Sunday, April 1, 2012

C.G.P. Grey is Wrong (on One Important Thing at the End of His IRV Video)

You've probably seen a couple of the snappy, well-enunciated videos produced by C. G. P. Grey; he's done pieces on the evil of pennies, the problems with copyright, and various aspects of British history, as well as a number of videos on political theory. I want to talk about his video The Alternative Vote Explained. The Alternative Vote is the British name for what Americans may better know as instant runoff voting, or perhaps as ranked choice voting, which are all mechanically identical; I will refer to it as IRV here. The first three minutes of the video are an excellent explanation of the method, including cute fuzzy animals in an easy-to-follow example. But right at the 3:00 mark, Grey makes an egregious mistake.

Grey claims that IRV's crowning achievement is that, unlike plurality voting, IRV doesn't have spoilers, but that isn't true, and it's very easy for me to show it. Consider first his "spoiler-proof" example. Gorilla and Leopard are running for office; Gorilla is about to receive 45% of the vote, and Leopard 55%; Leopard is going to win. But at this point, Tiger enters the race, and 15% of voters move from Leopard to Tiger, making the vote totals Gorilla 45%, Leopard 40%, and Tiger 15%:

Under plurality, that makes the winner change to Gorilla, and that's bad. Grey's claim, and this much is true, is that under IRV, those 15% of Tiger-favoring voters can have their votes reassigned to their second choice, Leopard, putting everything right with the world by making Leopard the winner again.

Persuasive Tiger

But what happens if Tiger is a bit more convincing? Consider the case where Tiger convinces not just 15% of Leopard voters to rank him first, but 30%. That makes the standings Gorilla still at 45%, Leopard 25%, and Tiger 30%:

This leads us into some uncharted territory, because now it's Leopard who is eliminated, and we don't know where Leopard's voters would now go for their second choices. But we can make some educated guesses. Taking a look at the video's earlier example (at the 1:47 mark):

We can see that there is a large contingent—amounting to 25%—of Owl-loving voters, who find themselves torn between Gorilla and Leopard. (Pedantic aside: You can imagine that Leopard gets 15% and Tiger 30% if you want to align this example with our alternate "persuasive Tiger" scenario.) If Owl were running in this race, those 25% of voters would have listed him first. But since he is not, they instead voted for other candidates. It seems that 3 out of 5 owls chose to vote for Gorilla (Turtle's 5% plus Gorilla's 25%, plus 15% from Owl, equals the 45% Gorilla is currently enjoying) while the other 10% are supporting Leopard. There is clearly a split in the Owl community about who the best non-Owl choice is. Suppose that the remaining 10% of Owl supporters, after the elimination of Leopard, re-join their brethren by supporting Gorilla as their second choice in this election, while the other Leopard voters all throw in with Tiger:

That would be a logical assumption. And it means that the final standings are now Gorilla 55%, Tiger 45%:

Let's take a look at that again: If just Gorilla and Leopard run, then Leopard wins. But if Tiger chooses to run, and is able to convince a few more Leopard voters to vote for him, then not only does Tiger still fail to win, he makes it so that Leopard doesn't win either. He actually makes it so that Gorilla wins, which is the exact same problem that we saw with plurality. In other words, we have a candidate who doesn't win, but by entering the race, can change the winner. This is the very definition of a spoiler and it (yes, once again) shows that IRV does, in fact, have spoilers.

Calling C.G.P. Grey

Let me thank Grey for his enlightening videos and his clearly-superior-to-my-own abilities with graphic arts (images not used with permission, but I assert that my usage would qualify as Fair Use.) But this portion of his video is promoting a demonstrably wrong version of the facts, but one which has nonetheless gained a large amount of mindshare and garnered a frightening number of repetitions, both before Mr. Grey's video and more so since. I call on Mr. Grey to address this error, and if he is interested in creating videos to promote actually spoiler-free election method reforms, I would like to point him to approval voting.


  1. Approval voting may not have spoilers in the sense you define them, but it does have a rather different problem. Suppose there are three candidates: Adams, Baker, and Carroll. And all of them have approximately equal numbers of supporters, so I don't really know who is leading. I really want Adams to win, but I also absolutely do not want Carroll. So I certainly would cast a vote for Adams but not Carroll.

    But what about Baker? If I approve him, I run the risk of making Baker win over Adams. On the other hand, if I do not, and the two who are really in contention are Baker and Carroll, I might allow Carroll to beat Baker.

    Approval voting has this problem about what to do about candidates I'm essentially neutral about. And that is why do not like it.

