[EM] Defensive strategy for Condorcet methods

[Kevin Venzke]

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?
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.

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

3. Bullet-vote for A. Nope, not if this is margins. That's just splitting
the difference or flipping 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.

> > 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.

I am skeptical about the concept of intentionally misleading polls,
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. 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.

 >>> , 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.

> 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 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.

> > 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.

> 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.

Kevin Venzke