CE Week #2: “When Math Warps Elections”
It is a little disturbing for democracy. One candidate could win with some rules and lose with others.
By Sharon Begley
NEWSWEEK
Updated: 4:05 PM ET Jan 26, 2008
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.
If Super Tuesday produces a clear GOP front runner, he could be one whom many and perhaps most Republicans will have to hold their nose to vote for in November. Our pick-your-favorite system, known as plurality voting, “may produce a winner who is the least acceptable to the majority of [GOP] voters,” says Steven Brams of New York University, a pioneer in the application of math to voting. That happened in the 2000 presidential election, when Ralph Nader got about 95,000 votes in Florida. George W. Bush’s winning margin was about 500. “Since a significant majority of Nader voters preferred Al Gore to Bush,” says Brams, “the winner was the candidate least preferred by most voters.”
One fix for that is approval voting, in which voters choose any number of candidates they deem acceptable. This not only would avert the distortions of 2000, but would let candidates regarded as unelectable draw their true share of supporters. “You don’t have to desert your preferred candidate for fear of ‘wasting’ your vote,” says Brams. Hypothetically, if supporters of Joe Biden, who dropped out of the Democratic race after Iowa, didn’t have to worry that a vote for him might benefit, say, Barack Obama, whom they like less than Hillary Clinton, they could have shown support for their man and his foreign-policy expertise by voting for both him and Clinton. That might have clarified somewhat how much voters value experience. “Election returns would better reflect the overall acceptability of candidates, rather than being distorted by considerations of electability or about wasting your vote,” says Brams. The best-known race decided by approval voting is for secretary-general of the United Nations. That, more than plurality voting, tends to ensure that an extremist candidate cannot best two centrists who split the majority’s vote and let the fringe candidate in.
With three viable Democrats remaining, it’s unlikely that the nominee will be someone whom most Dems rank their least favorite. But with four viable Republicans, that is a real possibility. If Florida 2000 wasn’t enough to get us to re-examine plurality voting, though, grumbling in the GOP ranks probably won’t be either. It is said that a nation gets the leaders it deserves. Maybe we also get the voting system we deserve.
URL: http://www.newsweek.com/id/105586
Like they said in the article…some may find this a little disturbing and I definitely do. It upsets me that our voting system can be manipulated so easily. I never really realized what this math has showed and I really find it quite interesting. One thing that I really liked was how they were pretty accurately able to show us how a third party candidate effects an election. In their little example when McCain won by a good margin in the race; however, as soon as Huckabee dropped out, Romey won by an even larger margin. It’s interesting, and almost scary, that just one person (not even a voter) can have such a large effect on the outcome. With this explanation and their facts Gore could have easily won Florida in the 2000 election if Nader hadn’t run and taken away as many votes as he did. I think that the Electoral College does need some “re-vamping” and I don’t really know that if because of this system things like this would happen or if it’s just something that comes with voting. If it is because of the Electoral College I really think that we should change things fast so that our vote actually matters and the candidate with the real majority of the people is elected.
Ugh. Or more appropriately, urgh!!! I always knew there was something decidedly fishy about election math, and my suspicions have been confirmed, though I did find the article a tad bit confusing. Come election year, the only statistical math I pretend to pay attention to are opinion polls. Generally, I try to avoid them unless I feel the source can be trusted; I always worry about the diversity of sampling – whether random sampling has been honestly employed – and generally pay attention to the size of the sampling error. Nevertheless, I never imagined the complexity of mathematics when electing a candidate. What was most startling was Bergley’s McCain-Romney example, which finally clarified for me the oddity that was the 2000 election. As Bergley implied, democracy has certain precedents, including fairness and clean representation, and I admit to entertaining chimerical notions on this issue. I would like to think that our election system is representative of majority opinion, but I am rapidly discarding that perception. Oh well; while this leaves me a smidge disillusioned, I’ll leave the solution-finding to someone who better understands statistical mathematics. It does make me wonder, though: if elections really aren’t fair mathematically, how different would past elections have been if the system wasn’t broken?
This article was pretty interesting. It brings up some very good points about how our election system is flawed and how it could be fixed, just as questions are always brought up about the Electoral College or anything else that isn’t perfect. Of course, in the election world, perfection is impossible and dispute is inevitable, especially when politicians are looking for an excuse to why they lost. The fact of the matter is, our system is the way it is and won’t change. Ever. This is based on the simple fact that it works. Our politicians may not always win with a majority or even a plurality as the article states, but our government is still functioning and America has done pretty well for itself. Once again we can give some credit to our founding fathers, who forged a government that has prospered despite extremely high levels of voter apathy and apparently presidents who most of us don’t really want. The former we know as the “paradox of mass politics” which basically points out how our government works despite the ignorance of its people. In fact, we have seen this paradox begin to wane in this most recent election: voters and Americans in general have been paying particularly close attention to this election and have been showing up to the primaries and caucuses in record numbers. As Jay Leno has said recently, the tables have turned—instead of the parents telling their kid “Hey, get off your lazy butt and go vote! Do something for the betterment of society!” the kid is now telling the parents to get off their lazy butts. This election has been good for America, flaws and math aside.
It has really interested me lately on the paths one takes to become president and as this article explains, the directions can truly vary. To me it seems to me more of luck than anything else. For instance McCain loyalist rallying behind Huckabee, trying to keep Mitt Romney from winning delegates on super Tuesday, however the wins on super Tuesday for Huckabee has put him back in the race and could prove to be McCain’s potential downfall. It’s all chance and if one little thing happens it can be winning or loosing. Which also shows how easy corruption and dirty politics can become a part of the government and elections. Paying off one person or starting one rumor can be the difference between wining and losing. For instance had Ralph Nader not been present in the 2000 election Gore probably would have been president. Also I have to say that election math is super confusing and this article points out serious flaws in our election process. My question is how are these things ever really going to get fixed, there’s many flaws and I don’t see change in the future.
Mallory Brown
NC – LATE
As malz said I too have been very interested in the paths that some of these people take to become president, and I totally agree that it is almost not who is the best confident it is who has the best luck in the primaries it seems. I also think it is quite funny that the entire McCain loyalist got behind Huckabee, trying to stick it Romney, which really back fired on them because now Romney is out of the race and Huckabee has gained momentum and also has started to become a feasible threat, and if not a threat the republican sure have made a large statement to the republican front runner. It also really dose show how easy corruption and dirty politics can become a part of the government and elections, just as malz was saying making one person look bad in any way even if it is not at all true, it just seems so very unfair… I also think that election math is very confusing and it seem as though there really are lots of problems that we need to fix. I have the same question as malz… how are these going to get fixed? Not just looked over but really fixed?