  2. Opinionator: there is a very simple solution to your problem. Flip a coin to decide whether or not to support Baker.

    It's a perfectly reasonable thing to do; it effectively gives a 1/2 vote to Baker. There would tend to be a lot of people who prefer Adams to Baker to Carroll, and using randomness in determining your ballots is a coordination-free strategy for supporting Adams more than Baker more than Carroll.

    The fact that this is a coordination-free strategy means that not only does it simplify things, it's immune to bad actors trying to abuse the coordination mechanisms. For example, there were vote trading schemes that cropped up in 2000, where people who would have normally voted for Gore in a safe state would pledge to vote for Nader in exchange for a voter in a battleground state who wanted to vote for Nader would pledge to vote for Gore. I don't know how much these were actually used, and of course there is no way to verify that the pledges were actually followed.

  3. That's a fine criticism, and I cover my response to it in this post:

    This is also touched on in my recent "tyranny of weak preferences" post (which, if I recall, you rather liked:)

    If you can't be certain who the top two candidates are, and your preference between Adams and Baker is significantly weakly than your preference between Adams and Carroll, I'd say go with the risk-averse strategy, and also approve Baker.

    That all said, this is where score voting may be able to allay your fears. Although I find the simplicity of approval voting convenient (since it is just "score 2", i.e., score with only two possible scoring levels, "approved" (1) and "not approved" (0)), if we can move the conversation to "how many scoring levels are needed", I'll consider that a win ;)

    Given perfectly strategic voters, approval and score are identical, although a wider-range score vote method allows for better results for more-honest populations.

    My guy says 5 to 9 should be sufficiently expressive, without being overwhelming (for voters are vote-counters.)

  4. If you have a relatively homogenous electorate s.t. the same media environment then the presumption of unimodality is reasonable or one could argue desirable. Perhaps that is an unstated presumption in this video? Either way, it would lower the probability of such a spoiler to occur.

    But if it did occur then the potential spoilers could recognize that they might spoil an election. This might be accepted to get the center-left(right) party to accommodate them. Or if that seems unlikely then they could vote strategically and the problem would be solved (and no, no angels would lose their wings by virtue of some people voting strategically). For unlike with FPP, those who'd be influenced to vote strategically would be the more moderate members of a major party that refuses to realign itself with the true political center.

    This is a long ways away from how FPP makes dissenters from the major parties vote strategically. IRV makes it so the two biggest parties, who together tend to comprise the de facto center, would need to follow the true center. FPP attenuates the rope between the true center and the de facto center. Perhaps Approval Voting would make it too short so that if the true center becomes unstable the de facto center is too unstable to get things done, since major reforms take more than one term to implement.

    Either way, in a two-period extension of the model, IRV would eventually get it right which would reduce the diff in value between IRV and AV. It is this "real life" tendency for IRV and AV not to be terribly different that is why I think people who prefer AV should strategically support the promotion of IRV, due to its first-mover and marketing advantages in our FPP-based system.


  5. You say:

    "That all said, this is where score voting may be able to allay your fears. Although I find the simplicity of approval voting convenient (since it is just 'score 2', i.e., score with only two possible scoring levels, 'approved' (1) and 'not approved' (0)), if we can move the conversation to 'how many scoring levels are needed', I'll consider that a win ;)"

    As you may know from other discussions I've had, you don't need to convince me of the value of score voting. I believe that the objections I have to approval voting are mostly met by three-level score voting, and pretty much completely met by five-level. The thing that gets me is that because approval voting is a special case of score voting, many score voting advocates iew approval votinf favorably, while I think that it is just like the fact that IRV is a special case of STV, but yet, STV is a pretty good PR system but IRV has lots of flaws. Just because an election method is a simpler case of a good method does not mean it should be supported by those who favor that good method.

  6. Politics is the art of the possible.
    Most advocates for IRV do so in hopes of getting STV later. The same reasoning is probably why SV advocates often push AV.

    The problems when voter "preferences" over candidates are ordinal for approval voting are even worse for score voting and get worse as you add additional rankings.

    What works well for Olympic judges doesn't per se work well in practice for popular elections.

    So it's a big non sequitur... Sometimes you gotta recognize that since there are an infinite number of single-member election rules and the status quo prevails when the alternatives proliferate, You've got to know when to hold 'em,
    Know when to fold 'em,
    Know when to walk away,
    Know when to run...

  7. @ Opinionator:

    It would be nice if this forum would be threaded with notifications. You probably will never read this:

    Runoffs would solve this:

    Approve both Adams and Baker. In the runoff, approve whichever candidate is the remaining. If Adams is not in the runoff, Adams never had a chance. At any rate, your choices in the runoff are clear cut.

  8. @Walabio,

    But runoffs are costly.

    It also is costly to wrangle over trying to get the right single-member alternative to FPTP when arguably what is most important is to improve the mix of single-member and multi-member/PR election rules.


