Inclusive Gregory – another serious problem with the Victorian Legislative Council’s Electoral System

My criticism of Group Voting Tickets at upper house elections is well known, but in the past I have also criticised the formula used at Senate and the Victorian Legislative Council elections to distribute surplus-to-quota preferences.

I’ll get into the technical detail of the problem inside the post, but the problem is that Victoria uses the “Inclusive Gregory (IG)” method to determine how to distribute surplus-to-quota preferences.

This method weights the transfer of surplus-to-quota votes in favour of parties that have already elected members, and weights against parties with no elected members.

Essentially ballot papers that have already played a part in electing members are given greater weight than ballot papers that have elected nobody.

I wrote about this problem back in 2014 when the use of IG resulted in the election of an extra Labor MLC for Northern Victoria Region ahead of a Country Alliance candidate.

And the problem has reared its head again in 2022 in the count for South-Eastern Metropolitan Region.

The output of my ABC Legislative Council Calculator for South-Eastern Metropolitan Region reveals the problem. (The problem currently appears as outlined below but may change with further counting.)

As it currently appears, after the election of the Legalise Cannabis candidate Rachel Payne, the IG method causes her surplus to massively over-represent Labor’s preference tickets and under-represent ballot papers for the Greens and Legalise Cannabis.

This over-representation brings Liberal Democrat David Limbrick close to winning the final seat, and the only reason Limbrick is even close to election is the distortion caused by the IG method.

The South-Eastern Metropolitan Count

The table below summarise the votes by source, and percentage by source, for Rachel Payne (Legalise Cannabis) when she is declared elected. This is called Count 23 in the calculator output. At this point Payne had 68,568 votes, the quota is 55,146, and Payne’s surplus to be distributed as preferences is 13,422 votes.

The fourth and fifth columns in the table show the votes distributed as part of the surplus at Count 24, and each party’s percentage of the surplus votes distributed. The final column shows the next available preference.

South-East Metro – Surplus of Rachel Payne (Legalise Cannabis)
Votes on Election Votes in Surplus Next
Vote Source Votes Pct Votes Pct Pref
Legalise Cannabis 16,399 23.9 1,230 9.2 LIB
Victorian Socialists 1,284 1.9 96 0.7 LDP
Reason Party 1,622 2.4 122 0.9 LIB
Animal Justice 4,314 4.3 324 2.4 LIB
Angry Victorians 918 1.3 69 0.5 LDP
Labor Party 21,395 31.2 9,880 73.6 LDP
Greens 22,636 33.0 1,698 12.7 LIB

The problem here is obvious. If the Labor Party makes up 31.2% of the votes held by Rachel Payne on election, why do Labor votes make up 73.6% of Payne’s surplus while the percentage for every other party is devalued?

This comes about because the Labor ballot papers transferred by the group voting ticket remain the same, but their value as votes decreases as the votes elect candidate. The simplified version of the count produced by the calculator has the following transfers for Labor’s votes.

  • At Count 1, Labor’s Lee Tarlamis held all 131,687 Labor votes and was declared elected.
  • At Count 2, 76,541 (23.13%) votes (131,687 ballot papers at 0.5812 transfer value) were transferred to and elected the second candidate on the Labor ticket, Michael Galea.
  • At Count 4, 21,395 (6.47%) votes (131,687 ballot papers at 0.1625 transfer value) were transferred to the third Labor candidate Tien Kieu)
  • At Count 22, Tien Kieu was excluded and 21,395 (6.47%) votes (131,687 ballot papers at 0.1625 transfer value) were distributed to Legalise Cannabis Victoria (Rachel Payne).

So at each point the number of ballot papers was the same on distribution, but their value as votes was reduced.

Except when the votes formed part of Payne’s surplus when their influence was siddenly inflated.

The transfers at Counst 2 and 4 are explained by votes being distributed at a reduced value called a Transfer Value. The following formula is very important.

Number of Votes = Number of Ballot Papers multiplied by the Transfer Value.

The real count is more complex than simplified calculator output in the above example. The calculator assume all votes are ticket votes at top of each party’s list.

