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.


4 thoughts on “Instant Runoff Voting, STV, AV, and the like

  1. Auditing STV/IRV is at this point an open issue, near as I can tell. To do a proper (which is to say risk-limiting, in my view) audit requires that we be able to tell, roughly speaking, whether and how much any discrepancies discovered in a random sample moves us toward a change in the outcome of an election. This is relatively straightforward with FPTP, requiring only that we look at changes in all the winner-loser margins. With STV (regarding IRV/AV as a subset), it’s not so simple. The count involves a series of decisions, some consequential and some not. It’s an interesting problem, and it deserves some serious attention.

    • I have worked on a paper with some preliminary evaluations (it’s under review still), and it appears the calculation of the margin for IRV is rather tricky, and in real elections trying to audit/verify the elimination order would require far too many ballots to be practical.

  2. Actually, Arrow’s theorem says nothing about the voting systems we use in elections. Arrow’s theorem define a voting system as a way to take the complete ordered list of preferences of each voter and produce a complete order list of preferences of society. In other words, it is a way not to select a winner or N winners, but to completely order all the candidates and elect a winner, a runner-up, a second runner-up, et cetera.

    That said, there are similar results about one-winner systems, or about N-winner systems, which say that a voting system cannot simultaneously satisfy a certain set of properties. But people always refer to Arrow’s Theorem instead.

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