Impossibility and elections

I’ve now read a few more of the essays in [amazon_link id=”1137383585″ target=”_blank” ]Economics for the Curious[/amazon_link], the collection of essays for young economists by the Lindau lecturers. Eric Maskin’s chapter, How Should We Elect Our Leaders, is the most accessible explanation I’ve read of Arrow’s Impossibility theorem in the context of elections, and is particularly interesting reading for anybody in the UK as we face the likelihood of an election outcome even more hung in 2015 than it was in 2010.

[amazon_image id=”1137383585″ link=”true” target=”_blank” size=”medium” ]Economics for the Curious: Inside the Minds of 12 Nobel Laureates[/amazon_image]

The chapter describes Maskin’s work with Partha Dasgupta looking at what voting system best satisfies the other Arrow conditions when the ‘unrestricted domain’ condition is removed by taking account of the fact that voters’ preferences are limited in plausible ways – for example, a left-wing voter will prefer candidates of the left to any candidates of the right. (Sen of course long ago identified the unrestricted domain condition as the least necessary of the Arrow conditions.) In this case, Maskin and Dasgupta prove that majority voting is clearly the best system.

As Maskin concludes here: “Majority rule is used by virtually every democratic legislature in the world for enacting laws. … It is interesting that there is a precise way in which majority rule does a better job than every other electoral method in embodying what we want out of a voting system. So, perhaps the next time your legislature votes in favour of an absurd law,, you can take consolation from the fact that … they at least used the correct method for voting!”