  9. @ dlw:

    DLW said...

    @ Walabio,

    > “But runoffs are costly.”

    But runoffs are powerful tools for vetting. If we really wanted to save money, we can just not have elections.

    > “It also is costly to wrangle over trying to get the right single-member alternative to FPTP when arguably what is most important is to improve the mix of single-member and multi-member/PR election rules.”

    I support proportional representation. ¿Do you know about AssetVoting for proportional representation? Unfortunately, we will still have some single-winner elections, so we might as well use a good single-winner voting system. A good single-winner voting system which we can easily implement is approval voting. We can later improve it by upgrading it to ScoreVoting.

  10. "It would be nice if this forum would be threaded with notifications. You probably will never read this:"

    You can subscribe to comments via RSS (for the whole site (which I do) or on a post-by-post basis) and when you comment (at least with a Google account, not sure about otherwise) there is a check box you can use to subscribe via email.

    Threaded would be nice, I wonder if that's configurable...

  11. @Walabio,

    there's more than one type of election rule for a reason.

    We need both single and multi-winner elections. Because we need both hierarchy and equality, continuity and change.

    Multi-stage elections are like hybrids. I myself like their use for a revamped version of our presidential elections. The Electoral College could be the final stage.

    So, since we live in a FPTP so-called democracy, we also need to rally, at the local level, around a single alternative to fptp for single-member elections. In the real world with Joe-Voter, I don't believe the diffs among alternatives to FPTP are that great. For this and other reasons I support FairVote's activism leadership and push for IRV, albeit I have suggested that they use a form of Approval Voting in the first stage to get 3 finalists and speed things up.

    As for PR, IMO we need to be pragmatic and get it in use in part as soon as possible to move our system towards a Winner-Doesn't-Take-All electoral system. Our current system tilts too easily to single-party dominion and this is why the two major parties cannot work together; they both want to dominate.


  12. @Opinionator
    "But what about Baker? If I approve him, I run the risk of making Baker win over Adams. On the other hand, if I do not, and the two who are really in contention are Baker and Carroll, I might allow Carroll to beat Baker.

    Approval voting has this problem about what to do about candidates I'm essentially neutral about. And that is why do not like it."

    Admittedly, this "later no harm" is a weakness with Approval Voting. But it's much less of a weakness than with other systems. At worst, Approval Voting gets you a compromise candidate when you use one of your votes to hedge against a crappy candidate. And unlike nearly all other systems, Approval ALWAYS lets you vote your favorite.

    Other systems like runoffs, IRV, and Borda are much worse. If you try to cover yourself in other systems, or even try to vote your favorite, then you risk having your least favorite win. So picking the superior voting system should be an easy decision.

    Is it better to have a system that risks electing your compromise candidate or one that risks electing your least favorite? Obviously, the system that only risks electing your compromise candidate is better.

    Conclusion: Approval Voting is your best bet.

  13. But when does one risk being persuaded not to rank one's favorite number?

    The answer is when it's one of the two biggest parties, but far enough from the true center that the other biggest party wins when the more centrist candidate gets eliminated.

    When we allow that party's positions are dynamic, the implication is therefore that the two major parties are coerced to reposition closer to the true center due to this possibility.

    The implications of electoral analysis that takes as given party positions or voter preferences is deceptive because of its lack of realism.

    The dominant strategies for parties will make it so that such an incentive for strategic voting is not likely or if it does happen likely to persist.


  14. But the same is true for plurality (that as you move away from the center you risk giving up the center and throwing the election to the "other side") and the parties DON'T reposition closer to the center. Instead, they sort of bobble about around the 25th to 30th percentile.

    Obama (despite claims of him being a far-left extremist, made by people who wouldn't recognize a socialist if Bernie Sanders bit their leg) is fairly close to the center of the Democratic party. And Mitt Romney is close to the center of his party. And neither was faced with strong opposition in their primaries ('08 for Obama, this year for Romney) *from someone closer to the political center*. The party zeitgeist doesn't allow it. John Huntsman did horribly. Mike Gravel did horribly.

    I understand why people want a separate party for the center: because the major parties DON'T move toward the center (even if you think that the simple model suggest they should do so.) And in THAT situation--which is the real situation--the center-squeeze present in plurality AND IN IRV, prevents such a party from ever having success.

  15. "while the other Leopard voters all through in with Tiger:"

    should read

    "while the other Leopard voters all throw in with Tiger:"

    --Jake Witmer (seeding the great google magic machine)

  16. Whoops, thanks. Fixed. (16 months and no one else noticed? And on the most-read post on the entire blog; almost 5x as many hits as #2!)