Instant Runoff Voting, STV, AV, and the like

One thing I’ve gotten interested in lately is Instant Runoff Voting (IRV), which is an alternative vote tabulation system to our “first-past-the-post” system here in the US. It’s also known as the Alternative Vote (AV), and in multi-winner elections, the Single Transferrable Vote (STV). I’ll probably blog a bit on-and-off about this topic, but for starters, there’s a lot of activism/partisanship when it comes to promoting different voting systems. Unfortunately, almost all voting systems under consideration fall victim to Arrow’s theorem, which says, basically, that you can’t have a method of aggregating people’s preferences that satisfies a bunch of desirable criteria (under some assumptions on how preferences are given).

IRV or STV is used to elect Representatives in Australia, and the Australian Electoral Commission has a nice video explaining the process. It also mentions the election monitors, which are called scrutineers. That always cracks me up. But I digress. AV has come up more recently in the UK, where people are thinking of using it for Parliamentary elections. The pro-AV side has its videos as well, which seem designed to appear to the beer-lovers out there. However, the polling on its popularity seems to indicate that the switch to AV will not happen. There’s opposition to AV from different sources, and even some small parties don’t think it will make a difference.

I’ve gotten interested in IRV because it’s used in California for some local elections. The recent mayoral election in Oakland was run via IRV, which requires a bit of voter re-education. The outcome of the election was quite interesting, wherein Don Perata, who won the largest share of first-choices, ended up losing because Rebecca Kaplan was eliminated and the second- and third-choices went to Jean Quan. This is exactly the kind of thing proponents of IRV want.

What is less clear is how the mathematics of counting IRV works, and how sensitive the counting process is to errors. A lot of people have written about the former, but there has been less work about the latter, and that’s something I’ve started working on, because auditing the outcome of elections is an important step in ensuring voter confidence in the results.

UPDATE: As Oxeador points out below, Arrow’s Theorem is actually a statement about producing a total order of all the candidates that satisfies a given set of criteria, not about single-winner elections. In particular, if you treat the IRV ordering as the order in which the candidates are eliminated, then IRV would fall under Arrow’s Theorem.