[EM] Defensive strategy for Condorcet methods

[Juho Laatu]

On 12.6.2011, at 0.26, Kevin Venzke wrote:

> Hi Juho,
> 
> --- En date de : Ven 10.6.11, Juho Laatu <juho.laatu at gmail.com> a écrit :
>>> --- En date de : Jeu 9.6.11, Juho Laatu <juho4880 at yahoo.co.uk>
>> a écrit :
>>>>> No, I wouldn't say that. I do think there are
>> methods
>>>> that offer two
>>>>> bad options and one of them is burial,
>> though.
>>>> 
>>>> (There is no working strategy, but there are some
>>>> options??)
>>> 
>>> Absolutely. I'm being honest when I say I don't know
>> how I would vote
>>> in the simplest election. If all I know is that my
>> preference order is
>>> A>B>C and the frontrunners are A and B, what
>> should I do? Let's go over
>>> it.
>>> 
>>> 1. Vote sincerely, A>B>C. On a gut level I
>> *don't want* to do this. B
>>> is the candidate I am trying to beat. Why do I want to
>> help him beat C?
>> 
>> Maybe you strongly dislike C and therefore want to make
>> sure that C does not win.
> 
> Sure... If...
> 
>> You however mentioned that A and B are the frontrunners.
>> Maybe C has no chance of winning this election (with sincere
>> votes at least). In that case it does not (technically)
>> matter how you will rank C. 
> 
> "With sincere votes at least" you're right, I can do whatever I feel like
> doing. I can be insincere. So can everyone thinking along the same lines.
> 
>> But also in this case (where C
>> is totally irrelevant in this election) you could have
>> secondary goals (the primary goal is to decide who wins this
>> time). Maybe you want to discourage C and his supporters so
>> that they would not try again in next elections, or maybe
>> you want to tell all the people how many people think C and
>> C's party is no good (people might follow your opinion).
> 
> This is all possible, but mostly I figure C is just a candidate who has
> only earned attention from me because I have to think about what to do
> with him strategically on my ballot.
> 
> I don't usually hate the also-rans, though I do tend to wonder if they
> are qualified. They don't get that much press.
> 
>> Maybe you want to vote sincerely in order to encourage also
>> others to do so and avoid elections becoming a playground of
>> strategists. 
> 
> It seems like that would work backwards. If I vote sincerely I am making
> it safer for others to lie.

Kristofer Munsterhjelm wrote about thresholds. If the society thinks that it is ok to vote strategically, then many may do so. If you vote strategically, others will be tempted to follow you.

> 
>> You could also vote sincerely because you want
>> the election to act as a poll that measures the opinions of
>> the society reliably and will offer guidance to the decision
>> makers for the next few years.
> 
> Will you argue this for sincere Range voting as well?

The thresholds with Range are very different. In competitive elections normalization and Approval strategies are so obvious that people must forget sincere ratings, go over the threshold, and start voting strategically. Sincere Range may however work fine for judges in sports events.

> 
> As a voter, I think I know best... Thus I don't want to vote sincerely
> if this creates a risk for me. Now if I lie, there is a risk as well,
> but only if there is actually a danger that C will win due to voting
> shenanigans. That has little to do with *me*, that would be what other
> voters are doing anyway.
> 
>>> This can actually help B and it will never help A. I
>> feel like a sucker
>>> if I expose myself to this risk for no possible
>> benefit. I do not need
>>> to know whether there is *really* a threat; it makes
>> no sense for me.
>> 
>> I guess the Condorcet logic should be that the risk of
>> indicating your sincere opinion (B>C) harms you with such
>> a low probability that it doesn't matter. The benefits
>> (maybe secondary) are bigger than the risk.
> 
> Well, the risk from voting C>B is also quite low, and there is actually
> some potential benefit there. Doubly so if most voters think as you do
> and go with the sincere route.

But if voting C>B is obvious to you, maybe it is obvious to all A>B>C voters. That could already mean quite a number of votes. And that could mean trouble. Maybe B>A>C voters would do the same. I wonder how many strategists it would take to make C a Condorcet winner.

