ON SCIENCE
Sharon Begley
When Math Warps Elections
It is a little disturbing for democracy. One candidate could win with some rules and lose with others.
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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Member Comments
Posted By: brokenladder @ 02/27/2008 2:36:01 AM
Comment: 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.
Posted By: Rinnovato @ 02/02/2008 8:05:35 AM
Comment: QUESTION: Does Hillary's Health Care Plan cover SUICIDE PREVENTION in the United States Armed Forces????
What no one is talking about is the impact of Hillary Clinton's lack of serious judgment. The Army has reported that 121 Soldiers committed Suicide, with over 2000 attempts in 2007. The stress of long tours in Iraq has forced some young men and women to take their own destiny in hand.
Hillary voted for this war... why isnt she apologizing to all parents who lost their children, either by enemy fire, friendly fire or suicide? She would not admit that she failed in judgment. OBAMA knew the war was wrong, and there was no clear strategy for the U.S. to exit out of Iraq when the mission was completed.
THE TRUTH is that Senator Dick Durbin admitted on the Senate Floor that members of the Intelligence Committee KNEW that President Bush and Dick Cheney were going to war on false pretences. John Edwards, who was on the Intelligence Committee at the time, voted for the war as well. You can watch at the following LINK the statement by Senator Dick Durbin: http://www.youtube.com/watch?v=AyonYGeyFb4
Some members of the Intelligence Committee voted AGAINST the War. Why wasnt Hillary's eyes open? She admits in the Senate that she SAW the Intelligence reports: WATCH HER HERE: http://www.youtube.com/watch?v=DkS9y5t0tR0
And on top of all these Suicides, McCain wants to keep them there for 100 years? If Iranians, Al Queda or the insurgents dont kill our troops, they will kill themselves. Not to mention that Al Queda was NEVER in Iraq before Bush, McCain and Clinton Invaded Iraq. But all three wanted Saddam Hussien out of Power and they wanted control of billions of dollars in Oil.
SHAME ON HILLARY CLINTON! Part of Being President is being Accountable!!! Take responsibility for your vote to "Authorize Military Force on Iraq" and finally admit that you were WRONG!
John McCain - This time you have left men behind... to die at their own hand.
Posted By: avfan @ 02/01/2008 12:10:29 PM
Comment: IRV and traditional runoffs are unsuitable for use in partisan elections because of the center-squeeze effect. In a three-way race where the candidates fall into a left-center-right arrangement, where the left and right candidates aren't too close to the fringe, then all else being equal the centrist will be eliminated in the first round.
The approval voting method favored by Brams doesn't have this problem. Approval voting is also much simpler than IRV, and doesn't require IRV's expensive and complicated ranked ballots.