Voting ranked by choice reveals the strange mathematics of elections

at first Study day, Daniel Ullman – a mathematician at George Washington University – has his students run an exercise. Ullman offers a three-way hypothetical election, with candidates designated as A, B, and C vying to win. Then he gave his students 99 voter profiles. This one prefers A to B and B to C. The next number wants A over C, C over B and so on, 99 times.

The class then conducts three different types of elections – “plurality”, where whoever gets the most votes wins; “Condorcet”, with successive head-to-head encounters; and ‘ranked selection’, where voters can indicate the order of their preference and the winner is calculated by successive legends.

You can guess what happens in the Ullman exercise. Each method of voting results in a different winner. There is no wrong way. Nobody cheated. But still: same votes, different counting, different winners. This looks bad, doesn’t it? But as a mathematician, Ullman knows better than most that numbers don’t always agree with the truth. “I shut down the data,” he says, describing how he designed this 99 voter profile to show how different math and goodwill can change the future. Elections are easy when they are overwhelming. If all voters agree, you don’t have to worry about these issues. But when the election approaches, these things matter. And getting close to elections is very common in the United States.”

The truth is that democracy only promises to reach a More A perfect union – not a perfect union in reality. For decades, a field of study called social choice theory tried to find new ways to threaten voting that rocked even harder. Voters are hard for them tampering with roads Large groups of people can express their preferences (votes of approval! Second-class votes! Judgment votes!) in a fair, equitable and meaningful way – to ensure that the “winner” is in fact winner. Classified-choice voting is the latest popular approach, and perhaps even better than a pluralist, winner-type election that takes everything most Americans know best (for some “best” values ​​anyway). It’s how New York City chooses a Democratic candidate for mayor right now, and if that election goes well, voting for the ranked selection could be how you cast your next vote, too.

If your goal For democracy is to get the most participation from voters – create the most representative sample of the body politic – the election is the survey mechanism to determine their true desires. But elections are also a cost-benefit demonstration. The cost to the voter is the time it takes to decide who to vote for and who actually votes – by mail or in person. (in some places the cost is higher than others, in longer queues or fewer options for early voting or by mail for example, and Higher for certain types of people, often of poor people and people of color.) The benefit is to have a policy enacted, or a desirable person in a position of representative authority. A good system would reduce costs, make voting easier, increase benefits, make voting more reflective of the voter’s wishes and, ideally, convert those desires into laws or procedures.

So while Americans are more familiar with plurality votes, this type of ballot may not accurately reflect their desires. This is especially true if the election involves a group of people on a ballot, not either – or a group of options. In the seeded-choice voting version used in New York—also sometimes called the instant runoff—if no one gets more than 50 percent of the vote in the first count, the candidate with the fewest votes is disqualified and the first place votes go. Whoever came in second place. Then there is another round of counting. As the 2018 San Francisco mayoral election watered down showed, It can take some time.

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