2017inReview

Fair Elections and STV

2017inReview

Today is Super Tuesday! Unless you read FiveThirtyEight, it’s not really as awesome as
other Super things. However, it does make a good excuse to talk about one of the more esoteric bits
of Stack Exchange: moderator elections. As I write this, Donald Trump is well on his way to winning the
Republican primary even though most people predict he’d lose a two candidate race. The problem can be summed up with this (hypothetical) chart:

Percentage First choice Second choice Third choice
33% Trump N/A N/A
22% Rubio Cruz N/A
22% Cruz Rubio N/A
8% Bush Rubio Cruz
8% Kasich Rubio Cruz
7% Carson Cruz Rubio

Trump supporters tend to be pretty adamant about their candidate, so let’s suppose they wouldn’t bother to vote if he weren’t running. And let’s suppose that Cruz and Rubio supporters would rather have the other candidate rather than Trump. And let’s suppose Bush, Kasich and Carson are stealing votes that would go to one of the leading “not-Trump” candidates. In this scenario, it’s clear that Trump is only in play because the rest of the field is divided. He’d lose to Rubio in a two-candidate race.

This is precisely the sort of paradox that single transferable vote (STV) systems are designed to resolve. While the math can be daunting, the idea is rather simple. Instead of waiting for candidates to drop out, an STV system allows voters to rank their preferences and resolve the voting accordingly. So in the example above, Carson, as the least-supported candidate, would be dropped and his votes would be transferred to Cruz.1 The new tally would be:

Percentage First choice Second choice Third choice
33% Trump N/A N/A
29% Cruz Rubio N/A
22% Rubio Cruz N/A
8% Bush Rubio Cruz
8% Kasich Rubio Cruz

Then the process of dropping the candidate with the least votes would continue until some candidate gets a majority:

Percentage First choice
67% Rubio
33% Trump

It’s as simple as that.2

Moderators on Stack Exchange are elected using single transferable vote because we believe it provides the best method for representing the interests of broad and diverse communities.3 Instead of forcing voters to judge whether a candidate might be popular among other voters, the system allows people to vote their preferences without throwing away their vote on losing candidates.

Footnotes:

  1. To simplify the explanation, I’m assuming all of the supporters of Carson would have identical preferences. In reality,
    other candidates, including Trump, would pick up some of those votes.
  2. Again, the real world is a bit more complicated because some people would have Trump as their second or third choice over Rubio. There would also be people who leave both Rubio and Trump off their ballots resulting in “wasted” votes. Finally, the party might decide it worthwhile to award delegates proportionally to, say, the top three candidates. On Stack Exchange, we use the more sophisticated Meek algorithm that solves all of these problems.
  3. Even the fact that we allow our users to select moderators at all is a bit unusual.

 

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