Several friends are collecting signatures to put Instant-runoff Voting, branded as Ranked Choice Voting, on the ballot in Massachusetts ( Ballotpedia, full text). I'm glad that an attempt to try a different voting method is getting traction, but I'm frustrated that they've chosen IRV. While every voting method has downsides, IRV is substantially worse than some other decent options.

Imagine that somehow the 2016 presidential election had been between Trump, Clinton, and Kasich, and preferences had looked like:

  • 35% of people: Trump, Kasich, Clinton
  • 14% of people: Kasich, Trump, Clinton
  • 17% of people: Kasich, Clinton, Trump
  • 34% of people: Clinton, Kasich, Trump
(This is very hypothetical; Kasich wasn't this popular.)

In a traditional election we'd have 35% for Trump, 34% for Clinton, 31% for Kasich, and declare Trump the winner. Under IRV we would eliminate the last-place candidate, Kasich, and divide their votes based on who was put down in second place:

  • 49% of people: Trump, Clinton
  • 51% of people: Clinton, Trump
Since Clinton has passed 50% we declare her the winner.

But let's take a look at how people would have voted in one-on-one elections:

  • Trump vs Kasich: Kasich wins 65% to 35%
  • Clinton vs Kasich: Kasich wins 66% to 34%
  • Trump vs Clinton: Clinton wins 51% to 49%
About 2/3 of people prefer Kasich to any other candidate on offer, but he doesn't win with a traditional election, and he also doesn't win with IRV. This election has a " Condorcet winner", someone who would win a one-on-one election against every other candidate, and IRV isn't designed in a way that it will always choose that person. [1]

Additionally, some proponents of IRV will say that voting your true preferences will never hurt you: that under IRV you never need to hold your nose and put someone first when really you prefer someone else. But there are cases where you can get an outcome you like more by putting a higher ranking on a candidate you like less. Consider an election like:

  • 32% of people: Clinton, Sanders, Trump
  • 33% of people: Sanders, Trump, Clinton
  • 35% of people: Trump, Clinton, Sanders

Now, this is a terrible election and there's no clear winner because people's preferences point around in a circle. Under traditional voting Trump wins, while under IRV Clinton is eliminated and Sanders wins. But if a few people preferring Trump > Clinton > Sanders had instead voted just Clinton > Trump > Sanders we could have had:

  • 32% of people: Clinton, Sanders, Trump
  • 33% of people: Sanders, Trump, Clinton
  • 32% of people: Trump, Clinton, Sanders
  • 3% of people: Clinton, Trump, Sanders

Then Trump would have been eliminated first, with only 32% of the first place votes, and his second place votes would have gone to Clinton, making her win. So by voting for a candidate they liked less, these voters got an outcome they liked more. Staying home and not voting would similarly have helped them.

I do want to be clear: no voting system handles situations like this well, and all reasonable voting systems have situations where you can come out ahead by voting in a way that doesn't reflect your true preferences. But "IRV means you can always vote your heart" isn't true.

So what do I think we should do? Since every voting system has downsides it's not enough to say that a voting system is flawed and so we shouldn't use it. But at the same time some voting systems are still better than others.

For example, a clear improvement over IRV would be to say that if at any point there's a candidate who would win a one-on-one election against every other candidate (a Condorcet winner) then that candidate should win. While it does make IRV a little bit more complicated, it means IRV will no longer eliminate candidates who are the closest there is to a consensus choice. This is called Condorcet-IRV or WoodSIRV, and turns IRV into a voting method that I would be very strongly in favor of.

(I think approval voting is probably a better choice, but it would be good to see more examples of it in practice in competitive elections first.)

[1] A bit of historical irony: in 2008 Greg Dennis, an IRV supporter, wrote in Why I Prefer IRV to Condorcet:

In this scenario, the presence of a candidate with strong core support causes a Condorcet winner with little core support to lose. Fortunately, despite the theoretical possibility of this scenario, the empirical evidence suggests that it is vanishingly rare in practice. In fact, if you look at the ballot data that is publicly available for the IRV elections held in the US (San Francisco, CA, Burlington, VT, and Pierce County, WA), for instance, you'll see that IRV and Condorcet agree on the winner every single time.
This was at a time when IRV had been used for only a few elections. The very next Burlington VT election, in 2009, ran into exactly this situation. This led to enough controversy that Burlington repealed IRV in 2010.

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Further reading on this: a voting theory primer for rationalists, which in particular mentions that RCV has lower "voter satisfaction efficiency" than just about any proposed alternative except first-past-the-post. (Approval does indeed do better, and the author supports it as a first step.)