Or would your C>B vote be just marginal noise in the election and only very few A>B>C and B>A>C voters would vote that way? In that case we can tolerate it.

> 
> The frustrating thing is that the B:C contest shouldn't matter... When
> I consider what to do with it I am mostly thinking with my "A vs B" hat
> on.
> 
>>> 2. Lie, and vote A>C>B. Now I'm a bad guy who
>> you think must have some
>>> strategy in mind for picking this manner of voting.
>> 
>> 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.

> 
>>> 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. Therefore a good advice to Condorcet voters is to rank candidates sincerely. 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. 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.

> 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.

> 
>>> 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.

> 
> 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.

> 
>> If others are likely to generate (sincerely or by strategic
>> votes) a loop, then your strategic options are a bit
>> different than otherwise. But it is hard to know if there
>> will be a cycle or not. I will not try to analyze all the
>> alternatives here, but there are still many options and many
>> risks.
> 
> Are there? If there are three candidates and no majority favorite and I
> like A best, I basically get to help control the B:C win. Particularly
> if a C win is (I am assured!) supposed to be impossible, there aren't 
> that many stratagic possibilities to consider I would think?

Ok, if there are three candidates and we use full rankings (and maybe bullet votes), then the number of strategic ballot options is not very high. But there are risks that may be too high when compared to possible benefits.

> 
>>> 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.

> 
> My only point is that if this counts as a "third" option it's still not
> a satisfying one. Otherwise I could bring a die into the voting booth
> and have six options.
> 
> So basically you are asking me whether there really ought to be a third
> option at all. Maybe the answer is no. But I do think that you should
> not ask me a question (or at least not use my answer) where my motives
> when answering the question have very little to do with the comparison
> you're asking me about. If I answer all my questions thinking about A vs.
> B, then somehow or another, you want to interpret me that way.
> 
>>> It's childish to vote like this.
>>> But actually, I think I might vote this way, just
>> because I wouldn't have
>>> to feel like either a sucker or a jerk for doing it.
>> 
>> It's your duty as a good citizen to give your sincere
>> rankings and this way help the society to better know the
>> opinions of the citizens. Falsifying your preferences is a
>> bit like cheating. Right?
> 
> I don't think it's your duty to give "sincere rankings." That would 
> destroy FPP. You may have some kind of duty but I don't think it's that.

FPP, Approval and competitive Range are different. You are expected to plan what would be the most efficient vote from your point of view.

I don't really know what we should call a duty. Maybe the duty of all citizens is to support the society a bit so that it will get better and not worse. In this case they should think that well working elections are in the interest of the whole society.

> 
> Lying is a bit like cheating. Actually I may have even suggested that
> when I described the dilemma. Didn't solve it for me though...
> 
>>>>> What? The voters are participating in
>> repeated
>>>> polling, and have the
>>>>> ability to see not just each poll's outcome
>> but what
>>>> they could have
>>>>> accomplished by doing anything else. Buriers
>> see that
>>>> burial is an
>>>>> advantage if the opposing side is sincere.
>> When
>>>> pawn-supporting voters
>>>>> compromise, the buriers have no reason to
>> revert to
>>>> sincerity. (They
>>>>> don't even know what sincerity is.)
>>>> 
>>>> You seem to assume repeated polling, sufficiently
>> accurate
>>>> results, unchanging results, similar results from
>> all the
>>>> polling companies, no intentionally misleading
>> polls, no
>>>> meaningful changes in behviour before the election
>> day, no
>>>> interest to give false information in the polls,
>> maybe no
>>>> impact of planned strategies on the voting
>> behaviour of
>>>> others, good enough control of the strategists (if
>> needed).
>>> 
>>> Your description isn't that unfair. Changes are
>> possible, but most methods
>>> and scenarios become pretty stable.
>> 
>> Last minute changes in opinions are possible. Their
>> strength may be different in different societies and
>> depending on random factors like last week debates, new
>> revealed scandals etc.
> 
> I would see changes in opinions as basically a reboot of the poll where
> the previous results don't matter at all. You must be talking about a
> last minute change so late that new polling information can't be 
> obtained.

