The Icelandic Voting System

Summary

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: There is some number of constituencies, each of which has: Some number of constituency seats (CS) Some number of adjustment seats (AS) Technically, you could have 0 constituency seats, but most places have some. In Iceland every constituency must have either 1 or 2 adjustment seats. So like, we have Southwest with 14 seats total, of which 2 are AS, while Northwest has 7 total, 6 CS and 1 AS. These are decided after each election (for the next election) by the national electoral commission, and take into account population in each constituency, so as to try to minimize the disparity of voting power. Divisor rules For this kind of system, you have a divisor rule, such as d’Hondt or Sainte-Lague. We use d’Hondt in Iceland. Scandinavia uses a modified Sainte-Lague. The rule is basically a quotient between votes and seats. d’Hondt is $q = V/(s+1)$ Where q is the quotient, V the number of votes a party gets, and s the number of seats they’ve already been allocated. By comparison, the Sainte-Lague method is: $q = V / (2s+1)$ Norway and Sweden use a modified Sainte-Lague, which starts at 1.5 instead of 1, so you get a sequence of 1.5, 3, 5, …. There are a number of other divisor rules, each optimized for a slightly different use case. The key difference here is that by scaling up the divisor, you’re valuing each seat much higher, resulting in it becoming proportionally easier to get the first seat, etc. It should be said that in some ways d’Hondt is the least fair of them, clearly favoring big parties, but it’s al...