Saari is no voting methods expert, because he shuns well established facts on this issue and makes an absurd and unfounded case for Borda voting, which is incredibly susceptible to strategic voting.
Range Voting is the better simpler alternative.
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Sharon Begley
When Math Warps Elections
It is a little disturbing for democracy. One candidate could win with some rules and lose with others.
From the magazine issue dated Feb 4, 2008
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Even if you do not live in an early-primary state, it's almost impossible to avoid online polls and "elections." How much their results square with reality remains to be seen, but one online poll is intriguing less for any predictive power than for what it says about the interaction of math and elections (and I don't mean the funny way they count votes in Florida). The American Mathematical Society and other scholarly groups have launched a site where you pick your favorite presidential candidate—as well as choose any of eight you deem acceptable and rank them from one to eight. (To play, go to www.amstat.org/mathandvoting.) Now the fun begins. The three different methods produce, when I tried it, at least two different winners.
For anyone who believes in democracy, this is a little disturbing. What it means is that "election outcomes can more accurately reflect the choice of an election rule than the voters' wishes," writes mathematician Donald Saari of the University of California, Irvine. One candidate could win with some rules and lose with others. In fact, as mathematicians analyze voting systems, they are turning up other oddities that can yield a "winner" who does not reflect the will of even a plurality, much less a majority. The discoveries are especially relevant this year. "The severity of the problem escalates with the number of candidates," notes Saari, and one thing this primary season has is a lot of still-viable candidates.
One of the most surprising aberrations mathematicians have found comes in a four-way race. There, of course, one candidate wins a plurality and another comes in last. Saari examines what happens if the third-place candidate drops out and, in the next round of voting, people have the same ordered preference as before (A is the first choice of the most, followed by B, then D). Consider an election with 30 voters, who mentally rank the candidates this way:
Three voters prefer John McCain to Mike Huckabee to Mitt Romney to Rudy Giuliani, in that order.
Six prefer McCain to Romney to Huckabee to Giuliani.
Three prefer Giuliani to Huckabee to Romney to McCain.
Five prefer Giuliani to Romney to Huckabee to McCain.
Two prefer Huckabee to Giuliani to Romney to McCain.
Five prefer Huckabee to Romney to Giuliani to McCain.
Two prefer Romney to Giuliani to Huckabee to McCain.
Four prefer Romney to Huckabee to Giuliani to McCain.
In our system, McCain wins, with nine first-place votes, trailed by Giuliani (eight), Huckabee (seven) and Romney (six). Now let's say Huckabee drops out. Cross out his name where he came in first, and notice who is now the first choice of his former supporters: two go with Giuliani and five with Romney. That pushes Romney, formerly in last place, to the top, with 11 first-place votes. As the GOP field prunes itself, don't be surprised if the new leader comes from the back of the pack.
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