[EM] Defensive strategy for Condorcet methods

[Juho Laatu]

On 13.6.2011, at 4.54, Kevin Venzke wrote:

> Hi Juho,
> 
> --- En date de : Sam 11.6.11, Juho Laatu <juho4880 at yahoo.co.uk> a écrit :
>>>> Maybe strategic, maybe misled to think that
>> ranking C above
>>>> B would always decrease the chances of B to win,
>> maybe you
>>>> want to discourage B by showing that he is not
>> much more
>>>> popular than C.
>>> 
>>> Why misled? I don't believe that ranking C>B always
>> hurts B any more than
>>> I think that ranking B>C always *helps* B defeat A.
>> No always about it.
>> 
>> You are an expert, so you do know. But it seems plausible
>> that there are always some voters that rank the worst
>> competitor (B) of their favourite (A) last, just to be sure
>> that they have done all they can to make A win. That is a
>> tempting but unfortunately irrational strategy.
> 
> Ah I see. It is funny that I can't figure out whether, if I were you, I
> would want to call this strategy irrational or rational.

This strategy could change the winner in the intended way sometimes, but applying this strategy without carefully considering its possible impacts may more probably harm the voter (and could therefore be called irrational).

> 
> You could say, if you wanted, that it's totally rational, because by and
> large no one else will do that (you would need to claim), so C won't win
> and it *does* make sense to bury.

It could make sense in the sense that B could be "weakened" if he almost lost to C, or if even some people felt that even C is better than B. Of course also psychological factors like voters feeling a bit happier after "giving B a lesson" could be counted. One the other hand strategies have also negative secondary effects and they should be counted too.

> That would be a coherent pro-margins
> stance I think.
> 
>>>>> If I thought B voters
>>>>> were going to use this same strategy against
>> me then
>>>> in voting like
>>>>> this I might just be defending myself.
>>>> 
>>>> You are also taking a risk that C will win,
>> despite of not
>>>> having any chances with sincere votes. If many A
>> and B
>>>> supporters rank C second and C has also some
>> first
>>>> preference supporters, C could become a Condorcet
>> winner.
>>> 
>>> You tell me whether C might win. I'm asking you! I'm
>> just one voter.
>> 
>> My argument above was, if one voter finds this strategy
>> interesting, then that strategy may be interesting to many.
>> With three candidates there are six different complete
>> rankings. Rankings that start with A and B are obviously the
>> most common, And rankings A>B>C and B>A>C are
>> maybe the most common ones. And this interest to bury their
>> second favourite under C may apply to all of them. 
> 
> Yeah, that is all very scary.
> 
>> Therefore
>> a good advice to Condorcet voters is to rank candidates
>> sincerely.
> 
> I just can't see how that follows. Of course, if you assume that the
> voters are just going to do what you say, then yes it's better overall.

Yes, that is the area where my concerns are. If I give a general advice to all to bury under C and nobody or only very few voters listen to me, then I'm ok, except that I'm not ok since people didn't respect my recommendations. If they all listen to me, then I have problems since C wins. I could also give a strategic advice to flip a coin and bury in case of heads. But I'm not sure if that would be enough or maybe too much to achieve the target. Or I could tell that only A supporters should bury, but that might mean that since B is in a symmetric position, B supporters could bury as well. Maybe some B supporter would give a similar recommendation to B supporters.

One key problem in Condorcet strategies is that often you need a certain number of strategic voters (not too many, not too few) to achieve the result, and often also the number of different opinion patterns among the voters must be within a certain range. And if one adds to this the uncertainly of polls and the richer set of different opinions in real elections when compared to theoretical examples, unwillingness of some voters to use strategies, inability to control the voting behaviour of all the voters, possible high number of required strategic voters, impact of other strategies and counter strategies, and possible changes in opinions against candidates that plan to use strategies, situations where one could give a general public recommendation to certain identifiable group of voters to vote in a certain strategic way are not very common.

In the discussed example where the frontrunners are assumed to have about equal support the biggest risk is maybe lost reputation (and votes) if one publicly recommends strategic voting (or does not discourage such plans) to steal victory. This depends a bit on the attitudes and morale of the society in question.

For the whole society it would be good if all candidates and parties would recommend sincere voting. Also from individual supporter groups' point of view sincere strategy may well be the best recommendation. I will not provide detailed examples here but I claim that in typical large political elections where voters make independent decisions, opinions are not very stable, people in general do not appreciate strategic plots, and many people will not resort to strategic voting, plots are almost never a useful tool (will not succeed, will backfire, or is negative advertising), even if one would not build specific strategy deterrents into the Condorcet methods.

