[EM] Defensive strategy for Condorcet methods

[Kevin Venzke]

Hi Juho,

--- En date de : Sam 11.6.11, Juho Laatu <juho4880 at yahoo.co.uk> a écrit :
> >> 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.

Ah I see. It is funny that I can't figure out whether, if I were you, I
would want to call this strategy irrational or rational.

You could say, if you wanted, that it's totally rational, because by and
large no one else will do that (you would need to claim), so C won't win
and it *does* make sense to bury. That would be a coherent pro-margins
stance I think.

> >>> 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. 

Yeah, that is all very scary.

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

I just can't see how that follows. Of course, if you assume that the
voters are just going to do what you say, then yes it's better overall.
You're looking at it from a different vantage point. But I don't see 
how you can actually show that it is good advice, at the voter level,
without insisting there is a real possibility of disasters.

> 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. 

??? Unless you mean compromise, i.e. "let's not vote for our own
candidate," I don't see how you can identify "defensive" vs. "offensive."
Are you saying their party is telling them it's time to lie because
they believe the opposing voters are going to lie? They are saying "don't
swerve" for the chicken game?

> 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.

Well, then I would stop.

Interesting question though, whether we could show mathematically (or
experimentally) that I as voter definitely would prefer to keep the 
method from becoming broken, assuming I actually have some influence on
that.

> > 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.

Yeah but under other methods I wouldn't say C is a good candidate. If
some other EM poster wants to claim they're going to vote for C... under
Bucklin... they can do that, but I want a good explanation.

> >>> 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.

I wonder how you figure it is that high. In my recently-mentioned sims
I only had around 90% of Condorcet voters using no strategy at all.
(95% for AWP, implicit or explicit.) Of course, this isn't a perfect 
model of society, but it makes me think the utility of insincerity is 
not immeasurably low.

> > 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.

Well, until people get word of it.

> >>> 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.

In a general context it is really unclear to me what this means. It's
like an IRV-oriented criterion that assumes you're doing eliminations.
It may be completely possible to satisfy you on this point, and also 
have a method that I don't find irritating. From what you've literally
written here I don't even see how it excludes WV.

> > 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).

Well, I think if the method is what is prompting people to organize
strategies, you already lost. If the method makes strategy X a good idea
then everybody's going to do that where appropriate. I don't see how the
society is going to judge strategy X as bad if it stems directly from
the method. If it's bad, it's all bad, and I expect to see reform
proposals.

The alternative is just... attacking symptoms of the real problem.

Another example that occurred to me is SNTV, where parties can gain more
seats if they e.g. tell their supporters to vote according to the digits
in their ID numbers. I wonder how many voters had a guilty conscience.

It's kind of funny that although people do sometimes prefer methods that
pick candidates with a lot of first preferences, I don't remember ever
hearing anybody complain that favorite betrayal or primaries (i.e.
candidates stepping aside before election day) have ruined the original
idea behind FPP, to elect the sincere FPP winner.

> >> 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.)

Actually it isn't unheard of in discussions of random methods for one
to object that the method is encouraging burial in some cases.

Is Condorcet//FPP a bad method?

How about a method where, if there is a cycle, we take the top three
FPP candidates (call them ABC in descending order). C wins if and only
if he gets 75%+ top-two rankings (i.e. A>C B>C C>?). Otherwise we will
elect whichever of A and B has the most ballots in the form A>C or B>C
respectively. Fun I think?

Kevin Venzke