Updating in favour of two-round delayed runoffs

I’m not a huge fan of IRV (Also known as AV or Hare voting), despite its status as being probably the most widely used single-winner ranked voting system in practice. It seems unclear whether it’s actually better than plurality voting, but it’s certainly not a lot better than plurality voting. About its only real redeeming value is that Single Transferable Vote is built out of it (and my generalized single transferable vote is still basically a form of IRV in disguise).

Still, people use it, which makes it worth thinking about and studying.

However, some examples I ran into yesterday have caused me to start to think that there are simple variations that are strictly better than IRV in the same way that Approval voting is strictly better than Plurality voting: It’s not that these systems are intrinsically amazing, it’s just that they are (or in this case may be) in all ways better than the systems they replace.

The variation is this: Instead of running potentially as many rounds as candidates, you only ever run two rounds. In the first round, everyone scores as per their plurality (first choice) votes. In the second round, the top two candidates from the first round stay in and everyone else drops out. You then elect whichever of those two candidates the majority prefers.

I’m not yet wholly convinced this is a strict improvement on IRV, but it leads to some things that I think in many cases will be.

The major reason I prefer it to IRV is that it acts as a rather pleasant blend of plurality and Condorcet method: As long as the Condorcet winner is one of the top two plurality winners, this will always elect the Condorcet winner.

Naturally the Condorcet winner is not always one of the top two candidates, but this is still a much stronger claim than IRV can make. The following election is one where the Condorcet winner is also the Plurality winner, but loses in IRV!

23 voters are electing a winner from 5 candidates: A, B, C, D and E.

  • 7 votes of A, B, C, D, E
  • 6 votes of D, A, B, C, E
  • 5 votes of B, A, C, D, E
  • 3 votes of C, B, A, D, E
  • 2 votes of E, D, A, B, C

The Plurality and Condorcet winner is A, but the IRV winner is B. The two round IRV winner is of course A because it is both plurality and Condorcet winner.

It can of course also go the other way when the Condorcet winner is not in the top two Plurality winners:

 

14 voters are electing a winner from 4 candidates: A, B, C and D.

  • 5 votes of D, B, A, C
  • 4 votes of A, B, C, D
  • 3 votes of B, A, C, D
  • 2 votes of C, B, A, D

The IRV and Condorcet winner is B, but the two-round IRV winner is A (the Plurality winner is D here): In this case the Condorcet winner is the third place candidate with the Plurality votes. In full IRV when C drops out it transfers enough votes to B to keep it in the race so A drops out instead of it and then it beats D, but in two-round IRV only A and D make it to the second round, and then A beats out D on majority preferences.

In many ways Two Round IRV is out-IRV-ing IRV here: The way in which IRV tends to fail to elect Condorcet winners is that it gives too strong a weight to first choice preferences. So this is a failure mode that is already present, it just happens that IRV manages to avoid it in this example and two-round IRV does not. I do think that B would be a much more solid choice of winner here (as well as being the Condorcet winner, it’s also the Borda winner), but I’m not very surprised that a system would get it wrong.

So my current feeling from these examples is that two-round IRV is not obviously worse than IRV and that the promise of “often” giving the Condorcet winner is a modestly strong recommendation for it over IRV.

I haven’t actually done the simulations to check (I couldn’t get the original code to compile and haven’t yet put in the effort to write my own), but I would also expect two-round IRV to look a lot smoother than full IRV because of this criterion – IRV has a lot of weird spiky edges in the geometry of voting that I would expect to be damped down by the fact that it usually agrees with the Condorcet winner where that’s in the same rough region as the Plurality winner.

So that’s my evidence for two-round IRV being surprisingly competitive with full IRV and possibly better. Additionally, it’s easier to explain and simpler to follow the reasoning of an election. IRV is not itself that hard to explain or follow the reasoning of, but it’s nice when a system can both be better and simpler.

In and of itself these differences aren’t very interesting and I suspect there’s likely not much in it, but it leads to additiona interesting variations. In particular:

  1. If we’re only doing two rounds, why on earth are we using such a bad voting system for selecting who makes it into the second round? Why not e.g. use Borda count and then do a majority runoff between the top two?
  2. If we’re only doing two rounds, is it really worth making it an instant runoff?

Both of these questions stem from a single root question: Why are we making voters go to all the work of providing a full ranking and then using so little of it?

Full rankings are quite a lot of work (even partial rankings are a fair amount of work), and while IRV in theory uses most of your ranking, two round IRV uses very little of it – it only looks at your first choice preferences and then the order in which you put two pairs. Why not just split this out into a normal non-instant runoff?

And, while you’re at it, if you’re using a normal non-instant runoff why are you bothering to use plurality voting for the first round? As I mentioned at the top: Plurality voting is a sign you should be using Approval voting.

So, if you’re using IRV why not consider the following non instant variation? My suspicion is that it will be outright better:

  1. in the first round, vote for candidates with Approval voting.
  2. In the second round, pick the top two candidates from the first round and do a simple majority vote between them.

It does require people to go out to the polls twice, which may be a reason to prefer IRV and variants for large scale elections (though there are plenty of examples of people doing it anyway). However for a lot of use cases it’s very practical to just run two rounds. e.g. I discussed the best democratic solutions for picking a lunch venue recently, where the polls are literally just people raising their hands. It’s not substantially harder to just pick the top two options from the previous election and hold another election for lunch venue.

So, for many and possibly most use cases if you’re tempted to use IRV I would recommend using the above delayed runoff system instead.

This may also be an improvement on straight Approval voting too: One of the problems I have with Approval voting is that it lacks the ability to express a nuanced distinction between two candidates: You can say “I’d be OK with either of these candidates” but you can’t say “But given a choice between them I’d definitely pick this one”. Adding a follow up runoff election adds some of that nuance back in.

One question is whether you always need the runoff election. Suppose only one choice makes it through the first election with a majority of approvals. Should you still run a runoff between that and the second choice?

My suspicion is yes, not because I expect it to reverse the decision in that case but because I think it’s likely to reduce tactical voting in the first stage: If there’s the possibility of no runoff election, you’ll want to very carefully choose your approvals so that your favourite candidate makes it to majority and any other candidate you favour doesn’t.

I don’t know how big a factor that is, and always holding the runoff certainly doesn’t eliminate tactical voting (nothing will except ignoring peoples’ votes in the first round and replacing it with a pure lottery over all the candidates. For many cases this might be a reasonable thing to do, but people seem not to like it very much).

This piece will end without a resounding conclusion, because I haven’t done enough work or reading to decide for certain, but I do feel fairly confident in the claim that a delayed two-round runoff with approval voting in the first round will often be a better choice than IRV and you should consider using it.

Also, if you enjoy these small election examples, I’m putting together a small ebook collating some of them. Let me know if you’d like to be a reader of an early draft.

Finally (you’re going to be seeing messages like this a lot over the next year), if you like reading about this sort of thing and haven’t already, do consider voting with your wallet and sending some money to my Patreon for supporting my blogging here.

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