[EM] Winning-votes intuitive?

[Adam Tarr]

Sorry for the huge quote block at the top of this message, but I tried to 
snip out that which was no longer relevant...

> >>> A beats B, 70% winning votes (25% losing)
> >>> B beats C, 52% winning votes (45% losing)
> >>> C beats A, 50% winning votes (40% losing)
> >>>
> >>> By virtue of a slight perturbation (the sort that would fall within
> >>> polling error margins in the real-world, nonzero-information case)
> >>> candidate A now wins the election.  In this case, if I (any many
> >>> others like me) randomly vote B over C, we change nothing, while if
> >>> I (any many others like me) randomly vote C over B, we may turn B's
> >>> victory over C into a defeat, and we turn C into a Condorcet
> >>> winner.  This causes the defeat of A, our favorite.
> >
> > Even if folks decide
> > independently to randomly complete, some voters may have some
> > inclination to cast the vote for the candidate they prefer
> > ever-so-slightly between those bottom two.  So co-ordination from the
> > top (random voting schemes based on the last digit of your phone
> > number, for example) would probably be called for to guarantee a
> > faction doesn't lean their "random" ballot completion one way, and
> > hurt its chances.
>
>That's an interesting question.  Does a lack of randomness hurt its chances?
>
>[snip]...your only way of influencing this outcome is by ranking or not
>ranking these two candidates on your ballot.  My contention is that you
>should rank them, and there is no need to do so randomly.  If you have
>reason to use an order-reversal strategy, then go to it, but otherwise,
>you can rank them arbitrarily, so long as you rank them.
>
>The point is this.  Except for the tie case, which is rare enough that
>we can discount it, your vote can only increase the size of the victory
>between the two candidates.  The danger is that it may flip the victory
>to go the wrong direction.  But since you don't know which direction
>that is, it is just as likely to flip it in the right direction. [snip]

OK, this is reasonable, in the zero or near-zero information case.  So what 
this means is that the optimal strategy, in winning votes methods, in the 
zero or near zero information case, in the case of natural cyclical ties, 
involves falsely ranking as unequal, candidates you consider to be equal.

I think that's an accurate statement of your conclusion, and I think it's a 
true statement.  But consider the impacts of this statement.

- First of all, this only applies if the direction of three-way ties is not 
known in advance.  If it is, then margins methods and winning votes methods 
have the same order-reversal (or order-fabrication) incentives.  Certain 
"too close to call" elections will fit this criterion, but not many.  Most 
of the time, you will have some sense of the frontrunners, or the direction 
of cyclic preferences.

- Secondly, this only applies if you have absolutely no preference between 
two candidates.  This is rather unlikely; if you have the slightest 
inclination and you don't know who will finish ahead, you may as well vote 
that inclination (as you just demonstrated in your previous post) rather 
than randomly voting.

What this means is that, in the zero-information case, you should vote even 
the most infinitesimal preference.  Vote on who wears better suits; who has 
a more soothing accent, whatever.  I don't think it's a horrible thing that 
winning votes methods ask you to express your preferences, no matter how 
small they are.  It's far more important to me that I not be forced to 
switch a sincere preference or falsely rank my favorite equal to another 
candidate in order to  get the desired result.

- Third, the effects of this insincerity tend to be symmetric.  You vote 
randomly on the bottom in your faction; I vote randomly on the bottom in 
mine.  Even if one faction has a sincere preference in second choice but 
another does not, the faction that does not is at no real advantage by 
virtue of their random voting (again, as you demonstrated in your previous 
post).  So in the end, this is no harm, no foul.  The proper response to 
your opponent's camp randomly completing their ballot is to do the same, 
unless you have some preference on the end of your ballot.  This stops 
being true if you know something about the polls (which is most of the 
time), but then this entire argument goes out the window.

- Finally, random completion only has an impact if there is a cyclic 
ambiguity.  If there is a sincere Condorcet Winner, the whole approach 
accomplishes nothing in margins methods.

Bottom line: what I want from a Condorcet method is the following things:

- a method that consistently elects the Condorcet winner if one exists.
- a method that produces a reproducible, seemingly fair, and reasonable 
(monotone, clone-independent, et cetera) result when there is no Condorcet 
winner.
- a method that provides as little incentive as possible to vote any way 
but a sincere ranking of candidates.

The major substantive criticism of winning votes methods seems to be that 
it  can fail the third criterion in a rather minor way in a certain 
relatively uncommon situation.  The criticism of margins methods is that it 
will either fail to elect the Condorcet winner, and/or cause dramatic 
insincere voting, in fairly common situations.

See my post, "[EM] Approval-Competed Condorcet... "more" strategy-free?" 
from 4/13 for an analysis of such insincere voting., along with some 
comments on how this election plays out with winning votes or 
Approval-Completed Condorcet.  My post, "Re: ACC, more strategy-free?" from 
4/14 goes into more depth on the strategic incentives in winning votes.

Also note that in margins methods, truncation can force all sorts of 
problems just like order reversal can.  I know this is unimportant in your 
eyes, but to me this means that these strategic issues are all the more 
likely to arise.  And in this case, the strategic response is not at all 
symmetric.

I mean, if we're so confident that the voters can jump through these 
strategic hoops and figure out the right order-reversals and so on, then 
why are we even bothering with voting reform?  This super-smart electorate 
can home in on the Condorcet winner by watching the polls carefully and 
adjusting their announced strategy to match the situation, a-la Cranor's 
DSV.  The fact that this argument is clearly bogus underlines, in my mind, 
that we need to make sincere rankings as close to the optimal strategic 
choice as we can.  And barring that, the difference between optimal 
strategy and sincere rankings should be very simple and very intuitive.

>[with reference to Approval Completed Condorcet on ABCDEF ballots]
>
>As for me, I like the ranked ballot because it allows a limitless number
>of candidates to be sorted.  It seems to me that with 6 candidates,
>there would be a tendency to use all grades, and therefore approve of
>exactly 3, which isn't necessarily what you want.

I doubt this is the case.  The reason we choose A,B,C,D,E,F is that it 
looks a lot like the report cards that most Americans are familiar 
with.  I'd expect the average voter to look at this and say, "I will give 
the guy I like an 'A' " and so forth.  In other words, I hope and expect 
that it would be treated like a cardinal ranking, which would produce good 
results most of the time.

In fact, I'd expect the media would release a candidate's "grade-point 
average" after the election, which gives some sense of the candidate's 
mandate.  ("Mr. X narrowly defeated Mr. Y, but his C average may make it 
difficult for him to push his reform package through congress...")  Of 
course this could lead to a bit of a stink if the winner had a lower GPA 
than the second-place candidate, but it would really be much ado about nothing.

Nevertheless, I would have no problem with a ranked ballot, NOTA-based 
implementation of Approval-Completed Condorcet.  I just think it would be a 
harder sell as a public election method.

-Adam

----
For more information about this list (subscribe, unsubscribe, FAQ, etc), 
please see http://www.eskimo.com/~robla/em