I basically don't buy the Condorcet winner argument, mostly because the utility and disutility of winning or losing isn't fixed. This is one of the reasons why I like score voting (or range voting) so much; candidates who are massively disliked lose heavily, whereas candidates who are broadly liked win, and from the candidate's point for view, increasing your score in the eyes of anyone is useful, regardless of their score for other candidates.

Yes, there are concerns about comparing utilities across people, but people tend to be pretty reasonable about this in the score voting framework. (It's strategic to give your favorite a 10, and your least favorite a 0, but empirically people often compress their scores much more, say giving everyone a rating between 6 and 8, which implicitly makes their vote a fifth as strong.) The main problem is when you add candidates who make differences so large that it dwarfs all other variation (at least among voters who think they have tiered preferences). That is, suppose you have an "Anyone But Trump" voter; their vote that maximizes the chance of someone besides Trump winning is to give Trump a 0 and every other candidate a 10. But now whether Clinton or Kasich wins depends mostly on the people who thought Trump was ok (or it was worth putting Kasich in the "as bad as Trump" camp). This is probably fine for the rare election where there's a surprise Trump, and is not great if there's always a Trump-like candidate running.

It's strategic to give your favorite a 10, and your least favorite a 0, but empirically people often compress their scores much more, say giving everyone a rating between 6 and 8, which implicitly makes their vote a fifth as strong

Can you say more about this? I would expect that it wouldn't take many competitive elections before most people would be submitting votes that are as strong as possible.

I would expect that it wouldn't take many competitive elections before most people would be submitting votes that are as strong as possible.

That seems right; the surprising thing is that people are willing to 'undervote' at all, and that they do so deliberately instead of through ignorance. But it makes sense, especially for downballet candidates where you vaguely suspect parks commissioner candidate A is better than B but don't want to put your full force behind A (because if other people are well-informed on the parks commissioner race, you want them to settle it).

Beyond ignorance, altruism sometimes motivates this, which is easiest to see for simple things like picking what restaurant to go to. If you're mostly indifferent between them but have a weak preference, it makes sense to do a compressed vote if you suspect other people might have strong preferences that you don't want to overwhelm.

Most problems and edge-cases in a voting (or preference aggregation or utility aggregation) mechanism are dwarfed by the fundamental incorrect assumption of equal weight per person for any decision. In reality, there are orders of magnitude difference in how much a given choice will impact different people, and in how strongly different people care about their choices.

Once you've decided to ignore that, you're well into the world where legitimacy (acceptance of the result with minimal disruption) is your goal, not optimization of preferences. And for this, there is a very strong advantage to the status quo.

Can you say some about how you think this should work?

I'm not sure "should work" is a phrase I'd use for this topic (topic being "large-group decision-making"). I'm kind of shocked anything works at all, and I suspect it's mostly because voting isn't the main process for deciding anything important.

If legitimacy/acceptance is the main criterion for a voting system, the first things to "fix" are not the geeky "better aggregation of private preferences" mechanisms that we love so much. The problems in trust come from the ludicrous deviations that multi-level aggregation (electoral college and arbitrary geographic divisions) and indirection/bundling of issues (voting for people or parties rather than issues) cause/reveal.

every voting system has downsides

You linked to an article about Arrow's Theorem, which only applies to ordinal (ranked) voting methods, not cardinal (rated) voting methods like Score Voting and Approval Voting.

In any case, it's worth noting that Approval Voting was adopted in Fargo, ND in November 2018, and will be used in June 2020.

There will be a 2020 ballot initiative in St. Louis to convert their current partisan March primary + April general with a non-partisan March open primary with Approval Voting, followed by an April top-two.

There will be twin 2020 ballot initiatives to get STAR Voting in Eugene, OR as well as in its surrounding Lane County, OR.

Cardinal voting methods will win in the long run.

every voting system has downsides

You linked to an article about Arrow's Theorem, which only applies to ordinal (ranked) voting methods

While Arrow's Theorem applies only to ordinal voting methods, other voting methods still have downsides, primarily that you need to be tactical: voting honestly won't always give you your best result.

cardinal (rated) voting methods like Score Voting and Approval Voting

Why are you classifying Approval Voting as cardinal?

Cardinal voting methods will win in the long run.

Why do you think this? You can think of there as being a range of complexity in terms of how much information is elicited from voters: single top preference (FPTP), all acceptable candidates (Approval), candidates in order (Ranked), candidates with ratings (Range). Where we end up on this seems like more a question of what ends up working well in practice than something we can answer from thinking about humans. I like Approval a lot, as I said in the post, but after seeing more hotly contested Approval elections I might understand new aspects of how it works in practice that would change my mind.

