Condorcet and later-no-harm

In recent discussions, I’ve had folks suggest that instant-runoff voting is fairer than Ranked Pairs. I disagree, but let’s cover the arguments.

Instant-runoff voting (STV@1) fails the Condorcet criterion

80 voters 70 voters 15 voters IRV winner
Sincere A > C > B B > C > A C > B > A B
Insincere C > A > B B > C > A C > B > A C

The majority of voters prefer C over B, but IRV elects B (failing the Condorcet criterion). Then 80 voters insincerely express a greater preference for C so as to ensure that B loses.

Ranked Pairs fails the later-no-harm criterion

80 voters 70 voters 15 voters RP winner
Sincere A > C = B C > B > A B > C > A C
Insincere A > C = B C > B > A B > A > C B

Ranked Pairs elects C. Then 15 voters insincerely express a greater preference for A over C resulting in a win for B.

Comparison

It’s clear then that both systems are subject to tactical voting. This isn’t surprising as the Gibbard-Satterthwaite and Duggan-Schwartz theorems show that no system is immune to these types of problems. If no perfect system exists, the question is which system’s flaws are more acceptable?

The later-no-harm flaw in Ranked Pairs only arises when demographics vote tactically, whereas the Condorcet flaw in Instant-runoff requires demographics to vote tactically to avoid a sub-optimal winner. If we could guarantee completely sincere expressions of preference, range voting would be superb. If we could guarantee perfect strategy for all voters, I’d be good with IRV. As it stands, we live with a mix of both and I think that Ranked Pairs does a decent job of straddling that divide.

If we’re talking about mind-share, STV certainly has a lot more going for it and I’ll support it in any referendum against FPTP. It’s just a little frustrating to see a better system go unloved.

14 Responses to “Condorcet and later-no-harm”

  1. acts_as_list  on August 27th, 2009

    “If we could guarantee completely sincere expressions of preference, range voting would be superb.”

    Actually, score voting (aka range voting) is superior to every Condorcet method I know of, with any mixture of honest or strategic voters. And actually Condorcet methods can behave quite badly under strategic behavior.

    Aside from all that, score voting is just vastly simpler/cheaper to administer and tally, and experimentally reduces spoiled ballots (whereas ranked ballots cause spoiled ballots to increase in frequency).

    I honestly do not know of a single advantage of any Condorcet method over score voting. I say this as someone who was a pretty strong Condorcet advocate at one time (before discovering scorevoting.net).

  2. acts_as_list  on August 27th, 2009

    Also, I consider it to be bad for a voting method to pass the “later-no-harm” criterion.

    The problem with later-no-harm is that it naively assumes that “later” means “later, after you’ve started by voting for your sincere favorite”. Of course, that’s not necessarily a sound assumption. With IRV, for example, it can be harmful to top-rank your sincere favorite candidate.

    The better criterion is favorite betrayal. Generally put, once you’ve started by maximally affecting the two front-runners, what can you then do that is essentially guaranteed not to hurt you.

    With score/approval voting, once you’ve supported your favorite front-runner, you can still safely support anyone you like more. Not the case for e.g. plurality and IRV.

    Also for EVERY Condorcet method: http://scorevoting.net/VenzkePf.html

  3. Brad Beattie  on August 27th, 2009

    Hey Clay, I’m not yet convinced of range voting. My intuition would say that it’s highly susceptible to tactical voting (likely as a result of the level of expression in the ballots). If I’m willing to listen, but scorevoting.net lacks the brevity to convince.

    I see a summary of points that I’ll go over that a bit later today. I have some feedback on it, but I’m a bit busy at the moment.

  4. Dale Sheldon  on August 27th, 2009

    That complaint, that it intuitively seems gamable, is one I’ve heard before. I’m convinced though that this is a case were intuition is wrong.

    The fear is that, if you really like one candidate, and mostly like another, your opinion won’t matter if someone else really likes the second and is willing to burry the first.

    And that’s true. But in that case, the worst that happens to you is you get a candidate you “only” mostly like, whereas in pretty much every other voting method, against tactical opposition your honest vote will result in you getting the worst possible candidate elected.

    With score, by expressing your willingness to compromise, you instead elect someone that everyone can find acceptable.

    So that intution isn’t strictly wrong, but it is misleading; you might occasionally “lose” a little bit through honest compromise; but the overall, longterm, aggregate result of using score voting is that the total loses for the electorate is lower than under any other practical method.

  5. Ted  on August 27th, 2009

    You should check out RangeVoting.org.

    Here’s an interesting thought experiment:

    Let’s say there is a cluster of points at 0.0 on the real line, and another at 1.0. 60% of the points are located at 0 and 40% at 1.

    You’re given a set of candidate points located anywhere on the line.

    The points (voters) have some way of ranking or rating candidates based on how far the candidates are from their position.

    What method will find the candidate closest to the centroid of the group, position 0.4?

