Moving to

I'm moving to Mostly.

I plan to use that site as a "self-marketing website" of sorts and to manage content in a way that I would otherwise not be able to do on blogger alone.

This blog will stay, ostensibly for more provisional ideas prior to refinement. I'll be gradually moving content (I still like) over to the other website. =)

Sunday, January 15, 2012

Coordination Problems and Approval Voting

I came across the following abstract. It is not too technical, and highlights the coordination problem that Approval Voting solves (i.e.: vote splitting leading to a strictly inferior outcome for most voters).
    This paper shows that information imperfections and common values can solve coordination problems in multicandidate elections. We analyze an election in which (i) the majority is divided between two alternatives and (ii) the minority backs a third alternative, which the majority views as strictly inferior. Standard analyses assume voters have a fixed preference ordering over candidates. Coordination problems cannot be overcome in such a case, and it is possible that inferior candidates win. In our setup the majority is also divided as a result of information imperfections. The majority thus faces two problems: aggregating information and coordinating to defeat the minority candidate. We show that when the common value component is strong enough, approval voting produces full information and coordination equivalence: the equilibrium is unique and solves both problems. Thus, the need for information aggregation helps resolve the majority's coordination problem under approval voting. This is not the case under standard electoral systems.
The conclusion the authors arrive at is not surprising (though the math might be novel, noting that the journal it is published in is regarded as top-tier in the economics establishment).

In the article, the benefit the majority perceives for the two preferred candidates is modelled as a combination of a "common value component" (with different values for the majority and the minority) and an "individual component".

What the authors conclude is that when the "common value component" for the majority is "large enough", then the use of approval voting produces a outcome with a perfectly coordinated majority (as if there were perfect information) where the candidate with the largest number of expected (approval) votes is the majority candidate preferred by more (majority) voters.

The intuition behind it is that the "common value component" serves as a signal of the possibility of a bad outcome is the majority does not coordinate itself. When the inferior outcome is a threat, the majority unites; when it is not, the majority falls into partisan voting.

The citation information of the article is as follows: Bouton, L. and Castanheira, M. (2012), One Person, Many Votes: Divided Majority and Information Aggregation. Econometrica, 80: 43–87. (Here is a link to a recent pre-print.)


Anonymous said...

Sounds like they're just saying that Approval Voting tends to elect Condorcet winners, when they exist. That's been known for a long time. E.g.

convexset said...

Indeed, you're right. Which is why I noted that it would have been the math that was novel, not the conclusions. However, math gives guarantees and makes precise if-then type statements.