30 March 2006

The math of voting, part 1

The summer of 1998 was a good one for me.  I was in summer school at Texas A&M and made two important discoveries.  One was the music of minimalist composers: Steve Reich, Terry Riley, John Adams, Philip Glass.  I listened to Reich's Music for 18 Musicians a lot that summer.  I also found a book by Philip Straffin called Game Theory and Strategy that pretty much changed my life, in that it got me started on the work that became my doctoral research.  Chapter 20, "Applications to Politics: Strategic Voting", was especially interesting to me.  I knew that insincere voting was a real problem in public elections, but I hadn't thought much about it.  The chapter began:

"In the 1980 United States presidential election, there were three candidates: Democrat Jimmy Carter, Republican Ronald Reagan, and Independent John Anderson. In the summer before the election, polls indicated that Anderson was the first choice of 20% of the voters, with about 35% favoring Carter and 45% favoring Reagan. Since Reagan was perceived as much more conservative than Anderson, who in turn was more conservative than Carter, let us make the simplifying assumption than Reagan and Carter voters had Anderson as their second choice, and Anderson voters had Carter as their second choice."

Now, these polls seem to have been a bit off in retrospect, since Reagan won the real election with a majority of the vote, but imagine there was a state whose voters actually broke down exactly like that.  So the voters' presumed preferences could be summed up like this:

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

The question is, which candidate most deserves to win the election in that state, just based on the voters' preferences and not how they actually vote?  I think an argument could be made for any of the three.  Reagan has the most first-place preferences and would win the election if all voters voted for their favorites.  If Anderson dropped out of the race, or if the Anderson voters decided to vote for their "lesser of two evils" instead of sticking to their guns, Carter would win; a majority of the voters prefers him to Reagan.  But I think the most deserving candidate, given the preferences, would actually be Anderson, even though he's the favorite of the fewest voters.  What do you think?  Post your opinion with a comment!  I'll continue analyzing this example election in a future post.

(Anyway, psephology is the study of elections, as I found out when looking up another word in a dictionary.  I study voting systems and the effects of strategic voting, so I like to call myself a psephologist.)


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