After the 2016 presidential election, many people began to question the legitimacy of the American electoral system and some even asked if there was another way to elect a president and, according to Eric Maskin, the answer to the latter question is yes. As part of an April 2 colloquium hosted by the Biology and Neuroscience departments, Maskin, a guest speaker from Harvard University, spoke about election theory and public policy in a conversation with Prof. Michael Rosbash (BIOL). Maskin received the Nobel Prize in Economics in 2007 for his contributions in the area of mechanism design theory, one of the fastest developing fields in microeconomic research.

“Empirical evidence shows that Donald Trump is president,” Maskin started with a scientific ridicule, “but the question that could be asked is, ‘How?’ That’s a question that could be asked at many different levels — I suspect that historians, political scientists and maybe even psychologists will be looking at that question in many years to come, [but] I am going to answer that on a very superficial level, which is that Trump became president because first he got the Republican nomination in 36 states and then he beat Hillary Clinton in the general election.” 

But from Maskin’s point of view, the most interesting thing of all is that for election victories in the first 17 primary states where he won, there were more people voting against Trump than for him. In the general election exists such a similar phenomenon — in states that Trump won, in every one of those states such as Florida, Pennsylvania and Wisconsin, the anti-Trump vote exceeded the pro-Trump vote, because in all such cases there were more than two candidates running. Trump won all these 17 Republican primaries because the so-called “mainstream Republicans,” including Marco Rubio, Ted Cruz, John Kasich and so on, split the anti-Trump vote among them. 

On the other hand, if the mainstream had coalesced for one single candidate, Marco Rubio for instance, Trump may well have failed. From some polls conducted by media organizations such as ABC and The Washington Post, both Rubio and Cruz were much more popular than Trump if it had beena two-person race — however both Cruz and Rubio ran and they split the vote. The same thing happened in Michigan, Pennsylvania and Wisconsin, where votes all went to Trump, because there was a third candidate who got more votes than the difference between Clinton and Trump. If there were only two, then most of these third-candidate votes would go to Clinton, Maskin said. 

After discussing the vote-splitting situation which occurred during the 2016 election, Maskin continued by saying that this is not a coincidence — vote-splitting has often “played a critical role” in presidential elections throughout U.S. history. One of the “most notorious examples” Maskin mentioned was the 2000 presidential election, when President George W. Bush defeated Al Gore by less than 600 votes, while at the same time 100,000 votes were given to the Independent candidate Ralph Nader, which may have otherwise gone to Gore. 

Maskin then suggested ways to improve elections, introducing two alternative types of voting algorithms invented by European mathematicians centuries ago. The first algorithm Maskin spoke about was the true majority rule, proposed by French mathematician Marquis de Condorcet two centuries ago. During the 2016 election, voters submitted their rankings of three candidates, Marco Rubio, John Kasich and Donald Trump. 40 percent ranked Trump prior to Kasich prior to Rubio, 35 percent ranked Rubio prior to Kasich prior to Trump and the remaining 25 percent ranked Kasich prior to Rubio and prior to Trump. Using the true majority rule, the percentages of voters ranking Kasich before Rubio as well as those preferring Rubio over Kasich could be combined. If this formula were used, Kasich would have defeated Rubio with a 65 percent majority. The same method could also be applied to the Kasich versus Trump comparison and would result in Kasich defeating Trump, Maskin said. Therefore, under the true majority rule, Kasich would be considered the winner rather than Trump, who would win under the current method, the plurality majority rule — in which the candidate with the most votes wins, even if they did not receive a majority of the votes.

Maskin then offered another method of decision rule proposed by Condorcet’s archrival, Jean-Charles Borda — the Borda Count rule, or rank-order voting. For every additional vote given, each candidate would be assigned points according to which place they get inside this voting preference rank: For instance, under a certain ranking treatment, whoever is ranked first gets one point, with the second person getting two points and the third getting three points and so on. In another example in which voters still rank Kasich, Trump and Rubio, Maskin proposed a scenario in which 40 percent of voters ranked Kasich before Trump before Rubio and the other 60 percent ranked Rubio before Kasich and before Trump. Maskin explained that in this case, Rubio would receive a total of 60 plus 40 times three points, i.e., 180 points, while Kasich would only get 160 points, defeating Rubio. This would be contrary to a vote by plurality majority rule, in which Rubio wins over Kasich.