And then some words more on recommending sincerity. If there are no good strategies to recommend, then sincerity is the best recommendation. The sincerity recommendation may include the reservation that in case someone finds a good strategy, then there is one, but until that day sincerity is the best option. And one doesn't lose anything with that since strategic plans will be visible on public elections, and people can react by counterstrategies if there is a need to do so. So, in the absence of any better rules (and that is common) sincerity is the best strategy.

> You're looking at it from a different vantage point. But I don't see 
> how you can actually show that it is good advice, at the voter level,
> without insisting there is a real possibility of disasters.

If all follow my advice, everything will be fine and the best candidate will be elected. If some group starts discussing strategies, then my recommendation (in this mail stream) must be to give false information in the polls. In the actual election people could then vote sincerely more freely. If for some reason supporters of exactly one of the leading candidates would plan to vote strategically, then maybe the supporters of the other leading candidate should do so as well, and intentionally elect rather C than the strategist (or their own favourite if the strategy of the other side does not work and their own candidate is more popular at the election day). One may also threaten to elect C to make the strategists give up their plan. I'm sure people will understand that sincere voting is better than strategic battles. Strategic voting will become dominant under certain conditions (e.g. in Approval) but in Condorcet the equilibrium of the society could be sincere voting. Strategies are so often irrational or inefficient or harmful that people could as well start avoiding them. I guess we should have some real life use to see how different societies will react. Maybe there are places where people and parties are so strategy and mistrust oriented that strategies will be generally used, but maybe not in most societies. I don't see much strategic interest today in TTR and IRV elections (except in Australia). Maybe Condorcet would fall into this category too.

> 
>> Maybe they should be given advice not to touch
>> strategies unless some reliable experts or their own party
>> tells them that it is time to use some (hopefully defensive)
>> strategy. 
> 
> ??? Unless you mean compromise, i.e. "let's not vote for our own
> candidate," I don't see how you can identify "defensive" vs. "offensive."
> Are you saying their party is telling them it's time to lie because
> they believe the opposing voters are going to lie? They are saying "don't
> swerve" for the chicken game?

I wanted to say that regular voters that are not experts in strategies of Condorcet methods should not try to invent and implement strategies on their own. Better to rely on advice from experts. And without any such clear advice, sincere voting is a good "strategy".

Offensive strategies are not very positive, and I hope that voters would react to them also by reducing their support to the strategists. That would mean that in close competitions it would not be wise to recommend strategies since one would automatically lose some votes.

> 
>> And we say that to them in order to convince them
>> that someone else will be awake and alert and will tell them
>> if the main rule of sincere voting one day has to be
>> canceled.
> 
>>> If
>>> the answer is no or almost never, and I'm the only
>> nutty voter that wants
>>> to vote A>C>B, lose nothing, maybe gain, with
>> everyone else voting
>>> sincerely, there's no harm done, right?
>> 
>> Except that you are encouraging also others to do similar
>> tricks. One day they might do so.
> 
> Well, then I would stop.

Maybe already earlier?

> 
> Interesting question though, whether we could show mathematically (or
> experimentally) that I as voter definitely would prefer to keep the 
> method from becoming broken, assuming I actually have some influence on
> that.

You might tell the strategists that you will give false information in the polls in order to make their strategic attempts fail. I also believe there are various norms of acceptable behaviour in the society. Probably you don't brag to others if you have stolen candy from kids. In the same way your neigbours might not like you if you would regularly brag about trying to cheat in the elections.

> 
>>> I'm going to lie, I probably
>>> *should* lie, but it doesn't matter, and you shouldn't
>> care much.
>>> 
>>> If you tell me C might win, that with or without me I
>> might expect voter
>>> insincerity to produce this outcome, then... Forget
>> about my strategic
>>> dilemma: Can this even be a good method?
>> 
>> If everybody says that C is a good candidate, then a good
>> method might make C win. Garbage in, garbage out.
> 
> Yeah but under other methods I wouldn't say C is a good candidate. If
> some other EM poster wants to claim they're going to vote for C... under
> Bucklin... they can do that, but I want a good explanation.
> 
>>>>> But outside of that possibility,
>>>>> maybe I just don't have any good options?
>>>> 
>>>> How about sincerity as the default rule?
>>> 
>>> No thanks. I want to cast an optimal vote just as I do
>> under FPP.
>> 
>> In Condorcet optimal=sincere (with about 100% probability).
>> You need to learn away from the FPP times when strategic
>> voting (= vote for one of the two leading candidates) was
>> the norm.
> 
> I wonder how you figure it is that high. In my recently-mentioned sims
> I only had around 90% of Condorcet voters using no strategy at all.
> (95% for AWP, implicit or explicit.) Of course, this isn't a perfect 
> model of society, but it makes me think the utility of insincerity is 
> not immeasurably low.

