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The Icelandic Voting System (2024)

It’s election season here in Iceland! The election is on Saturday, 30th of November, so next Saturday from when this is written. Every time elections are upcoming, somebody inevitably asks me how the voting system here works, probably expecting a simple answer. So, here’s a stab at it. Iceland uses a biproportional apportionment system, as do Norway, some cantons of Switzerland, some German regions, and a few other places. Such systems have a few general features:

It has been proven that there is one and only one mathematically sound way to calculate the results, as shown in this paper by Balinski & DeMange, which describes a bilinear optimization exercise aiming at minimizing entropy. The biggest drawback is that it might seem unfair to require the average voter to understand entropy minimization in order to have a clear sense of how elections work. After a few remote sessions, Þorkell came and visited me in Sarajevo, where I lived at the time, and over the course of a weekend we banged out the first version, supporting the Icelandic system and the optimal entropy method described in the Balinski paper.

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