Electoral reform: a different answer

A few weeks ago I attended a talk by Eric Maskin, who this year was awarded the Nobel Memorial Prize in Economics for having laid the foundations of mechanism design theory.

Eric Maskin seems to be quite an interesting person. He lives in a house that was once occupied by Albert Einstein. I imagine that would make a great pub quiz question. Perhaps even more startlingly, Eric Maskin dresses up as Albert Einstein at Halloween.

Professor Maskin came to Edinburgh en route to Sweden to talk about voting systems, a topic related to mechanism design.

Arrow’s impossibility theorem implies that no voting system is perfect at satisfying a number of desired criteria. These criteria are:

  • The Pareto principle — if everyone prefers x to y then y should not be elected
  • Anonymity — every voter should be treated equally
  • Neutrality — every candidate should be treated equally
  • Independence of irrelevant alternatives — the ability of x and y to win an election should not be affected by the entrance of a candidate z
  • Transitivity — if x is preferred to y and y is preferred to z then x should be preferred to z

That fourth one is probably the one that grates with most proponents of electoral reform. We can reel off instances where independence of irrelevant alternatives has been violated. For instance, had Ralph Nader not run in 2001 then Al Gore would almost certainly have become President of the USA. A fragmented left in France allowed Jean Marie Le Pen to enter the final run-off with Jacques Chirac in 2002, when there was every chance that Lionel Jospin would have won such a face-off.

Interestingly, Eric Maskin thinks that if the SDP / Liberal alliance hadn’t run in 1983, Michael Foot’s Labour party would have won the general election. What a thought!

Just thinking about this sent me under a dark cloud. The design of institutions clearly has a disturbingly massive effect. The voting system is much more important than the voters themselves, particularly when you couple this thought with the paradox of voting.

The system that Eric Maskin concentrated on is Simple Majority Rule. This method has voters submitting rankings of candidates, just as in Single Transferable Vote. Then you take these rankings and use them to compare candidates in a head-to-head scenario, two candidates at a time. By comparing just two candidates at a time, you get rid of the problem with independence of irrelevant alternatives. If one candidate is preferred over another by >50% of the voters, he wins the election.

Well, almost. Unfortunately, this system is susceptible to Condorcet’s paradox. For instance, >50% of voters may prefer Labour to the Conservatives, >50% of voters may prefer the Conservatives to the Liberal Democrats and >50% of voters may prefer the Lib Dems to Labour. In other words, simple majority rule violates the transitivity principle.

The view of Eric Maskin is that to worry about transitivity is too pessimistic. For him, the Condorcet paradox is possible, but highly unlikely. This is because candidates can be lined up on a spectrum from left to right, and voters tend to vote in accordance with these positions.

As such, he suggests that simple majority rule is good as a least-worst voting system as it meets all of the desired criteria apart from transitivity which is unlikely to be violated. No other voting system works this well as often.

Of course, because the possibility of the Condorcet cycle even exists, there must be a tie-breaker. This is probably cause for a whole new debate in itself!

The talk provided some food for thought. For several years now I have been convinced that there needs to be a move away from the First Past the Post system. For the past few years I have been strongly in favour of Single Transferable Vote.

During the talk, one person in the audience specifically asked Eric Maskin about Single Transferable Vote. He said that STV can still violate independence of irrelevant alternatives, and pointed out that a similar system to STV was used in the 2002 French election.

I’m not entirely convinced that STV is all that similar to the run-off system used in French Presidential elections. The main problem with the French Presidential election (and the other examples that have been highlighted), as Proferssor Maskin pointed out, was the fact that voters were unable to rank candidates. Well, voters can rank candidates in STV.

Nevertheless, Condorcet cycle aside, I find the simple majority rule approach quite appealing. Yet we hear very little about it. If you are interested in electoral reform, I would say it is worth looking into a bit.


  1. I’m 100% certain that STV isn’t similar to the system used in France, I even wrote a long post on it called “Why preferential systems beat run-off ballots“, I loath the French system, because it causes splinters and ffalse choices, I love STV.. I’ll look into his idea more, but the big problem from the way you’ve explained it is simplicity, people like to know how their vote will be counted. I’ll need to look into it more.

    Still, interesting idea, thanks for posting about it.

  2. I think you’re right. That is definitely the main reason why we hear little about this method. I found myself having to concentrate quite hard to completely get my head round it because it is not very intuitive at first. The fact that when totting up the votes you only ever concentrate on two candidates at a time is completely alien, but once I got over it I found the system quite interesting.

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