Condorcet doesn't need polls, or at least not accurate polls. Rough understanding on which candidates are generally considered good and discussion on the merits of each candidate in the newspapers is enough. No need to plan your vote based on the polls (except maybe in the case of an unwanted strategic intent).

> 
>>> especially when the polling doesn't work as
>> predictably as in FPP, where
>>> the belief that candidate X is strong is generally
>> going to help X.
>>> 
>>> I don't really believe in "planned strategies" that
>> are kept secret.
>> 
>> Yes, this is important since some strategies require some
>> coordination, either to advice the voters in general or even
>> to make sure that correct number of voters vote in some
>> certain way. And when the plans leak out, that may have
>> impact on the voting behaviour, maybe typically so that the
>> strategists will lose some votes. Actually one reason why I
>> think party led strategies will not be very common is that
>> in most cases it may be wiser to use one's energy and
>> reputation in making one's own candidate look good and
>> thereby gain more votes than trying to steal the votes using
>> tricks that voters may not approve.
> 
> 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).

> 
>>>> Truncation is one typical
>>>> strategic defence in some Condorcet methods. I
>> prefer poll
>>>> level preemptive defence to this since that way we
>> can avoid
>>>> e.g. Condorcet becoming "more plurality like".
>>> 
>>> If it works, sure, but if it doesn't, I would guess
>> margins is the
>>> "more plurality like" in the sense that the winner's
>> first preference
>>> count will probably be greater.
>> 
>> I'm not sure that would be rational though.
> 
> Isn't the assumption that a strategic defense is necessary? If your
> polling idea doesn't work then don't voters need to use something else?

Well, maybe parties that want to get rid of the good election method would try to encourage all irrational and destructive behaviour (e.g. to increase and restore the power of the party insiders). The biggest risk may thus be interest to destroy the system, not the faults of the system. I also hope that the false poll information trick would serve only as a threat (that would not be used ever) against people that might try to increase the level of strategic voting. I don't think any strategies are necessary. If there are some poll based strategies, maybe in the next elections people would give false information in the polls. And already in the current elections all the decent parties would encourage people to boycott the plotting party.

> 
>>>>> I do believe that rough information on the
>>>> frontrunners is enough to
>>>>> tell you *who* to bury, if you were going to
>>>> 
>>>> Yes, there is no point in burying anyone else but
>> those
>>>> that are ahead of one's own favourite. The
>> information on
>>>> which candidates are about to beat one's favourite
>> should
>>>> however be correct with good probability.
>>> 
>>> I hope we are fortunate enough to have such a
>> concern.
>>> 
>>>>> , and also who might
>>>>> consider compromising to avoid a risk.
>>>> 
>>>> I'm afraid this information is already quite
>> difficult to
>>>> collect and may not be very accurate and
>> reliable.
>>> 
>>> This refers to the supporters of pawn candidates, so
>> to my mind it is
>>> almost just the inverse of who are the frontrunners.
>> 
>> 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.)

Juho



> 
>>> If the nature of burial is that nobody thinks to do it
>> without some kind
>>> of plan, then I am not nearly as worried about it. But
>> since I myself
>>> am not sure what I ought to do when I "can't" use
>> defensive truncation
>>> anymore, I am concerned.
>> 
>> I'm living in the hope that once Condorcet methods will be
>> used more than they have been so far, people will see that
>> the risks of giving one's sincere opinions are low.
> 
> That sounds like around half of what one needs to realize though.
> 
>> (Actually the key point of the false poll strategy is to
>> make the actual election strategy free. I'd be happier with
>> sincere elections and inaccurate polls than with accurate
>> polls and strategic ballots (reversed or truncated).)
> 
> Yes, that's a good goal.
> 
> Kevin Venzke
> 
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