particular candidate each constitutes a separate transfer’
Consider in particular the third limb of the definition. Clause 8 in turn deals with the distribution of an excluded candidate's votes. It seems, then, that the legislation suggests that, during the distribution of an excluded candidate's votes, a continuing candidate should be declared elected only once ‘all the votes … that were transferred to [the excluded candidate] from a particular candidate’ have been distributed.
So far, this is unremarkable. It creates a system of segmented exclusions, where exclusions are performed one stage at a time. Usually, such exclusions are segmented according to the value of ballot papers, but it is not unreasonable to segment according to which candidate the ballot papers were received from.
Looking more closely at clause 8, clause 8(b) provides:
if votes have been obtained by the excluded candidate on a transfer from a particular candidate … and ballot papers transferred to the excluded candidate from that candidate express the next available candidate for a particular continuing candidate —
(i) the total number of those ballot papers must be multiplied by the transfer value at which the votes were so transferred to the excluded candidate; and
(ii) the number so obtained … must be added to the number of votes of the continuing candidate; and
(iii) all those ballot papers must be transferred to the continuing candidate.
In accordance with clause 19, the reference to ‘a transfer from a particular candidate’ must include a transfer of ‘all the votes’ of a previously excluded candidate. Naturally, the distribution of all the votes of a previously excluded candidate may include ballot papers of multiple different transfer values. This now creates a contradiction in clause 8(b)(i), which requires ‘the’ number of such ballot papers to be multiplied by ‘the’ transfer value. Clearly, if there are ballot papers of multiple different transfer values, there can be no single ‘the’ transfer value.
In order to be consistent with clause 19, clause 8(b) could be reworded in similar terms to clause 5, which does not have this issue; for example:
if votes have been obtained by the excluded candidate on a transfer from a particular candidate, the total number of ballot papers of the excluded candidate transferred to the excluded candidate from that candidate that each —
(i) express the next available preference for a particular continuing candidate; and
(ii) have a particular transfer value,
shall be multiplied by that transfer value, the number so obtained … shall be added to the number of votes of the continuing candidate and all those ballot papers shall be transferred to the continuing candidate.
However, the above is not the interpretation which appears to have been applied in WA. Consider the result for the Agricultural Region in the 2021 state general election.
The candidate Bass Tadros receives 197 firstpreference votes. They then receive votes as follows:
 4 votes from the exclusion of Svetlana Ivanchenko
 22 votes from the exclusion of Steven Hopkins
 24 votes from the exclusion of Peter Wallis
 31 votes from the exclusion of Andrew Ballantyne
 65 votes from the exclusion of Brett Tucker
 61 votes from the exclusion of JM David
 131 votes from the exclusion of Greg Norris
 1 vote from the exclusion of Lawrie Carr
 1 vote from the exclusion of Russell Sewell
 194 votes from the exclusion of Peter Turner
 27 votes from the exclusion of Parminder Singh
 329 votes from the exclusion of Connor Whittle
 3 votes from the exclusion of Courtney Henry
 502 votes from the exclusion of Michael J O'Loghlen
 12 votes from the exclusion of Aaron John Horsman
 5 votes from the exclusion of Trevor Young
 1441 votes from the exclusion of Leo Treasure
 5 votes from the exclusion of Luke Clarkson
 2436 votes from the exclusion of Peter Leam
 44 votes from the exclusion of Rod Caddies
Tadros now has 5535 votes and is to be excluded.
Recall from the definition in clause 19, each lot of ballot papers transferred to Tadros from each particular candidate is a separate ‘transfer’. From clause 8, the distribution of Tadros's ballot papers is to be effected one such transfer at a time. Clause 8A provides that those transfers should be considered ‘in the order in which they were received, the earliest transfer being dealt with first’. Finally, clause 9 has the effect that candidates should be declared elected only at the conclusion of processing any of those transfers.
It would seem, then, that one should distribute Tadros's 197 firstpreference votes, then check to see if any candidate reaches the quota, then distribute the 4 votes received from Ivanchenko, then check for election, then distribute the 22 votes from Hopkins, check for election, and so on.
However, in the actual result, Steve Martin is declared elected after 5444 votes are transferred from Tadros, which does not accord with the transfers received by Tadros. The closest figures one can obtain are 3055 (if transferring all ballot papers received up to Clarkson's exclusion) or 5491 (up to Leam's exclusion).
It would therefore appear that a different procedure has been applied in WA (what procedure, exactly, is unclear). Since, due to the issue with clause 8(b), the legislation cannot in fact be given effect as drafted, this is not strictly unreasonable.
New South Wales
In New South Wales, the weighted inclusive Gregory method is used for NSW local government elections. The procedure is prescribed by Schedule 5 of the Local Government (General) Regulation 2021 (NSW).