    I ask this because I think we’re best served when the winner of a single-winner election is the most centrist candidate.

    It is interesting to me that no ranking method will select the centroid candidate in this example. To do so, you would need to have enough of a cluster of supporters around the centroid candidate who put that candidate in first place to prevent the other two factions from having a majority.

  6. Brad Beattie  on August 27th, 2009

    I guess the next question is if range voting tactically reduces to approval voting (aka RV{0,1}), why not just use approval voting?

  7. Dale Sheldon  on August 27th, 2009

    While their performance under tactical situations is identical, score has higher potential performance gains than approval does as you allow for more sincere voters. So best case, you gain a lot; worst case, you lose nothing.

    Now, I don’t know if your an IRV fan but in case anyone reading is:

    Interestingly, tactical IRV and tactical plurality have the same performance as well; but IRV has a higer potential than plurality as you allow for more sincere voters.

    So if you’re down on score because it’s tactically identical to approval, you should be MORE down on IRV, because it’s tactically identical to plurality, and plurality is much worse than approval.

    To answer your next question, which is “But IRV voters will be more likely to be sincere!” I would say that 1.) that’s not a question 2.) there’s no evidence to support that and 3.) even if it’s true, Bayesian regret simulations show approval out-performing IRV even with a 50% honesty handicap (http://rangevoting.org/StratHonMix.html); so even on the off-chance you’re “right” about the enhanced sincerity, you’re still wrong about IRV.

  8. homunq  on August 27th, 2009

    It’s true, score voting is better than condorcet for any *given* and *random* mix of strategic and honest voters. But, since the circumstances under which strategy successfully improves one’s results are much broader for score voting, it is plausible that it would not lead to the same proportion of strategy. Also, there is a real possibility that one group of voters would be more strategy-prone, in which case it could give much worse results. Thus, it is still very much an open question which is better, and probably the answer depends somewhat on circumstances.

    (My personal favorite method is a score-condorcet hybrid which I call Score DSV).

    Obviously, both reforms are a gigantic improvement over plurality.

  9. Brad Beattie  on August 27th, 2009

    Obviously, both reforms are a gigantic improvement over plurality.

    That’s the key right there. So long as we have some kind of electoral reform that improves representation, I don’t quite care what it is. It’s likely that STV has the largest body of support in Vancouver due to its familiarity. There are problems with STV, but there are problems with any voting system. The question should probably be “what can we plausibly transition to given the current situation?” It’s a highly contextual question.

  10. homunq  on August 27th, 2009

    I think score voting is one of the best solutions available. But it’s simply not true that there’s no possible downside versus approval. If one ideological group is more strategic, that group will gain a significant advantage. This is much much less of a possibility with approval. That’s why I like score DSV – basically, score voting renormalized to the smith set.

  11. Brad Beattie  on August 27th, 2009

    That’s why I like score DSV – basically, score voting renormalized to the smith set.

    Could you provide an example of this? I’m curious to see it in action.

  12. Brad Beattie  on August 27th, 2009

    1. Condorcet aggregate functions are more complicated than range voting’s. Agreed, with the fridge caveat.
    2. Rating ballots are more expressive than preferential ballots. Not notably. I think we could agree that a rating ballot for n candidates isn’t more expressive with a range to 1..m where m > n. So if we’re just talking 1..n rating ballots, there’s a decent, if not 1-to-1, mapping with preferential ballots.
    3. Range voting can be used in American voting machines. Moot for me as a Canadian.
    4. Range voting satisfies the WDS-Condorcet winner criteria. Agreed, but this ignores tactical voting. With the Condorcet criterion, we can safely assume that votes in the theoretical two-candidate races (pairwise comparisons) aren’t subject to tactical voting. With range voting, not so much.
    5. The Condorcet winner criteria isn’t really good. I’m not convinced by the arguments. I understand them, I’m just not convinced that it’s a bad thing.
    6. Condorcet systems are subject to tactical voting that can lead to bad results. All systems are, even range voting.


    I got tired of reading at that point. I know it’s not intended as proof by verbosity, but the lack of brevity makes the core arguments inaccessible. I really am open to the idea that range voting could be a better system than my current Condorcet preference. I just don’t see it at the moment.

  13. acts_as_list  on August 27th, 2009

    Ted,

    Ah yes! Here are some fun pictures of what you’re talking about.
    http://scorevoting.net/IEVS/Pictures.html

    It can help to think of voters as positions on a map, and candidates as potential sites of some great new recreation center that everyone wants to have as close as possible to his home.

    What voting method can voters use that will yield the location which is statistically closest to the centroid of the voter distribution?

    Bayesian regret calculations say score voting.

    Oh that also works if you move into n-dimensional issue space, instead of just 2d.

  14. homunq  on August 28th, 2009

    I made a page about it on the electorama wiki


Leave a Reply