Ranking selection voting reveals the weird math of elections

In the first On the day of class, Daniel Ullman, a mathematician at George Washington University, asked his students to do an exercise. Ullman proposed a hypothetical tripartite election in which candidates designated as A, B, and C compete for victory. Then he gave 99 voter profiles to his students. This person prefers A to B and B to C. The next one wants A instead of C and C instead of B and so on, 99 times.

Then the whole class conducts three different types of elections-“plural”, the person with the most votes wins; “Condorcet”, a continuous face-to-face duel; and “ranking selection”, where voters can indicate their preference order and pass consecutive Count to calculate the winner.

You can guess what will happen in Ullman’s practice. Each voting method will produce a different winner. No one method is wrong. No one cheated. But still: the same votes, different counts, different winners. This looks terrible, right? But as a mathematician, Ullman knows better than most people that numbers don’t always add up to the truth. “I keep the data close,” he said, and described how he designed these 99 fictitious voter profiles to show how different, well-meaning mathematics can change the future. “When a landslide occurs, elections are easy. If all voters agree, we don’t have to worry about these issues. But when the election is over, these things are important. Near elections are common in the United States.”

The fact is that democracy only promises to achieve more The perfect combination-in fact it is not a perfect combination. For decades, a research field called social choice theory has been trying to find new ways to change the way of voting, and this way has become more intense.The picky voters have Tinker A large group of people can express their preferences in a fair, equitable and feasible way (yes vote! Second vote! Judgment vote!)-to ensure that the “winner” is actually winnerRanking selection voting is the latest popular method, and may even be better than the majority type of winner-take-all elections that most Americans know best (for some “better” values ​​anyway). This is how New York City now chooses the Democratic mayoral candidates. If the election goes well, the ranking vote may also be the way you cast a vote.

If your goal Because democracy is about obtaining the maximum participation of voters—creating the most representative sample of political bodies—then elections are an investigation mechanism that captures their true desires. But elections are also a cost-effective proposal. The cost of voters is the time it takes for them to figure out who they voted for and actually vote—by mail or in person. (In some places, the cost is higher than in others, the queue time is longer or there are fewer options, such as early or mail voting, and Some types of people are taller, Usually the poor and people of color. ) The advantage is to formulate a policy, or an ideal person to act as a representative authority. A good system will reduce costs, make voting easier, and increase revenue, making voting more reflective of the wishes of voters, and ideally, turning these wishes into laws or actions.

Therefore, although Americans are most familiar with majority votes, such votes may not most accurately reflect their wishes. This is especially true if there are a bunch of people voting in an election, not one or the other, but a whole set of options. In the version of ranked selection voting used in New York (sometimes called immediate run-off), if no one gets more than 50% of the votes in the first round of voting, the candidate with the fewest votes will be eliminated and their first place The ballot will disappear to those whose voters rank second. Then there is another round of counting. As shown by the weakening of the 2018 San Francisco mayoral election, May take a while.