Ezra Klein has a new podcast episode out discussing proportional representation (PR), so I thought I would point out that there is a little discussed variant of PR that doesn't require redrawing any districts and can even be used for singleton offices like the President.

As the title of this post suggests, the idea is to achieve proportionality over time. In traditional PR, if one party gets 60% of the votes and another party gets 40%, then the first party gets 60% of the available seats and the other party 40%, both rounded to the nearest seat. In temporal PR, if one party consistently gets 60% of the votes and the other party consistently 40%, then the first party wins control of a singleton office 60% of the time and the other party wins control of it 40% of the time.

One very simple temporal PR system is "let a random voter decide the result of each election". This system has the right long-term average behavior, but can easily produce results which seem intuitively unfair, like when one of two evenly matched parties wins an election four times in a row (as will happen by chance 12.5% of the time). This method is also vulnerable to real or perceived attacks on the method of choosing the random voter ...

"The Wasted Vote Refund" is a slightly more complicated temporal PR system, but with provably minimal variance. In this scheme, voters gain a vote in every election, and that vote does not go away unless their candidate wins. The tricky thing is what happens if you do vote for the winner. In that case, the winners must collectively pay N votes, where N is the total number of voters. If the winners do not have N votes -- and they often won't -- they must borrow them from the losers, giving the losers even more votes in the next election. Mathematically, if the winning party has M members with M+S votes (where S are the votes they have stored from previous elections), then when M+S < N, after the election everyone in the winning party has 0 votes, and each of the L losers have an additional 1 + (N - (M+S)) / L votes as compared to before the election. In the other case, when M+S >= N, the losers have only an additional 1 vote and each winner has ((M+S)-N)/M.

Here's a concrete example for people who like concrete examples more than algebra: Party A and Party B both have 50 members who always vote. At the start of the first election, they all r...

Rachel Grey

Rachel Grey