[EM] Defensive strategy for Condorcet methods

[Juho Laatu]

On 9.6.2011, at 5.28, Kevin Venzke wrote:

> Hi Juho,
> 
> --- En date de : Mer 8.6.11, Juho Laatu <juho4880 at yahoo.co.uk> a écrit :
>>> --- En date de : Mer 8.6.11, Juho Laatu <juho4880 at yahoo.co.uk>
>> a écrit :
>>>> There has been quite a lot of
>>>> discussion around the strategic vulnerabilities of
>> Condorcet
>>>> methods on this list recently. In general I think
>> Condorcet
>>>> methods are one of the least vulnerable to
>> strategies, and
>>>> in most typical elections their vanilla versions
>> are simply
>>>> good enough. In the case that people would start
>> voting
>>>> strategically there is one interesting defensive
>> strategy
>>>> that has not been discussed very much. The
>> defensive
>>>> strategy is to not tell your sincere opinions in
>> the polls.
>>>> Most Condorcet strategies are based on quite
>> accurate
>>>> understanding on how others are going to vote. If
>> I expect
>>>> someone to play foul play, I might just refuse to
>> give the
>>>> required information to them, and recommend others
>> to do the
>>>> same. (Also giving planned false information to
>> mislead the
>>>> strategists is possible, but more difficult.)
>>>> 
>>>> This approach does not work about irrational
>> voters that
>>>> will bury anyway, just in case that might help.
>> But the
>>>> point is that in Condorcet elections the best
>> strategy, in
>>>> the absence of good information on the
>> preferences, is to
>>>> vote sincerely. In real life this strategy could
>> be
>>>> mentioned as a possibility in the case that
>> strategic voting
>>>> becomes threatening. The outcome hopefully is such
>> that all
>>>> parties, experts and media would recommend voters
>> to vote
>>>> sincerely and not try strategies. That would be
>> better to
>>>> all than having to live without the interesting
>> polls. What
>>>> do you think? Is this a way to drive away possible
>> evil
>>>> spirits and strategy promoting parties, experts
>> and media?
>>> 
>>> I don't see this working because you will never be
>> able to disguise who
>>> the frontrunners are.
>> 
>> I agree that there is always some information on the
>> popularity of different candidates (also without any polls).
>> But does this mean that it would be a working strategy
>> (=likely to bring more benefits than harm) e.g. to always
>> bury one of the assumed frontrunners under one of the
>> assumer non-frontrunners? Is there some well known strategy
>> that would work in this situation?
> 
> 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??)

> 
>>> 
>>> In my recent simulations, when some voters saw the
>> advantage of using
>>> burial strategy
>> 
>> Was this decision ("saw the advantage") based on highly
>> inaccurate information like being able to guess who the
>> frontrunners might be?
> 
> 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).

> 
> 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.

> 
>>> , 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. 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.

> 
>>> 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.

> 
> 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. 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".

> 
> 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.

> , 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.

> 
> 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'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.

Juho



> 
> Kevin Venzke
> 
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