05 July 2007

The math of voting, part 2

In a previous post I introduced an example election in which the voters have the following sincere preferences:

45% Reagan > Anderson > Carter
20% Anderson > Carter > Reagan
35% Carter > Anderson > Reagan

(Whether these preferences reflect the sentiments of the nation during the 1980 presidential election or not is not important.  Think of them as the preferences of the voters in some hypothetical state; the winner gets that state's electoral votes.)

I then asked which candidate most deserves to be the winner; the answer depends on the voting system used and the voting behavior of the voters.

In a plurality election, where each voter is allowed to vote for just one candidate, Reagan would win if every voter is sincere.  But the Anderson voters would do better by insincerely ditching Anderson and voting for Carter instead to keep Reagan from winning.  So the plurality system sometimes encourages insincere voting.  I'm sure you already knew that.

But what if it's an Instant Runoff Voting election, where voters rank the candidates and candidates are eliminated one by one?  If all voters rank sincerely, then Anderson will have the fewest first-place votes and will be eliminated first.  Then Carter would win the election 55% to 45% over Reagan.  At first glance, this result makes sense:  Anderson voters voted sincerely and still helped their compromise defeat their least favorite candidate.  Ah, but now it's the Reagan-first voters who could benefit by voting insincerely—they could rank Anderson in first place, watch Reagan get eliminated and Anderson beat Carter 65% to 35%.  That way they at least get their second choice.

So both plurality and IRV sometimes reward insincere voting.  Which system is better?  Or is there some other system that beats 'em both?  Stay tuned!


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