I would like to see general rules for Condorcet voters or parties (who can then give advice to the actual voters) on how to vote strategically. Those rules would be based on getting various poll results one week before the election. If someone could demonstrate that sincere strategy would be useful to individual voters more seldom than applying some other strategy (and improve the expected results), then I might think that sincerity is not the best strategy to recommend in Condorcet methods. Maybe the best strategy to recommend would be the sincerity with some deviations in some special cases.

I guess in my definition of sincerity I counted only successful offensive strategies as deviations from the optimal sincere strategy. One could have also defensive strategies that do not change the result of the election. That is not fully sincere, but not a strategy failure ether. And I claim that it is also typical that such defensive strategies are usually not really needed since the probability of offensive strategies succeeding is anyway low. And you could add to this equation also the threat that use of strategies raises interest in strategies also among the others.

> 
>>> BTW the idea of advising voters to just vote
>> sincerely, as a substitute
>>> for explaining the method to them in detail, makes me
>> choke.
>> 
>> Above I referred to people that the voter trusts as sources
>> of truth to him. If your friends and neighbours, your party
>> and your community all tell that it is safe to vote
>> sincerely, then maybe it is.
> 
> Well, until people get word of it.

In large public elections we would probably hear of those strategies before they are applied. That makes sincere strategy worth recommending while waiting for the strategists to emerge.

(I note that there are two kind of strategic advices, permanent ones that are valid in all elections, and strategies that parties or experts will recommend when they identify strategic opportunities in the current election.)

> 
>>>>> 3. Bullet-vote for A. Nope, not if this is
>> margins.
>>>> That's just splitting
>>>>> the difference or flipping a coin.
>>>> 
>>>> Isn't that how it should be? A>B=C is pretty
>> much the
>>>> same as sincere opinion "I don't know which one is
>> better, I
>>>> might as well flip a coin".
>>> 
>>> I'm talking strategy here. Margins is giving me a dial
>> that goes from
>>> B>C on one end (labeled "bend over") to C>B
>> ("cheat") on the other end.
>> 
>> No, they are called "sincere" and "weird" :-).
>> 
>>> I don't like these options and I feel like this dial
>> shouldn't matter and
>>> I shouldn't have to answer the question. The halfway
>> option doesn't
>>> mean "I don't know which one is better," not
>> strategically. It means "do 
>>> it halfway between the two extremes," 50% of each.
>> What are the odds I
>>> want it exactly at 50%? My own problem isn't that I am
>> *indifferent*
>>> between two candidates. I just don't know how I should
>> mix my poisons.
>> 
>> In margins (and maybe in other variants too) ties should
>> not carry any other additional meaning but that the voter
>> didn't support X>Y nor Y>X.
> 
> In a general context it is really unclear to me what this means. It's
> like an IRV-oriented criterion that assumes you're doing eliminations.
> It may be completely possible to satisfy you on this point, and also 
> have a method that I don't find irritating. From what you've literally
> written here I don't even see how it excludes WV.

There are maybe two ways to understand what the election methods do. 1) Elect the candidate that is best according to some (sincere) philosophy based on the given (hopefully) sincere opinions of the voters. 2) Generate a set of (whatever kind of) rules and let the voters cast their votes in the best way they can to make the outcome best possible for themselves. In the first approach we should have an interpretation on what ranking two candidates equal means from the utility and sincere preference point of view. If the intended meaning of equal ranking is the same as flipping a coin (and often it is about the same), then also the results should be the same (in the first interpretation). In the second interpretation any rules are ok as long as other stated requirements are met (e.g. equal treatment of all voters).

WV is not excluded even in the first interpretation if there is a good explanation (that corresponds to some "sincere" philosophy) to why pairwise defeat strengths are measured the way WV does. It is quite natural to say that the number of voters on the opposing side is an important criterion (but may leave open the question does the number of voters in favour of that candidate have some meaning as well). I think the margins (sincere) philosophy is easier to explain than the WV philosophy.

