The classified election vote reveals the strange mathematics of the election


The first class day, Daniel Ullman -a mathematician at George Washington University- had his students do an exercise. Ullman presents a hypothetical three-way election, with designated candidates such as A, B and C fighting for victory. He then gave his students 99 electoral 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.

Then the class makes three different choices – a “plurality,” in which the one who gets the most wins; a “Condorcet,” with successive head-to-head confrontations; and “ranked choice,” in which voters can indicate their order of preference and a winner is calculated by means of successive trades.

You can guess what happens in Ullman’s exercise. Each voting method gives a different winner. None of the methods is wrong. No one was fooled. But always: Same votes, different accounts, different winners. Sounds bad, doesn’t it? But as a mathematician, Ullman knows better than most that numbers don’t always add up to the truth. “I do the data closely,” he says, describing how he conceived those 99 voter profiles made to show how different, bona fide mathematicians can change the future. “Elections are easy when they are broken. If all voters agree, we don’t have to worry about these issues. But when elections are close, these things count. And close elections are very common in the United States. ”


The fact is that democracy promises only to achieve one no longer perfect union – not really perfect. For decades, a field of study called social choice theory has tried to find new ways to shake up the vote that has shaken it even more. Finicky voters have tinted with fashions large groups of people can express their preferences (votes of approval! square votes! votes of judgment!) in a fair, just, feasible way – to make sure the “winner” is actually the winner. Classified choice voting is the last popular approach, perhaps even better than the plurality-of-choice election to take all Americans know best (for certain “best” values, though). That’s how New York City chooses a Democratic candidate for mayor now, and if the election goes well, the classified election vote may be the way to go in your next ballot.

Yes your goal because democracy is about getting the most share of participation from voters – creating the most representative champion of the political body – then elections are the investigative mechanism to capture their true desires. But elections are also a cost-effective proposition. The cost to the electorate is the time it takes for them to understand who to vote for and actually cast the vote – by mail or in person. (In some places the cost is higher than in others, in longer lines or fewer options for, say, early voting or by mail, and higher for certain types of people, often poor and people of color.) The benefit is of enforcing a policy, or of a desirable person in a position of representative authority. A good system reduces costs, makes voting easier, and increases benefits, making voting more reflective of voter wishes and, ideally, turning those wishes into laws or actions.

So while Americans know the most votes to plurality, this type of scrutiny might not more accurately reflect their desires. This is especially true if the election has a crowd of people at the polls, not either – or but a panoply of options. In the version of the classified vote used in New York – also sometimes called immediate run-off – if no one receives more than 50 percent of the votes on the first count, the candidate with the lowest vote is eliminated and their first place goes to the one in which those voters are ranked second. Then there’s another round of counting. As the 2018 San Francisco mayoral elections have shown, it may take a while.

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