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In the first on class day, Daniel Ullman — a mathematician at George Washington University — gave his students an exercise. Ullman presents three hypothetical elections, competing to win the nominees nominated by A, B and C. It then gives students 99 voter profiles. This one prefers A over B and B over C. The next one wants A over C and C over B and so on, 99 times.
The class then holds three different types of elections – “plurality,” because the one who gets the most votes wins; A “condorcet,” with head-to-head rivalries; and a “qualified option,” where voters can indicate their order of preference and the winner is calculated by successive tals.
You can guess what happens in Ullman’s exercise. Each voting method gets a different winner. None of the methods are wrong. No one has cheated. But still: same votes, different counts, different winners. Sounds bad, right? But as a mathematician, Ullman knows all too well that numbers don’t always add truth. “I close the data,” he says, describing how he designed those 99 voter profiles to show how bona fide mathematicians can change the future. “Elections are easy when it comes to land movements. If all voters agree, we don’t have to worry about these issues. But when the election is near, those things are important. And being close to the election is very common in the United States. “
In fact, it only promises to bring democracy closer more perfect unity — not really perfect. Over the decades, an area of research called social choice theory has tried to find new ways to shake the vote even harder. Finicky if elected ways to tinker large groups of people can express their priorities (approval votes! square votes! trial votes!) in a fair, equitable and viable way to ensure that the “winner” is truly winner. The last popular approach is to vote on the number of votes chosen, perhaps better than all the elections held by plural-type winners that most Americans know (for some “better” values, however). New York City is electing a Democratic candidate for mayor right now, and if those elections go well, an elected vote may also be the way to cast your next vote.
If your goal because democracy is about getting the most out of voters — creating the most representative sample of the political body — then elections are the survey mechanism for capturing their true aspirations. But elections are also a cost-benefit proposition. The cost to the voter is the time they need to know who to vote for and actually vote for, either by mail or in person. (In some places the cost is higher than in others, with longer lines or fewer options, such as early voting or email, and it’s bigger for people of certain types, often poor people and people of color.) The advantage of the benefit is that a person is substituted for a policy or a desirable person in representative authority. A good system would reduce costs, make voting easier, and increase benefits by reflecting the voter’s wishes and, most importantly, turning those desires into laws or actions.
So while Americans are familiar with plurality voting, this type of voting does not reflect their wishes more accurately. This is especially true when a lot of people vote in elections, not a yes-or-no-choice set. In the version of the classified ballot used in New York — also called an immediate call — if no one gets before 50% of the vote, the candidate with the fewest votes is expelled and the first-place voter is the one who got the second-most vote. Then there is another round of counting. As the 2018 San Francisco mayoral election showed, it may take a while.
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