[EM] Defensive strategy for Condorcet methods

[Kevin Venzke]

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.

> 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?

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.

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.

> > 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. 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? 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?

> > 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.

BTW the idea of advising voters to just vote sincerely, as a substitute
for explaining the method to them in detail, makes me choke.

> 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?

> > 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.
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.

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.

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.

> > 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.

> >> 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?

> >>> 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?

> > 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