# Ranked choice voting reveals bizarre election calculation

At first day of class, Daniel Ullman, mathematician at George Washington University, gives his students an exercise. Ullman presents a hypothetical three-way election, with nominated candidates like A, B and C vying for victory. Then, he gives his students 99 voter profiles. This one prefers A to B and B to C. The next one wants A to C and C to B And so on, 99 times.

Then, the class organizes three different types of elections: a “plurality”, in which the one who obtains the most votes wins; a “Condorcet”, with successive confrontations; and “ranked choice,” in which voters can indicate their order of preference and a winner is calculated through successive counts.

You can guess what’s going on in Ullman’s exercise. Each voting method results in a different winner. Neither method is wrong. No one cheated. But always: same votes, different counting, different winners. Sounds bad, right? But as a mathematician, Ullman knows better than anyone that numbers don’t always match the truth. “I bring the data together,” he says, describing how he designed these 99 voter profiles invented to show how different, good faith math can change the future. “Elections are easy when they are landslides. If all the voters agree, we don’t have to worry about these issues. But when the election is near, these things matter. And close elections are very common in the United States. “

The point is that democracy promises to achieve only one After perfect union, not really perfect. For decades, an area of ​​study called social choice theory has attempted to find new ways to tip the vote even harder. Capricious voters have tinkered with the means large groups of people can express their preferences (approval votes! Quadratic votes! Judgment votes!) winner. Ranked choice voting is the latest popular approach, perhaps even better than the pluralist all-winner type elections that most Americans know best (for some values ​​of “best,” anyway). This is how New York City chooses a Democratic mayoral candidate right now, and if this election goes well, ranked choice voting may also be how you vote your next ballot.

If your goal because democracy consists in obtaining the greatest participation of the voters – creating the most representative sample of the body politic – then the elections are the mechanism of inquiry to capture their true desires. But elections are also a cost-benefit proposition. The cost to the voter is the time it takes to determine who to vote for and actually vote, by mail or in person. (In some places the cost is higher than in others, in longer queues or fewer options for, say, early or postal voting, higher for certain types of people, often poor people and people of color.) The advantage is having a policy adopted, or a desirable person in a representative position of authority. A good system would reduce costs, facilitate voting, and increase benefits, making a vote more representative of the voters’ wishes and, ideally, converting those wishes into laws or actions.

So while Americans are more familiar with plurality voting, this type of ballot may not reflect their wishes as closely as possible. This is especially true if the election has a group of people on a ballot, not one or the other, but an array of options. In the version of ranked choice voting used in New York City – also sometimes called an instant second round – if no one gets more than 50 percent of the vote in the first count, the candidate with the fewest votes is eliminated and their votes cast. first place start. to whoever these voters ranked second. Then there is another round of counting. As the moderate election of the mayor of San Francisco in 2018 showed, it may take a long time.