Voting about Voting

On May 5th we will have the opportunity to vote in a referendum on whether to change the system we use to elect Members of Parliament – from plurality to instant-runoff voting (IRV). Because this change could potentially benefit some political parties at the expense of others it is difficult to find unbiased advice, and because most people don’t know the basics of voting theory there have been some astonishingly silly statements made about both systems. This is not helped by the fact that the government is using non-standard nomenclature – instead of plurality and IRV they refer to first past the post (FPTP) and the alternative vote (AV).

To make sense of the debate you really need to do a bit of background reading, so check out the Wikipedia article about single-winner voting systems. Towards the end of that article there is a table comparing fifteen different systems in terms of twelve different desirable characteristics. Plurality satisfies only four of these criteria (three of which are also satisfied by IRV) whereas IRV satisfies six. So based purely on number of criteria satisfied the new system would seem to be better, the only disadvantage being that it does not satisfy the monotonicity criterion. And let’s be quite clear, they are both “one person, one vote” systems – everyone has equal voting weight.

But wait a minute you say, according to that table the Schulze method satisfies eleven of the twelve criteria (including all those satisfied by IRV) why wouldn’t we use that? Why not indeed! IRV and the Schulze method are both ranked voting methods so the ballot forms and instructions to voters would be identical, it would just use a fairer way of determining the winner. In particular the Schulze method satisfies the Condorcet criterion. A Condorcet winner is a candidate who would win a two-candidate election against each of the other candidates. A voting system satisfies the Condorcet criterion if it chooses the Condorcet winner when one exists. Neither our current method nor the alternative we are being offered satisfy the Condorcet criterion.

You might also be wondering why someone couldn’t just design a voting system that satisfies all the criteria? Well they could try, but they might first want to read about Arrow’s impossibility theorem.

I have always been critical of the current system because it effectively forces many people into giving their vote to the lesser of evils rather than their favoured candidate. I will vote yes in the referendum because AV, whilst not being ideal, certainly seems fairer than FPTP. Switching to AV would reduce the unfair advantage of the largest established political parties and could reduce the chances of any single party gaining a majority of seats in Parliament – opinion varies as to whether that would be a good or bad thing.

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