Politics.co.uk Blog

Thursday, 28 April 2011

The voting systems you won't find on the referendum paper

Two months after the 2010 general election, 18 voting experts gathered at the Chateau du Baffy in Normandy for a rather unusual session. They were discussing the relative merits of a number of other, lesser-used voting systems, before choosing which one they believed was the best. In the end, first-past-the-post was unanimously rejected, as I wrote about last week:
Voting experts reject first-past-the-post
You can also have a look at the academic research paper if you want to delve into the details further.

Here's a pick of some of the mind-bending alternatives they considered:

Approval voting

This is one of the more positive options on offer, perfect for those voters who feel constrained by only having one vote. Under approval voting, each voter approves as many candidates as they want. The candidate with the most 'approvals' is the winner. If you wanted to encourage the democratic process, for example, you could vote for all the candidates on the ticket as a 'well done for taking part'. Or you could vote for all but one, to punish a particular candidate. Best of all, voting for the Conservative and Lib Dem candidate would be a vote of approval for a coalition government... the options are endless.

Tournament score

In this system voters submit a ranking of their candidates. Each candidate is then assessed on how many of their challengers they beat under what is known as "pair-wise majority rule" – that is, a straight fight between the two for a majority. The candidates with the largest scores are chosen. There's one problem here, though – it's not clear how ties are broken. Explaining this one to the British public might take some doing.

Two-round majority

A first-round election takes place in which each voter backs one candidate. If no candidate gets an overall majority, all but the top two candidates are knocked out and a run-off takes place. This is used around the world, but has its pitfalls. In France, for example, there is a real possibility the far-right Marine Le Pen could beat the Socialists into the runoff against Nicolas Sarkozy.

Coombs

This is a variant on the alternative vote. Rather than knocking out the candidate that came last, if no-one has an overall majority the eliminated candidate is the one who is most often ranked last. It's named after the academic who came up with the idea in 1964.

Majority judgement

This appears one of the most baffling of all. Voters assess each candidate based on a graded verbal scale (eg Cameron is 'satisfactory', Clegg is 'marvellous', Brown is 'hopeless'). The median result for each candidate is then calculated. A "linear approximation scheme", whatever that is, is then used to choose the elected candidate. Wow.

Minimax procedure

If the voting system is being decided on which has the best name, this must surely be among the frontrunners. The aim of this voting system appears to be to find the candidate who is the least unpopular. Each voter ranks their candidates. Then each candidate is assessed by the size of the majority of all the other candidates against them. The winner is the one which has the smallest majority gathered against him or her.

Range voting

Why bother ranking candidates relative to each other, when you could mark them out of ten? Each voter assesses each candidate by giving them marks. The elected candidate is simply the one who receives the most points when all the marks are added together. This system is also known as "utilitarianism". Try putting that on a referendum ticket.

Leximin

This is another 'the least unpopular' type of method. Each voter grades each candidate according to some kind of scale – it doesn't really matter what. The winner is the one who gets the fewest of the worst possible grade. This is calculated through a mathematical equation which, I'm afraid, I don't understand in the slightest.

Plurality

Each voter chooses one candidate and the candidate with the most votes is elected. Oh, wait – we've heard that one before, haven't we? It is, according to the research paper, "the most common voting rule in the Anglo-Saxon world". It has another name, too: first-past-the-post.

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