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  • '"I never voted for anybody. I always voted against." - W.C. Fields, quoted in "W.C. Fields: His Follies and Fortunes"'.

  • Imagine we want to build a new space port at one of four recently settled Martian bases, and are holding a vote to determine its location.

  • Of the hundred colonists on Mars, 42 live on West Base, 26 on North Base, 15 on South Base, and 17 on East Base.

  • For our purposes, let's assume that everyone prefers the space port to be as close to their base as possible, and will vote accordingly.

  • What is the fairest way to conduct that vote?

  • The most straightforward solution would be to just let each individual cast a single ballot, and choose the location with the most votes.

  • This is known as plurality voting, or "first past the post."

  • In this case, West Base wins easily, since it has more residents than any other.

  • And yet, most colonists would consider this the worst result, given how far it is from everyone else.

  • So, is plurality vote really the fairest method?

  • What if we tried a system like instant runoff voting, which accounts for the full range of people's preferences rather than just their top choices?

  • Here's how it would work.

  • First, voters rank each of the options from 1 to 4, and we compare their top picks.

  • South receives the fewest votes for first place, so it's eliminated.

  • Its 15 votes get allocated to those voters' second choiceEast Basegiving it a total of 32.

  • We then compare top preferences and cut the last place option again.

  • This time, North Base is eliminated.

  • Its residents' second choice would've been South Base, but since that's already gone, the votes go to their third choice.

  • That gives East 58 votes over West's 42, making it the winner.

  • But this doesn't seem fair either.

  • Not only did East start out in second-to-last place, but a majority ranked it among their two least preferred options.

  • Instead of using rankings, we could try voting in multiple rounds, with the top two winners proceeding to a separate runoff.

  • Normally, this would mean West and North winning the first round, and North winning the second.

  • But the residents of East Base realize that while they don't have the votes to win, they can still skew the results in their favor.

  • In the first round, they vote for South Base instead of their own, successfully keeping North from advancing.

  • Thanks to this "tactical voting" by East Base residents, South wins the second round easily, despite being the least populated.

  • Can a system be called fair and good if it incentivizes lying about your preferences?

  • Maybe what we need to do is let voters express a preference in every possible head-to-head matchup.

  • This is known as the Condorcet method.

  • Consider one matchup: West versus North.

  • All 100 colonists vote on their preference between the two.

  • So that's West's 42 versus the 58 from North, South, and East, who would all prefer North.

  • Now do the same for the other five matchups.

  • The victor will be whichever base wins the most times.

  • Here, North wins three and South wins two.

  • These are indeed the two most central locations, and North has the advantage of not being anyone's least preferred choice.

  • So, does that make the Condorcet method an ideal voting system in general?

  • Not necessarily.

  • Consider an election with three candidates.

  • If voters prefer A over B, and B over C, but prefer C over A, this method fails to select a winner.

  • Over the decades, researchers and statisticians have come up with dozens of intricate ways of conducting and counting votes, and some have even been put into practice.

  • But whichever one you choose, it's possible to imagine it delivering an unfair result.

  • It turns out that our intuitive concept of fairness actually contains a number of assumptions that may contradict each other.

  • It doesn't seem fair for some voters to have more influence than others.

  • But nor does it seem fair to simply ignore minority preferences, or encourage people to game the system.

  • In fact, mathematical proofs have shown that for any election with more than two options, it's impossible to design a voting system that doesn't violate at least some theoretically desirable criteria.

  • So while we often think of democracy as a simple matter of counting votes, it's also worth considering who benefits from the different ways of counting them.

  • The United States' use of the electoral college to elect presidents instead of the popular vote has become increasingly contentious in recent years.

  • How exactly does this system work?

  • And is it fair? Or antiquated.

  • Find out here.

'"I never voted for anybody. I always voted against." - W.C. Fields, quoted in "W.C. Fields: His Follies and Fortunes"'.

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B1 US TED-Ed base voting north east south

Which voting system is the best? - Alex Gendler

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    Celine Chien posted on 2020/09/15
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