Sections 7 and 10, similar to their WA counterparts, have the effect that a continuing candidate, who is raised up to or above the quota at the conclusion of a transfer, is elected. Again, the application of the rules, then, turns on the definition of what is a ‘transfer’. Unlike the WA rules, however, the NSW rules do not explicitly define what a ‘transfer’ is.
The equivalent of WA's clause 8(b), NSW's section 9(2)(b), provides:
the total number (if any) of other votes obtained by the excluded candidate … are to be transferred from the excluded candidate in the order of the transfers on which the excluded candidate obtained them (the votes obtained on the earliest transfer being transferred first) as follows—
(i) the total number of ballotpapers transferred to the excluded candidate from a particular candidate and expressing a next available preference for a particular continuing candidate are to be multiplied by the transfer value at which the votes were transferred to the excluded candidate,
(ii) the number so obtained (disregarding any fraction) is to be added to the number of votes of the continuing candidate,
(iii) all those ballot papers are to be transferred to the continuing candidate.
Again, there is reference to ‘the’ transfer value of particular ballot papers, but because the NSW rules leave the term ‘transfer’ undefined, it is perhaps possible to give this provision some meaning, by interpreting ‘transfer’ in this section to mean a distribution of ballot papers of one particular value. This has previously been discussed further by Andrew Conway in a review of the NSW legislation here.
The application of this aspect of the NSW legislation is elucidated by the NSW Electoral Commission's functional specifications for local government elections.
The functional specifications provide, essentially, for ballot papers to be divided into parcels, each of one value, and for the distribution of an excluded candidate's votes to be segmented parcel by parcel. This is consistent with interpreting ‘transfer’ in section 9(2)(b) to mean a distribution of ballot papers of one particular value, i.e. the transfer of a single parcel.
However, the functional specifications also provide that candidates are to be elected (and stop receiving further votes) only after the transfer of all the excluded candidate's parcels. To be consistent with the legislation, this requires ‘transfer’ in section 10(1) to be interpreted differently, as the transfer of all the excluded candidate's votes.
Another issue arises when distributing surplus votes of an elected candidate in section 7(4), which provides:
If by a transfer the number of votes obtained by a candidate exceeds the quota, the surplus is transferred to the continuing candidates next in the order of the voters’ respective preferences in the following manner—
(a) [the surplus fraction is calculated] …,
(b) in relation to any particular ballotpapers [the continued transfer value is calculated] …,
(c) the total number of ballotpapers for surplus votes of the elected candidate that each—
(i) express the next available preference for a particular continuing candidate, and
(ii) have a particular continued transfer value,
are to be multiplied by that continued transfer value and the number obtained (disregarding any fraction) is to be added to the number of votes of the continuing candidate and all those ballot papers are to be transferred to the continuing candidate.
Note that section 7(4)(c) refers to separating ballot papers according to next available preference and according to continued transfer value, but does not explicitly refer to separating ballot papers according to parcel. Indeed, the reference to ‘total’ ballot papers for surplus votes points away from such an interpretation. The legislation appears to suggest that there should be one calculation only for each combination of next available preference and continued transfer value.
The functional specifications, however, provide that the surplus distribution is instead to be performed parcel by parcel, with each parcel handled separately, even if multiple parcels have the same (continued) transfer value. Since fractions are disregarded at each stage, this could potentially have a significant impact on the result.
This interpretation could be consistent with the legislation if ‘transfer’ again means the transfer of a single parcel, and the phrase ‘If by a transfer’ is interpreted to mean that section 7(4)(a) applies a single time once any transfer causes the candidate to exceed the quota, but section 7(4)(b) and (c) apply separately to each transfer received by the candidate.
This seems highly contrived, but again, given the ambiguity of leaving ‘transfer’ undefined, it is also perhaps not strictly unreasonable.
Summary
The WA and NSW legislation each contain curious drafting choices which make the application of the rules somewhat ambiguous. The WA Electoral Commission and NSW Electoral Commission have each applied interpretations which, in some cases, are perhaps not the most obvious interpretations, but which are not necessarily inconsistent with ambiguous legislation.
In the case of candidate exclusion, it is interesting to comment that the WA Electoral Commission has applied an ‘exclusive’ approach, where candidates can be elected part way through the exclusion of a candidate, before all the excluded candidate's ballot papers are distributed (‘exclusive’ because a distinction has been drawn between the ballot papers transferred before and after that candidate's election). The NSW Electoral Commission has applied a more ‘inclusive’ approach, where all the excluded candidate's ballot papers are treated equally, and candidates are elected only once all such ballot papers have been distributed. It has been argued that the ‘inclusive’ approach to exclusions is more consistent with a weighted inclusive Gregory method of surplus distributions.^{1}

Gilmour J. Developing STV rules for manual counting to give effect to the weighted inclusive Gregory method of transferring surpluses, with candidates' votes recorded as integer values. Voting Matters. 2006; (22): 21–25. http://www.votingmatters.org.uk/ISSUE22/I22P5.pdf ↩