In 2016, the State of Maine voted to apply ranked choice voting in congressional and gubernatorial elections and then in 2018 voted to extend this voting process to the allocation of its electoral college votes. Recently, the New York Times ran an editorial calling for the Empire State to consider ranked choice voting; in Massachusetts, there is a drive to collect signatures to have a referendum on this on the 2020 ballot. Ranked choice voting is used effectively in American cities such as Minneapolis and Cambridge and in countries such as Australia and Ireland. So what is it exactly? Mystère.

First let us discuss what it is not. In the UK and the US, elections are decided (with some exceptions) by plurality: the candidate who polls the largest number of votes is the winner even if this is not a majority. Although simple to administer, this can lead to unusual results. By way of example, in Maine in 2010, Republican Paul LePage was elected governor with 38% of the vote. He beat out the Independent candidate who won 36% and the Democratic candidate who won 19%.

One solution to the problems posed by plurality voting is to hold the vote in multiple rounds: if no one wins an absolute majority on the first ballot, then there must be more than two candidates and the candidate with the least votes, Z say, is eliminated and everybody votes again; this time Z’s voters will shift their votes to their second choice among the candidates. If no one gets a majority this time, repeat the process. Eventually, someone has to get a true majority.

Ranked choice voting is also known as instant-runoff voting: it emulates runoff elections but in a single round of balloting. First, if there are only two candidates to begin with, nothing changes – somebody will get a majority. Suppose there are 3 candidates – A, B and Z; then, on the ballot, each voter lists the 3 candidates in the order of that voter’s preference. First, the count is made of the number of first place votes each candidate received; if for one candidate that number is a majority, that candidate wins outright. Otherwise, the candidate with the least number of first place votes, say Z, is eliminated; now we add to A’s first place total the number of ballots that ranked Z first but that listed A as second choice and similarly for B. Now, except in the case of a tie, either A or B will have a clear majority and will be declared the winner. This will give the same result that staging a runoff between A and B would have yielded but in one trip to the voting booth where the voter has to rank the candidates A,B,Z on the ballot rather than choosing only one.

There are other positive side-effects to ranked choice voting. For one thing, voter turnout goes up; another thing is that campaigns are less nasty and partisan – you want your opponents’ supporters to list you second on their ballots! One can also see how this voting system makes good sense for primaries where there are often multiple candidates; for example, with the recent Democratic field of presidential candidates, ranked choice voting would have given the voter a chance to express his or her opinion and rank a marginal candidate with good ideas first without throwing that vote away.

After the 2010 debacle in Maine (LePage proved a most divisive and most unpopular governor), the Downeasters switched to ranked choice voting. In 2016 in one congressional district, no candidate for the House of Representatives gathered an absolute majority on the first round but a different candidate who received fewer first place votes on that first round won on the second round when he caught up and surged ahead because of the number of voters who made him their second choice. Naturally, all this was challenged by the losing side but they lost in court. For elections, the U.S. Constitution leaves implementation to the states for them to carry out in the manner they deem fit – subject to Congressional oversight but not to judiciary oversight. Per Section 4 of Article 1: “The Times, Places and Manner of holding Elections for Senators and Representatives, shall be prescribed in each State by the Legislature thereof; but the Congress may at any time by Law make or alter such Regulations, …”

Ranked voting systems are not new and have been a serious topic of interest to social scientists and mathematicians for a long time now – there is something mathematically elegant about the way you can simulate a sequence of runoffs in one ballot. Among them, there are the 18th Century French Enlightenment thinker, the Marquis de Condorcet, and the 19th Century English mathematician, Charles Lutwidge Dodgson, author of Dodgson’s Method for analyzing election results. More recently, there was the work of 20th Century mathematical economist Kenneth Arrow. For this and other efforts, Arrow was awarded a Nobel Prize; Condorcet had a street named for him in Paris; however, Dodgson had to take the pen name Lewis Carroll and then proceed to write Alice in Wonderland to rescue himself from the obscurity that usually awaits mathematicians.