> 
>>> Well, I think the real world already has examples of
>> party-led strategies.
>>> What I don't think we see is such strategies that need
>> to be concealed
>>> from the other voters.
>> 
>> I would vote against parties that try to win the election
>> with the help of insincere strategies.
>> 
>> I know that e.g. in Australia parties use strategies. One
>> should fight not to let things go that far (=don't accept
>> the idea of mandatory full rankings; make some noise if
>> politicians try to steal your voting rights from you).
> 
> Well, I think if the method is what is prompting people to organize
> strategies, you already lost.

That is a question of balance. Maybe the sincere side has more weight.

> If the method makes strategy X a good idea
> then everybody's going to do that where appropriate.

That tends to be the case. That is, if there is a strategy that all voters can always use to their benefit. Luckily Condorcet methods do not have any very obvious such candidate strategies. Plurality, Approval and Range are less lucky.

> I don't see how the
> society is going to judge strategy X as bad if it stems directly from
> the method. If it's bad, it's all bad, and I expect to see reform
> proposals.

In my interpretation 1) above the idea is to collect sincere opinions. If our method is Range people could quickly learn that normalization and exaggeration tend to be more efficient than sincere ratings. As a result they will understand that interpretation 1) does not work and they should use the method in line with interpretation 2). If our method is Condorcet there is a good chance that also interpretation 1) will work. The society would rule e.g. burial strategy as bad if the dominant way of thinking is that it is a good thing to be able to just give sincere rankings and not worry about strategic voting, and that it is good to do so also because that way the society can always elect the best candidate based on complete set of ranking information from the voters. They also think that electing someone else than what the sincere philosophy of 1) says would be wrong. The majority is not able to force all voters not to vote strategically. But if after few elections the strategic votes would be just noise that does not influence the outcome (or its possible influence in close elections can not be measured) then people could forget their strategic voting related concerns (including those voters that used strategies so far).

> 
> The alternative is just... attacking symptoms of the real problem.
> 
> Another example that occurred to me is SNTV, where parties can gain more
> seats if they e.g. tell their supporters to vote according to the digits
> in their ID numbers. I wonder how many voters had a guilty conscience.

That is a balance. If everyone votes strategically and not doing so would mean that I get worse results than the strategists do, then maybe also I should consider moving to interpretation 2). If I don't expect that to happen, then maybe my natural instinct is to vote sincerely, defend sincerity, and show good example to others, for the benefit of the whole society.

> 
> It's kind of funny that although people do sometimes prefer methods that
> pick candidates with a lot of first preferences, I don't remember ever
> hearing anybody complain that favorite betrayal or primaries (i.e.
> candidates stepping aside before election day) have ruined the original
> idea behind FPP, to elect the sincere FPP winner.
> 
>>>> Ok, but I hope Condorcet is safe enough to allow
>> supporters
>>>> of yet unknown candidates to indicate support to
>> their
>>>> favourites. The resulting risks (and the benefits)
>> should
>>>> not be high.
>>> 
>>> Of course I think it depends, especially since we are
>> talking about
>>> burial in this last bit. Do you think it is impossible
>> to propose a
>>> Condorcet method that would just be bad? If I promise
>> not to be grossly
>>> nonmonotonic, stay deterministic, keep Majority
>> Favorite, avoid big
>>> clone problems: do you think I could come up with a
>> bad one?
>> 
>> A bad method could be also safer in the sense that the
>> burial strategy might lead to unexpected results. We could
>> for example pick a random winner if there is a top cycle.
>> Maybe that will be a deterrent to the burial strategists.
>> (That could be even a too strong deterrent since people
>> might start compromising and bullet voting because of their
>> fear of cycles.)
> 
> Actually it isn't unheard of in discussions of random methods for one
> to object that the method is encouraging burial in some cases.

Also in my example above random results could mean an improvement of the result to some voters, like to those B supporters whose sincere opinion is B>>>>A>C and who believe that with sincere votes A's winning probability will be higher than B's.

> 
> Is Condorcet//FPP a bad method?

Not my first favourite but I think it has also many good properties.

> 
> How about a method where, if there is a cycle, we take the top three
> FPP candidates (call them ABC in descending order). C wins if and only
> if he gets 75%+ top-two rankings (i.e. A>C B>C C>?). Otherwise we will
> elect whichever of A and B has the most ballots in the form A>C or B>C
> respectively. Fun I think?

These methods were already discussed in other mails. I just note that if A>C means that A supporters should rank C second in order to increase their chances to win in case of a top cycle, then things get quite tricky. Burial strategists probably ranked C second, and that could increase their chances of fooling the system.

Juho



> 
> Kevin Venzke
> 
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info