Wednesday, February 22, 2006

Porportional paradoxes

Speaking of ranked porportional representation (which Katy points out is used in Ireland, and is also used for city council elections in Cambridge, Mass, my hometown), an amazing book that deals with the game theory of voting systems is Paul Hoffman's Archimedes' Revenge.

A credo of porportional representation is that voters don't have to vote strategically, because each voter maximizes his or her satisfaction with the electoral outcome by simply ranking the candidates in honest order of preference. Hoffman points out that this isn't true: it is possible to worsen the voting outcome by voting for a candidate you support rather than omitting that candidate or placing them lower than you really feel. In fact, he demonstrates that there can be no voting system that does not create cases where a voter can benefit from voting against his or her own preference.

He also talks about the seemingly simple system of apportioning numbers of Congressmen to different US states, which, like porportional representation, creates some confounding situations. Apparently in the early 1900s one state realized that if there were any other number of total House members from 300-400 (instead of the actual number at the time), they would be given one more representative under the system. That is, if there were fewer total Congressmen, they would get one more. Hoffman also shows how this case is also inevitable under any conceivable apportionment system.