After writing the last post, I realized that I’d written a New Yorker style review: used the book as a resource to talk about the issues it raises, rather than the book.  So how’s the book itself?  Good, as you should expect from Poundstone.  He talks about a lot of specific elections, so there’s nothing abstract about possible bad results.  And the portraits of particular electoral thinkers are interesting.  Did you know Lewis Carroll worried quite a lot about voting systems?

 My one complaint is that he never actually goes through Arrow’s proof; he barely even explains what the trouble is.  If Gödel can be explained, surely Arrow can be.

If there’s a common thread to problems with voting systems, it’s lack of information.  The more information your vote gives, the better.  Plurality systems suck because they only include one bit, who you voted for; that tells us nothing about how strong your support is or how you feel about the other candidates.  

 Alternative systems all give more information.  (From this perspective, the acrimonious debates between supporters of different systems mostly come down to the lack of yet more information: what you think other voters are doing, and whether you’ve modified your vote in response to that.)