To understand the problem of Payne’s surplus distribution, let’s look at the votes held by her grouped by Transfer Value. Payne’s vote consists of –

  • 47,173 votes from six parties representing 47,173 ballot papers at Transfer Value = 1.0
  • 21,395 Labor votes representing 131,687 ballot papers at Transfer Value = 0.1625

The problem when Payne’s surplus is distributed stems from the Inclusive Gregory Transfer Value formula which is –

TV = (Surplus Votes) divided by (Total Ballot Papers)

The divisor is Total Ballot Papers, not Votes. Because the Labor bundle in Payne’s total has many more ballot papers, the use of the above formula weights the preferences to be distributed in a manner that means Labor votes are over-represented in the surplus.

The Transfer Value for Payne is 0.0750, and working out how many votes are transferred from each source party is Votes Transferred = 0.0750 times (Ballot Papers)

Because the Labor candidate’s ballot papers make up such a large proportion of the ballot papers held by Payne, Labor’s ballot papers disproportionally end up in the surplus distributed, crowding out votes from other parties.

How to Fix this Problem

The Inclusive Gregory method was essentially invented to conduct manual counts. Trying to keep track of multiple transfer values was considered too complex for a manual count. With Inclusive Gregory, whenever a candidate reaches a quota, all ballot papers distributed as part of the subsequent surplus moved at the same transfer value. There are no new Transfer Values created.

With counts now computerised, the solution is the Weighted Inclusive Gregory (WIG) Method, already introduced for WA Legislative Council and NSW local government elections.

The Weighted Inclusive Gregory Transfer Value formula is (Surplus Votes) divided by (Total Votes)

On Payne’s exclusion in the South-East Metro count, the WIG Transfer Value would be (13422/68568) = 0.195747.

This would be applied to the votes for each party, not the ballot papers.

The 22,636 Green votes (22,636 ballot papers times old transfer value 1.0 times new transfer value 0.195747) would become 4,431 votes or 33.0% of the surplus, the same as the proportion of Green votes held by Payne on election.

The Labor calculation would be 131,687 ballot papers times old TV (0.1625) times new TV (0.195747) = 4,189 votes, 31.2% of the surplus, the same percentage of Labor Votes as formed part of Payne’s total vote.

If the Weighted Inclusive Gregory method were used for this count, then the Liberal Democrats would not receive the huge boost of Labor preferences produced by the Inclusive Gregory Method.

The Weighted Inclusive Gregory Method removes the bias built into the Inclusive Gregory Method that favours the vote of parties whose votes have already elected members.

The Gregory Method

Just for completeness, the Gregory Method used in the ACT and Tasmanian Hare-Clark system uses the following Transfer Value formula.

Gregory TV = (Surplus Votes) divided by (Last bundle of Ballot Papers received)

For candidate with a quota of votes on first preferences, the ‘last bundle’ is the first preference tally. Gregory, IG and WIG reduce to the same formula for candidates with more than a quota on first preferences.

Being based on the last bundle, the Gregory Method does not include votes held by a candidate before they reached the quota. So it is not inclusive of all votes, hence the name for IG and WIG.

Fractional Methods

Gregory, IG and WIG are all fractional transfer methods where all ballot papers are distributed on the election of a candidate but at a fractional value, the Transfer Value.

The alternative method is random sampling, used for the NSW Legislative Council since 1978 and for the Senate from 1949 to 1983. The Transfer Value was calculated by the Gregory Method, but then used to determine a number of ballot papers to be drawn from the total ballot papers held by the elected candidate. The sampled ballot papers were effectively distributed at Transfer Value = 1.

The difficulty of getting a proper random sample is why Fractional methods have become the preferred method.

Sampling Exhausted Votes

The NSW Legislative Council and the ACT Hare-Clark system both exclude ballot papers with no further preferences before calculating Transfer Value. This method requires a default where a ballot paper cannot increase in value to deal with the situation where the number of ballot papers to distribute is less than the surplus.

The introduction of WIG for NSW local government elections has included a provision to exclude exhausting preference before calculating the transfer value.