Why are you classifying Approval Voting as cardinal?

Ordinal voting systems force you to express a strict preference between all candidates; cardinal voting systems allow you to have candidates tie. For any election with at least three candidates, there has to be a tie if you're using approval voting.

Defining "cardinal" as "allows you to rank two candidates as equal" is a very weird use of the term, but it does appear to be standard:

Cardinal voting methods will win in the long run.

(What kind of long run? Why is this to be expected?) Popularity is not based on only merit, being more complicated than the simplest most familiar method sounds like a near-fatal disadvantage. Voting being involved with politics makes it even harder for good arguments to influence what actually happens.

Australia has been using a much more complicated ranked system since 1918, and Ireland has used an even more complicated weighted proportional system. The entire state of Maine adopted IRV, and cardinal systems are much simpler. It's not a fatal disadvantage.

The Approval Voting system is arguably simpler than the status quo, because you remove a rule. The one that stays your vote is invalid if you vote for multiple candidates.

Maybe "near-fatal" is too strong a word, the comment I replied to also had examples. Existence of examples doesn't distinguish winning from survival, seeing some use. I understand the statement I replied to as meaning something like "In 200 years, if the world remains mostly as we know it, the probability that most elections use cardinal voting methods is above 50%". This seems implausible to me for the reasons I listed, hence the question about what you actually meant, perhaps my interpretation of the statement is not what you intended. (Is "long run" something like 200 years? Is "winning" something like "most elections of some kind use cardinal voting methods"?)

Is utilitarianism an ordinal voting system?

If you could get people to honestly report the change in utility they would experience, then you could choose the things that would give the largest utility increases. But since you can't assume honesty it doesn't work.

So you agree that it's a voting system.

I don't think it's intuitive that "give me a full account of all of your desires" wont end up working better than "give me an extremely partial picture of your desires"

This will all be interesting to see play out and I do agree that we can improve the election process.

I do wonder just how well it will actually improve the end outcome: better government and better representatives. From my perspective one of the main problems is that representatives are simply not representative of any real majority of the population or exposed to any real incentives to pursue what might be call common/general good over the special interests and partisan policies.

Am I correct in thinking that these problems are more obvious when using ranked-choice to elect a single candidate? When electing a number of people, it would be much better than just picking in order of number of votes.

This is all focused on single-winner elections, which is the main kind we have in the US.

The standard way elections for multiple slots are handled in the US is you vote for up to N people, and the N with the most votes win. Switching to approval voting would be as simple as changing "vote for up to N" to "vote for any number".

(There's also generalization of Instant Runoff called Single Transferrable Vote, which Cambridge MA uses for City Council)

Here's an example "vote for up to 4" ballot, for Boston City Council: Ballots for Nov 3 2015_tcm3-52198.pdf

How common are Condorcet winners?

About 2/3 of people prefer Kasich to any other candidate on offer [...]

I think this is misleadingly phrased. It's true that Kasich wins by 2/3 to 1/3 no matter which other candicate you pit him against, but it's not true that 2/3 of people prefer him to any other candidate on offer. Only 14% + 17% = 1/3 of people have him as their first choice.

Your thesis stands, though, and I've updated on it.

The statement is ambiguous, and depends on whether you're binding "2/3 of people" or "any other candidate" to a value first. It can mean either the intended:

for each other candidate on offer:
    about 2/3 of people prefer Kasich to that candidate


there exists a group of about 2/3 of people that:
    for each other candidate on offer:
         everyone in the group prefers Kasich to that candidate

I think the ambiguity is clear in context, however, since the latter is so clearly false.

A 2/3 majority prefer Kasich to any other candidate. The point is that Independence of Irrelevant Alternatives dictates that if a group prefers X to Y, and prefers X to Z, that they logically must prefer X if all three are options. It's like if I ask you to choose between chocolate and vanilla and you pick chocolate; if I tell you strawberry is also an option, that shouldn't make you switch to vanilla.

if a group prefers X to Y, and prefers X to Z

There's no group that prefers Kasich to Trump and also prefers Kasich to Clinton. It's 2/3 in each case, but those two groups of 2/3 only have an overlap of 1/3.

I'm not familiar with voting theory, so I might be missing the point, but the sentence "there exists a 2/3 majority of the voting population all of whom prefer Kasich to any other candidate" is false. (The problem might be the ambiguity of the English language: it is true that "for any candidate besides Kasich, there exists a 2/3 majority who prefers Kasich to that candidate".)

There's no group that prefers Kasich to Trump and also prefers Kasich to Clinton.

That is irrelevant.