Over the last several years, Harvard economist Eric Maskin has been delivering a talk asking: “How Should We Elect Presidents?”
Should the candidate with the most votes win? Not necessarily, according to Maskin.
Maskin blames the U.S. system of plurality voting—whereby each voter casts their vote for one candidate and the candidate with the most votes wins, even if that number is short of a majority—for the general election mess of 2000, when the outcome was decided by a divided Supreme Court.
Now, he proposes, plurality voting has abetted presumptive Republican nominee Donald Trump, who made his startling ascent with minority support from his party. “There is something very wrong with plurality voting,” Maskin told me in March, the day after Trump won the Republican primaries in Florida, Illinois, Missouri, and North Carolina—all with only a minority of votes.
“In 2000, the disaster was Bush winning in Florida when a majority were really in favor of Gore,” he said, adding that maybe the Trump disaster will be enough to incite serious discussion on the topic of voting reform. Because, as he noted, “There will be a next time, if history is any indication.”
Democracy, Maskin argues, would be better served by the “majority rule” method. He proposes one version of majority rule in particular: the Condorcet method, named after its inventor the Marquis de Condorcet, an eighteenth-century French political scientist and mathematician. This method, which Condorcet described in his 1785 Essay on the Application of Analysis to the Probability of Plurality Decisions, works much like a rating system, such as Google Page Rank for websites and Rotten Tomatoes for movies (it was in Iowa that Trump dodged a protestor’s rotten tomatoes, and ultimately lost the state to Cruz). Rather than picking one candidate, the voter ranks all the candidates—or as many of them as she wants to rank—saying, perhaps, “I choose Trump first, Kasich second, and Cruz third.” Voters submit their preferences and the winner is the candidate who, according to the rankings, would beat each of the other candidates in head-to-head contests.
Maskin offers a hypothetical: Suppose 40 per cent of the population likes Trump the best, and then Kasich, and then Cruz; 35 per cent like Cruz the best, and then Kasich, and then Trump; 25 per cent like Kasich best and then Cruz and then Trump. “If you have plurality rule, then Trump wins easily, he gets 40 per cent of the votes,” said Maskin. But with majority rule, Kasich ends up being the majority winner; and if it were a head-to-head contest between Trump and Cruz, Cruz would beat Trump as well. Both Cruz and Kasich would beat Trump in a head-to-head contest, but both lose to him in a plurality vote. “There is something very wrong with plurality voting,” Maskin said (he crunched the numbers further in a recent New York Times op-ed with his Harvard colleague Amartya Sen).
Maskin’s ongoing voting investigations are in collaboration with Cambridge’s Partha Dasgupta. They formulated a theorem proving there is a precise sense in which majority rule is the best voting method, and they published their result in a 2008 paper, “On the Robustness of Majority Rule.” This type of work is called mechanism design theory, which is a bit like a reverse engineering of economics. Economists usually analyze events to determine why they happened, or to predict events in the future. With mechanism design, Maskin sets his sights on a favorable outcome for an event—an election executed democratically—and then he seeks a method or mechanism that will achieve that end.
Maskin and Dasgupta’s proof uses combinatorial mathematics and other tricks of the trade, such as intellectual innovations in social choice theory by the Stanford economist Kenneth Arrow, Maskin’s doctoral advisor. Arrow is the founding father of modern voting theory, and his namesake Arrow’s Impossibility Theorem indicates, to paraphrase, that there is no perfect way to make social decisions based on voters’ preferences, since no system can satisfy all the desirable criteria or axioms (the Dasgupta-Maskin analysis uses standard axioms based on Arrow’s work: consensus, equal treatment of voters, equal treatment of candidates, no spoilers, and decisiveness, i.e. there is always a clear-cut winner).
“Stepping back and looking at it philosophically rather than technically,” Arrow told me, “we are not prepared to say that a majority should always triumph”—there are laws, for instance, that protect minority rights, such as Native American sacred sites. But when it comes to electing presidents, majority rule satisfies all the axioms more often than any other voting system. “It tends toward a middling candidate,” Arrow noted. “It may not be the first choice of many people, but it is the second choice of a lot of people. No system will always work, but at least a system like that may work fairly often.”
Although there is one caveat. “I’m assuming people are rational,” he said—and by that he wasn’t meaning to pass judgment on the Trump insurgency. Rather, he said, “All I mean by rational is [that people] can rank the candidates: best, next best, and so forth.” (But as for Trumpism, he said: “I don’t understand it at all. No matter what your political position, he’s demonstrating no capacity. He just doesn’t make sense in any formulation.”)
Of course, Maskin’s hypothetical rankings, bumping Trump out of favor, involve imaginary numbers. But there’s hard data in an analysis of the primaries conducted by FairVote, a non-profit organization that has led the discussion on electoral reform since 1992, undaunted by the naysayers. “‘Oh, it’s never gonna happen.’ I’ve heard that so many times in my life. I was in a rock band and we never imagined we’d be on MTV,” said Krist Novoselic, chair of the FairVote board of directors, and the bassist and co-founder of Nirvana, in a recent FairVote trailer for its “Reform 2020” campaign. “So things turn around. I’m an optimist.”
Ranked choice voting is gradually gaining momentum. This spring, New York City Council’s agenda called for the State Legislature to enactment legislation allowing ranked choice voting for citywide primary elections. On November 8, the option of a statewide ranked choice voting system will be on the ballot as a referendum question in Maine. And those Republican primary numbers, run though ranked choice system, support a certain optimism. “If the GOP had used majority rule, Republican voters would have benefited because they could have expressed themselves more fully,” said Maskin. “And the party would have benefited because voters themselves might well have stopped Trump early on, before he built up momentum.”
Maybe next time.
Meanwhile, there is small comfort to be found in a later essay by Condorcet, Sketch for a Historical Picture of the Progress of the Human Spirit, written while he was on the run during the French Revolution and published posthumously in 1794. Therein Condorcet notes the importance of “savoir ignorer” — “knowing how not to know, in the end, what it is still, what it always will be impossible to understand.”
Siobhan Roberts is a science writer based in Toronto. Her latest book is Genius At Play: The Curious Mind of John Horton Conway.
Top photo: Shutterstock.
We actually had a referendum on something similar to this in the UK a few years ago. Unfortunately, people voted No.
My local Pacifica station uses a ranking system to pick board members.
I’ve always been thinking for all forms of votes with more options than yes/no that instead of picking your #1 favourite, you should make a ranking which is then evaluated over all candidates. It would also help alleviate the problem with those wasted votes for less popular candidates. If you #1 only gets a few %, and it becomes a very close race between what would be your #2 and #3, you’d rather have your #2 pick actually count. This is why some people also vote tactically and don’t give their one and only vote to their actual favourite, but rather whom they consider the lesser evil among the candidates most likely to win. Rankings would implement those tactical votes as an actual feature while still allowing to pick your actual favourite as #1.
Australia has had preferential voting, which is what you seem to be advocating, for a hundred years now. I don’t know why others don’t use it.