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What's fairest for a voting referendum?

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Martin Rosenbaum | 08:50 UK time, Wednesday, 10 June 2009

This is a little off-topic maybe, but I've been thinking about one aspect of the electoral reform debate which I've not seen mentioned anywhere else.

(If there's a connection with freedom of information, perhaps it's that electoral reform and FOI are both aspects of constitutional reform which some see as part of a democratic renewal process.)

Ballot boxElectoral reform is now rising up the political agenda. It's widely accepted that a new voting system is such a fundamental change that it could only be adopted if a referendum on the idea was held first. But that surely prompts the question: what should be the voting system used in such a referendum?

The outcome could be very different according to that decision.

Suppose there were four options on offer for voting systems - the current First Past the Post system (FPTP), the Alternative Vote (AV) supported by some Labour electoral reformers, the Single Transferable Vote (STV) backed by the Liberal Democrats, and Borda, a points-based system advocated by those who see it as a more consensual approach. (A full explanation of each system is given below).

Suppose also that there are 100 voters and they happen to be divided into four opinion groups, with their order of preference for the voting system as follows:

Table of votes

So what would happen if there was a referendum with all four options on the ballot paper with the votes counted under the various systems (assuming no tactical voting).

If FPTP was used to count the result of the referendum, it would win; if AV was used it would win; if STV was used it would win; and if Borda was used it would win.

Under FPTP only the first preferences matter, FPTP has the most and it wins.

Under AV, the bottom two on first preferences (STV and Borda) are eliminated; FPTP gets no second preferences while AV gets 24 (from those who put STV first) to add to its 27 first preferences, so it scores 51, overtakes FPTP's 28 and wins.

Under STV, just Borda is eliminated on the first round. Since the 21 second preferences of those who put Borda first go to STV, on the second round STV has 45 votes and AV is now bottom as it still has 27. So AV is now eliminated, STV picks up another 27 votes in second preferences, so it now has 72 votes and beats FPTP, still on 28, in the final round.

Under Borda, FPTP scores 205 points, AV scores 257, STV scores 268, while it is Borda which seizes victory with 270.

Thus under this distribution of public opinion, each system wins if and only if the votes are counted in line with that system.

So what would be the fairest system for a referendum on electoral reform? Maybe what we need is a referendum to decide which voting system should be used in a referendum...?

Notes on each voting system:

• First-past-the-post (FPTP), the system currently used for UK general elections. Voters have one vote and the candidate with the most votes wins.

• Alternative vote (AV), as used in Mayoral elections, also known as the Supplementary Vote. Voters mark a first and a second preference. The first preferences are counted and all except the top two candidates are eliminated. The second preferences of the eliminated candidates are examined and where they are for either of the top two they are added to that candidate's total. The candidate from the initial top two with the highest total of first preferences plus second preferences transferred from eliminated candidates wins.

• Single transferable vote (STV). Since the point of such a referendum would be to choose one voting system, this case would be like STV in a single-member constituency where it works as follows. Voters list candidates in order of preference. After the first preference count, the bottom candidate only is eliminated, and his/her second preferences are added to the totals for the other candidates in line with those preferences. After this the candidate who is now bottom is eliminated, and more second/third preferences are transferred. Then the bottom candidate is eliminated and this process continues until only two are left and the candidate with the higher total of votes including transferred preferences is elected.

• Borda count - as with STV, voters list candidates in order of preference, but unlike STV Borda is a points-based system. If there are four candidates and the voter puts them all in order of preference, a first preference is worth four points, a second is worth three points, a third is worth two, and a fourth is worth one. The candidate with the highest points total wins.


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