[EM] Condorcet strategy

[James Green-Armytage]

Ernie Prabhakar wrote:
>But if they've guessed wrong by two votes, they could hand it to C,  
>right?
and:
>At least for me, its hard to take seriously strategy problems that only  
>occur in what is effectively a statistical tie, or require  
>foreknowledge of greater precision than possible with polling data.   
Also, Dave Ketchum wrote:
>PROVIDED they have perfect information:
>      To few and they get nothing.
>      Too many and C wins - the voting pattern suggests this would be a 
>catastrophe and whoever proposed it better hide in a hole.


	Yes, this is a good point, which a few people have brought up. Here's one
thing that has occurred to me...

1. If it only takes a small portion of changed votes to steal the
election, then the probability of the changed votes backfiring is higher.
2. If the probability of the changed votes backfiring is low, then it
takes more changed votes to steal the election.

	For example... 
Given the sincere votes
27: A>B>C
25: B>A>C
24: C>A>B
24: C>B>A
(27 first for A, 25 for B, 48 for C),
	Only 4 reversed votes (B>A>C to B>C>A) are necessary to change the winner
to B. However, if the B-->C defeat was weaker than the A-->B defeat, C
would take it... in this case they are only 1 vote apart. So yes, a 2 vote
mistake in the estimate of A:B, plus an extra C>A vote, and it would
backfire. Not a lot of comfort room.
	
Given the sincere votes
28: A>B>C
27: B>A>C
23: C>A>B
22: C>B>A
	It would take 7 reversed votes (B>A>C to B>C>A) to change the winner to
B. But they (the B voters) would have had to be off by at least 5 votes in
their estimate B:C contest for the strategy to backfire.

Continuing with this trend, we eventually get to an example like this:
46: A>B>C
44: B>A>C
5: C>A>B
5: C>B>A
	It would take 42 reversed votes (B>A>C to B>C>A) to change the winner to
B. But they would have to be off by at least 40 votes in their estimate of
the B:C contest for the strategy to backfire.
	
	So I will have to admit that while it isn't *necessary* for buriers to be
coordinated, it would greatly increase their chance of success. Because it
seems that the sort of situations where reversing has a high reward-risk
ratio are ones in which a lot of people need to reverse.
	So, what if there was a semi-coordinated effort to reverse on the part of
several the B voters? (Let's say, in the 28/27/45 example above.) When the
A voters learned about it, they would get mad and there would be buzz
among them about the possibility of truncation. But then, how would the B
voters be able to convince the A voters that they had changed their mind
and wouldn't reverse any more? What if there was a genuine B>A>C portion
of the electorate which showed up in the polls and some of the A voters
mistrusted it and thought it was strategic... and threatened to truncate
in reply? What if some supporters of C managed were able to start a rumor
that the A or B voters were planning to strategically truncate when in
fact they were not?
	If there is no communication in the last example here, no strategic
coordination, what are the incentives for a rational voter with a given
set of preferences? Let's take a B>A>C voter. Surely they will rank B>A
and B>C, but what about A and C? If there information was a fuzzy picture
of the sincere preferences (fuzzy: +/- 5 points or so), with no indication
that anyone would try anything strategic, then it would seem that neither
an A>C vote or a C>A would be likely to make a difference, since the A:C
comparison isn't close at all. But what has a higher probability, that an
A>C vote will change the winner from A to C, or that a C>A vote will
change the winner from A to B?
	When you're considering this question, you might want to ask what the
relative utility of the candidates are for each voter. For example, if the
sincere ratings for people are something like
46: A 90 > B 20 > C 10
44: B 90 > A 20 > C 10
5: C 70 > A 40 > B 30
5: C 70 >B 40 >A 30
	You might run into more burying problems than if the sincere ratings were
more like this
46: A 90 > B 80 > C 10
44: B 90 > A 80 > C 10
5: C 70 > A 40 > B 30
5: C 70 > B 40 > A 30
	However, even in the first scenario here, C very much does not deserve to
win.


Dave Ketchum wrote:
>IRV will award to one of the other candidates with first rank votes
>(lower 
>ranks can affect which of them).  Not seeing A unless a few voters change 
>ranking qualifies as UNSTABLE from here.

	Maybe it is too strong to say that the problem makes Condorcet worse than
IRV in public elections. After receiving everyone's feedback over the last
few days I do feel a bit better about the strategy situation in Condorcet.
	At the same time, I would still feel more comfortable with a two-round
procedure in a public election though. I think that these sort of
strategic problems can occur, and *might* become rather serious.
	And for any kind of small group vote, I strongly recommend the
multiple-round procedure rather than a vote that is binding after the
first or second round.
	Maybe the best thing to do is to try Condorcet for real elections as much
as possible. If a close examination of the results doesn't yield any
indication that the burial strategy is a big problem, then maybe it isn't.
I don't know myself, really, I just want to keep a process of critical
examination going.

Dave Ketchum wrote:
>
>If this argument managed to kill Condorcet, 
I wrote:
>This is definitely not my intention.
Dave wrote:
>
>And whoever took their eyes off the road to use a cell phone had no bad 
>intention to kill an accident victim - we need to think on expectable 
>results of our actions.

	What bothers me about the Center for Voting and Democracy, and its
satellite groups, is that they have already made up their minds about what
methods to advocate, and they have mostly given up on critical discussion
involving those methods. Any discussion that calls into question the
perfection of IRV is regarded as potentially dangerous and thus to be
avoided.
	Somehow your warning here seems to have a similar effect. Forgive me if I
have misunderstood, but you seem to be suggesting that I avoid honest
criticism of Condorcet because it might cast doubt on something that you
would like to be seen as unambiguous, whether it is in fact unambiguous or
not.
	I prefer to take a different approach. I think that any time you give up
critical discussion of a proposal, no matter how good your intentions are,
you run the risk of shutting out important information.
	I have a lot of respect for Condorcet's method, and I will probably go on
advocating it for the rest of my life. However, I think that a discussion
of its trouble areas is not only beneficial but also necessary if we want
it to gain wide acceptance. Whether we discuss such things in full at this
time or not, it will surely be discussed at any time when Condorcet is
being considered for a big public election. And the burial issue is the
main trouble area that I'm aware of for Condorcet methods. How serious is
it? I don't know, and I hope that it isn't very serious. What I do know is
that the question is important.

best,
James