He prefers a method known as the Borda Count, in which voters also rank candidates in order of choice, but their first choice receives a certain number of points, their second choice a smaller number of points, and so on.
Professor Saari is not alone in favoring a particular voting method. Princeton's Eric Maskin zealously advocates Condorcet voting. NYU's Steven Brams promotes approval voting, and so on. That scholars fail to agree on the meaning of the same facts reflects the truth that there is no "perfect" voting system.
There is no objective means to weigh competing values in areas such as rewarding breadth of support or core support, or the balance between upholding majority rule and achieving consensus.
Most politically engaged reformers focus on instant runoff voting (IRV) instead of other alternatives, because it improves the status quo in ways that are easy to see and is more reflective of voters' expectations of fairness.
Political and civic leaders like President Obama, Sen. John McCain, consumer advocate Ralph Nader and the League of Women Voters of Minnesota agree on the value of IRV. Compared to plurality voting, IRV diminishes the "spoiler" impact of third party and independent candidates. Compared to traditional two-round runoffs, IRV saves taxpayer dollars, reduces the influence of money in politics and maximizes turnout.
IRV also nicely balances the value of first choice support with the value of broad support. Plurality voting rewards only core support.
In contrast, the Borda Count tilts toward rewarding broad support by allowing votes to count for more than one candidate at a time. As a result, Borda can elect candidates who might come in dead last in our current system, but be many voters' second or third choice.
Borda also could defeat a candidate who under today's rules would earn an absolute majority of 51 percent of the vote. Many voters would react skeptically to such results.
Worse, Borda makes it easy for voters to game elections. Nicolaus Tideman, author of "Collective Decisions and Voting," includes Borda in his list of voting methods that "have defects that are so serious as to disqualify them from consideration." The system's inventor, Jean-Charles de Borda himself, stated that the system should be used only for situations where voters are disinterested judges.
Consider Borda and a famous example of the "spoiler dynamic," the 2000 presidential election in which Republican George W. Bush defeated Democrat Al Gore by 537 votes in the halted Florida recount, even as more than 97,488 people voted for Green Party nominee Ralph Nader. Given that more Nader backers supported Gore than Bush, it's clear that under instant runoff voting, Gore would have won Florida and the presidency.
But there's no way to know what would have happened with Borda. With Borda, ranking a second choice counts directly against the chances of your first choice. Some Bush voters might tactically have ranked Nader and other independent candidates ahead of Gore. If more Gore voters honestly chose to rank Bush as one of their top choices, then Bush would have won simply due to his voters engaging in better tactical voting.
Instant runoff voting avoids this problem because your ballot never counts for more than one candidate at a time. Unlike Borda and most other alternative voting methods, ranking additional choices never hurts your first choice. As with every voting method, there are cases where candidates might benefit from insincere voting, but with IRV such situations are too convoluted to be an effective tactic.
That IRV has fair results and isn't prone to gaming explains its successful track record in thousands of hotly contested elections -- from nearly a century of elections for Australia's House of Representatives to decades of elections in Irish presidential races. Professor Saari's examples of its theoretical flaws may interest fellow mathematicians, but they are irrelevant for those wanting to improve American democracy.
Rob Richie is executive director of FairVote, a national nonprofit organization that says it works "to transform our elections to achieve universal access to participation, a full spectrum of meaningful ballot choices and majority rule with fair representation for all."