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This is a book review of Gaming the Vote by William Poundstone.  The book is subtitled "Why Elections aren't fair, and what we can do about it".

It's an excellent book.  Poundstone makes often abstruse arguments clear, without dumbing things down.

This is not a book about hanging chads, fake votes, and things like that.  Rather, it's about the problems of our current method of voting - called plurality voting - and some better alternatives.  Plurality voting is the worst of all seriously considered schemes.

More below the fold

The first half of this book describes the problem - the spoiler effect - in great detail, going into the Nader effect in 2000 (so well known to us all) but also many other spoiled elections, old and new, national and local, and the efforts by the Democrats and Republicans to help third parties that they thought would hurt the other major party.  Lots of interesting stuff here, but my main interest is in the second part, where Poundstone talks about various schemes for voting.

When there are only two candidates on the ballot, it doesn't matter what method is used, they all give the same result.  But when there are more than two, even if the third, fourth, etc. attract only a few voters, then weird stuff happens.  Here are some of the main systems.

Plurality voting, which we're all familiar with, is when you  'pick one' and vote.  

Approval voting is when you can vote for as many as you like.  You pick all the candidates you approve of, and check their names.  

Borda count is when you rank the candidates, from most to least preferred.  Then, in (say)  a four candidate race, every first place vote is worth 3 points, every second place vote is worth 2 points, every third place vote is worth 1 point, and every fourth place vote is worth 0.  This is a very easy system to manipulate, and isn't preferred by any serious voting theorist.  It's the scheme used in some sports polls, and has led to scandal.

Condorcet voting also involves ranking all the candidates, but is based on the idea that the winner should be able to beat each opponent in a two way race.  Unfortunately, this isn't always achievable, and it is possible for there to be what is called a "Condorcet cycle" like the familiar 'rock paper scissors' game.

Instant runoff voting is probably the most commonly used alternative to plurality voting. Again, all candidates are ranked.  If one candidate gets a majorithy of first place votes, then he/she wins.  If not, then the votes of the person with the fewest first place votes are re-assigned, based on the second-place choice of those voters.  So, if, say, out of 100 voters

Bush gets 45 first place votes,   35 second place votes, 30 third place
Gore gets 45 first place votes,   35 second place        30 third
Nader gets 10 first place         40 second              50 third

then no one has a majority of first place votes, and Nader's 10 votes are reassigned to Bush and Gore, based on who those voters picked second.  This works very well if there are two major candidates and some minor ones, but can lead to odd results when there are several candidates with reasonable numbers of first place votes.

Then there is my favorite (and the other main contender) range voting.  In this, each candidate is rated, rather than ranked.  That is, you give each candidate a grade (0 to 10, or 0 to 100, or whatever) then the person with the highest average wins.  Computer studies show that this is probably the
best scheme.  Objections to it (mostly from the IRV people) are more political than mathematical.  I don't think those objections make much sense.  In a way, this is the most familiar scheme.  Anyone who's ever been graded (that is, everyone) has had this applied to them.  One objection is that people don't have enough information to give sensible ratings to people - but psychological experiments show that rating is often easier than ranking.  You can also leave a rating blank, if you like.

Part of what I wrote here is accepted by every theorist - that is, plurality voting is a terrible system.  The rest is hotly debated.  In particular, debates between IRV people and range voting people get extremely heated (it's almost comical).  I've read just this one book, and used my math training and common sense to choose.  That leads to my poll question

Originally posted to plf515 on Tue Apr 22, 2008 at 04:42 AM PDT.

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