UPDATE – Western Metropolitan Region

A similar problem is currently (9am Friday 2 December) occurring in Western Metropolitan Region. Of the 71,263 votes held by Legalise Cannabis on passing the quota, only 19.3% came from Labor. But in the distribution of the Legalise Cannabis surplus, 68% of the preferences come from Labor, and on the current count, are largely responsible for the Liberal Party winning the final seat at the expense of the DLP.

4 thoughts on “Inclusive Gregory – another serious problem with the Victorian Legislative Council’s Electoral System”

  1. This sounds horrible, tho way over my head. Thank you, Antony, for persistently trying to fix our broken and irrational Vic voting system!

  2. Every system you list except inclusive Gregory is reasonable & legitimate, although random sampling was not achievable.
    Inclusive Gregory seems to ignore the existence of calculators and the reality that bundles of papers with a label showing their current value are what should be actually distributed

  3. Explaining the difference among the various surplus transfer methods can make even politics junkies’ eyes glaze. Here’s my approach for getting the basics across, which seems (fingers crossed) to work.

    Suppose you’re soliciting public support for some worthy project using a GoFundMe or crowdsourcing system. You need $100,000 to get it done.

    You start off with your website set up inviting people to make $2 donations. But after a few weeks or months, only (say) 20,000 people have donated, so you only have $40,000 in the kitty; you’re still $60,000 short.

    (For simplicity let’s assume only one donation per person, to make the analogy to an election closer).

    So, you re-code the website to invite people to make $1 donations instead. This does the trick, for whatever reason, and another 80,000 people click to donate, pushing your total to [$40,000 + $80,000 =] $120,000. You’ve reached your target, hurrah! In fact you now have a surplus of $20,000. But this in turn creates a problem.

    Suppose you have promised (or the rules of the crowdfunding site require) in general terms that any surplus will be refunded to donors who show receipts. How, exactly? There are at least four alternative methods for doing this, and they correspond to electoral rules as follows:

    (1) Refund 1 dollar to every $2 donor – “after all, they were first to donate, so they should take priority in getting a refund”. This would return the $20,000 to the first 20,000 donors. (This method is not actually used for any STV system I’m aware of, although if a candidate reaches quota on first preferences then the ballots in his or her first parcel received will be considered for transfer, because it’s also the last parcel that candidate received. Personally I favour it on the rationale that it reduces what would otherwise be an incentive to vote tactically for your second or third choice first if you think your real first preference is sure to get elected anyway. But this is an outlier position).

    (2) Refund 25 cents to every $1 donor, on the rationale that “they were the ones who caused the bucket to overflow” (this analogy is used by many STV advocates in support of last-parcel-received transfer). This would return the $20,000 excess to the last 80,000 donors. This system — “last-parcel-received Gregory” — is used in Tasmania).

    (3) Refund 20 cents to every donor, whether they gave $2 early on or $1 later on. This would return the surplus $20,000 to all 100,000 donors. This corresponds to Uniform Inclusive Gregory as used for the Senate. While simpler, it can be criticised as unfair. Someone who donated a larger amount, earlier on, receives back only one-tenth of what they contributed, whereas someone who donated a smaller amount, later in the peace, is refunded one-fifth.

    (4) Weighted Inclusive Gregory would be analogous to refunding every donor one-sixth of what they donated, as the total surplus is six-fifths of what was needed. So the 20,000 two-dollar donors would get back 33.33 cents* each (total $6,667) and the 80,000 one-dollar donors would be refunded 16.67 cents* each (total $13,333).

    [* Allow for some rounding error here, of course. In real life, maybe future crowdsourcing software could be set up so it doesn’t actually deduct your pledge until the project either reaches its fundraising goal or is declared abandoned as a failure, and what it then debits from your PayPal or whatever is the lower of your initial pledge or your adjusted share of the actual total, as computed by one of the above methods. This would avoid the silliness of mailing out eighty thousand checks for 16.67 cents apiece].

    (5) Finally, the original 19th-century versions of STV would have simply drawn 20,000 of the 120,000 donors’ names out of a hat and given the lucky winners one dollar each. The slightly more refined early-20th-century versions, used for the Senate 1948-1983 and still used today for the NSW Upper House, would have drawn 6,667 of the two-dollar donors and 13,333 of the one-dollar donors, ie with set quotas from the two groups, in case a purely random draw overall might be too lopsided).

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