Maskin then shifted the discussion to the principles regarding the criteria for judging the quality of these models. He discussed four principles, including consensus, equal-treatment, neutrality and no-splitting — also known as Independence of Irrelevant Candidate. According to Maskin, the consensus principle means that if everyone agrees on A over B, the latter will not be elected. The equal treatment principle means that votes should be counted equally and if voters are switched, the result is still the same since it doesn’t matter who these voters are — for example, Trump getting a vote from voter A while Rubio getting one from voter B is equivalent to Trump getting one from B with Rubio getting the vote from A at the same time. Per the neutrality principle, candidates are to be treated equally and the no-splitting principle suggests that whichever candidates — A or B — wins, that candidate’s victory must not depend on whether candidate C is running or not. For example, if Trump wins Rubio for a two-people election, then no matter whether a third person is added to make the election get expanded or not, Trump still needs to win against Rubio.

Applying the principles to Condorcet’s majority method and Borda’s rank-order method, Maskin pointed out that both satisfy the first three rules: consensus, anonymity and neutrality. Only Condorcet’s majority method fits the IIC rule, however, which could make people prefer this method to Borda’s. Maskin also demonstrated that the majority method is flawed in situations where three candidates are running, but have three rankings of similar percentages. For example, if 35 percent of voters rank Trump before Rubio before Kasich, 33 percent Rubio before Kasich before Trump and the other 32 percent Kasich before Trump and before Rubio, there may be results that the a first candidate defeating a second, with the second one winning over the third, yet the third being figured out winning over the first, becoming a cycle--A>B, B>C, C>A, which causes trouble for decision-making, known as “Condorcet Cycle” (in the Trump, Kasich and Rubio case, Trump wins over Rubio over Kasich then back over Trump) such that a more default principle, the decisiveness principle, is badly violated. Such a principle requires that winners always exist, yet it is in huge conflict with Condorcet’s seemingly flawless method, Maskin said.

Addressing the fact that none of the proposed models fulfilled all five principles, Maskin stated that there was no method that could do so, citing the 1951 book “Social Choice and Individual Values” by the economist Kenneth Arrow. Arrow is the creator of “Arrow’s Impossibility Theorem,” which states that there is no method that could satisfy all five principles. Maskin clarified that this theorem insists on looking for electoral methods that work for any likelihood of ranking — yet the good news is that some rankings are unlikely to come true.

“For example, in terms of Trump’s ranking, Republicans either loved Trump or hated him, causing rankings either putting him at the top or at the last position,” Maskin said, noting that such “polarized” results could happen only for a few candidates. In this way, Maskin argued that we could focus on voting methods that work well for restricted — but not all — classes of rankings to satisfy the five principles: consensus, anonymity, neutrality, IIC as well as decisiveness. 

Maskin then addressed a theorem named after him and another renowned expert, Partha Dasgupta. The Dasgupta-Maskin Majority Domination Theorem states that “if a voting method works well for some particular class of rankings, then true majority works wells for that class.” Under the Majority Domination Theorem, people would conclude that the true majority method would be the best. Maskin then proposed a hypothetical case of switching the currently used plurality majority method to the true majority one for the general election in 2016. In it, a number of voters either chose to not vote or chose to vote for third-party candidates like Michael Bloomberg or Jill Stein rather than vote for Hillary Clinton or Trump. Maskin supposed that 42 percent would rank Trump before Bloomberg before Clinton, 40 percent would rank Clinton before Bloomberg before Trump and the other 18 percent would rank Bloomberg before Clinton before Trump. Then, even though Trump would become the plurality winner, Bloomberg could win over Trump 58 percent to 42 percent and over Clinton, 60 percent to 40 percent, in terms of becoming the true majority winner. 

Such a model would also work in elections in countries other than the United States. In the case of Brexit, for example, the preference ranking of British Parliament Members could also be found with only a few specific types. Maskin supposed that if hypothetically, 25 percent ranked Hard Brexiters (H) over Soft Brexiters (S) over Remainers (R), while another 35 percent ranked S over R over H and the other 40 percent ranked R over S over H, then Soft Brexiters could beat both Remainers 60 percent to 40 percent and Hard Brexiters 75 percent to 25 percent, thus becoming the majority winner entity. This could have made the current state of Brexit somewhat easier, he said.

Maskin concluded his speech, explaining that Maine and cities such as San Francisco and Minneapolis are already using true majority rule in their elections. Since the decision of what method is used is up to the states, then there is no constitutional change needed.