[EM] Defensive strategy for Condorcet methods

[Juho Laatu]

On 10.6.2011, at 3.04, Kevin Venzke wrote:

> Hi Juho,
> 
> --- 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.

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. 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). Maybe you want to vote sincerely in order to encourage also others to do so and avoid elections becoming a playground of strategists. 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.

> 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.

> 
> 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.

> 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.

> But outside of that possibility,
> maybe I just don't have any good options?

How about sincerity as the default rule?

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.

> 
> 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".

> 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?

> 
>>> 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 am skeptical about the concept of intentionally misleading polls,

Yes, they are difficult to plan and coordinate. I might however advice voters that resort to giving false information in the polls not to give random answers but some strange and unpredictable ones instead (to avoid false answers becoming balanced white noise that cancel each others out).

> 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.

> If
> this is really a problem, then, ok, my simulations aren't covering this.
> 
>>> If what you're asking is whether this could be
>> thwarted by not revealing
>>> any polls to the voters, then I can't address that. My
>> voters have to
>>> have polls in order to learn how the method works.
>> 
>> In some methods like Approval poll information is needed to
>> cast a vote in line with the typical recommendations on how
>> to vote (= approve one of the frontrunners etc.). One could
>> also have Approval elections without such information. In
>> that case voters would not vote strategically but would
>> maybe mark those candidates that they approve for the job.
>> 
>> In Condorcet the basic assumption is however that voters
>> can sincerely rank the candidates. Doing so tends to improve
>> the outcome of the election. The strategy of making polls
>> unreliable may thus improve the outcome of the election.
> 
> Yes, if you can make polling unreliable, it would be very irritating
> when the election method is Approval or FPP, and it might help Condorcet.

Yes, Approval and FPP need good polls. In Approval they may be also a problem, if they e.g. lead two candidates into a game of chicken. This may happen also in FPP, although not very often since typically there are only two major candidates, or if there are three, people could bullet vote their favourite anyway and never think about the possibility of helping their second favourite. Condorcet is a pretty pretty system in this sense.

> 
>>>> , the defensive strategy used in response
>> seems to be
>>>>> compromise strategy, as opposed to truncation
>> or
>>>> burial-in-turn, things
>>>>> that risk ruining the result.
>>>>> 
>>>>> That is, there are voters who know they can't
>> expect
>>>> to gain anything
>>>>> by voting sincerely, so they play it safe.
>>>> 
>>>> I agree that there are situations where some
>> voters will
>>>> not lose anything by using whatever strategy with
>> even some
>>>> infinitesimal hope of improving the outcome (e.g.
>> when they
>>>> know that otherwise the worst alternative will
>> win). But how
>>>> can they know (based on the limited available
>> information)
>>>> that sincere voting will not help them? Do they
>> know for
>>>> certain that some strategy is more likely to help
>> (and not
>>>> harm) them?
>>> 
>>> I'm talking about voting for a sincere favorite who is
>> not believed to
>>> be a contender. If that candidate can't win, and could
>> be a liability,
>>> then you could logically decide to dump him.
>> 
>> Ok, with favourite candidates that have no chance of
>> winning one can usually do pretty much whatever one wants.
>> That typically does not make the results of this election
>> better nor worse. 
> 
> It should also be a *design goal* that this does not make the results of
> the election better or worse.
> 
>> Often it makes however sense to make the
>> result as favourable to this favourite candidate as possible
>> since there are also secondary targets like helping this
>> candidate win in the next elections or just showing how much
>> support this line of thinking has among the electorate.
> 
> Yes, it's possible. I don't see a way to incorporate that experimentally.
> 
>>>>> So I expect that methods with greater burial
>> incentive
>>>> will just have
>>>>> more (voted) majority favorites
>>>> 
>>>> I didn't quite get this expression. Would this be
>> bullet
>>>> voting by majority or what?
>>>> 
>>>>> , and candidate withdrawals
>>>> 
>>>> Does this mean having only few candidates or
>> ability to
>>>> withdraw after the election and thereby influence
>> the
>>>> counting process or...?
>>> 
>>> What I'm saying is that methods with greater burial
>> incentive will
>>> probably see supporters of pawn candidates stop voting
>> for those
>>> candidates, and those pawn candidates would probably
>> drop out of the race
>>> more often. (I think that compromise incentive and
>> nomination 
>>> disincentive go hand-in-hand.)
>> 
>> Ok, if there were such threats.
> 
> Hopefully from my first comments of this mail it's clearer what kind of
> threat I have in mind.
> 
>>> This is as opposed to the theory that methods with
>> great burial incentive
>>> will see a larger number of train wreck outcomes as
>> voters play chicken
>>> with each other.
>>> 
>>>> I didn't quite catch what the impact of this to
>> the
>>>> usefulness of the reduced poll information based
>> defensive
>>>> strategy would be. Could you clarify. Did you say
>> that
>>>> already very rough information on which candidates
>> are the
>>>> frontrunners would give sufficient information to
>> the
>>>> strategists to cast a working (=likely to bring
>> more
>>>> benefits than harm) strategic vote (in Condorcet
>> methods in
>>>> general or in some of them)?
>>> 
>>> The relevance is more to the question of defensive
>> strategy under
>>> Condorcet methods, than to your proposal.
>> 
>> Note that I proposed a preemptive defensive strategy to be
>> applied instead of concrete ones. I don't really like the
>> idea that people would start falsifying their preferences in
>> the actual election in order to defend against actual or
>> imagined strategic threats. 
> 
> Haha. Every method has this problem to some extent, nothing to do with
> burial even.

Yes, but Condorcet is maybe closest to helping us out from that miserable state. The false polls trick could be used to force also the last voters with tendency to apply strategies to forget even the remaining small weaknesses of Condorcet with respect to strategic voting.

> 
>> 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.

> 
>>> 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.

> 
>>> I am mostly concerned about burial in methods that
>> seem to encourage it
>>> without voters even having a specific plan.
>> 
>> I wonder where the accurate line goes on which Condorcet
>> methods are vulnerable to burial and which ones are not :-).
> 
> I do not know, but I have an interest in the question.

My guess is that the widest borderline actually goes roughly between Condorcet methods and other methods.

> 
>> I'm afraid that in Condorcet methods there might be many
>> voters that rank their worst competitor last in the (not
>> very well founded) hope of improving the results from their
>> point of view :-).
>> 
>> More seriously, maybe some concrete written rules to voters
>> on how to bury in Condorcet elections (on in some Condorcet
>> version) would demonstrate that poll information can indeed
>> be efficiently used by regular voters in some real
>> elections. I tend to think that in many environments burial
>> would not be a problem, and in line with this mail thread,
>> maybe one could simply weaken the available poll information
>> and education of the voters if strategies start appearing.
> 
> 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.

(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).)

Juho


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