[EM] Juho,5/25/12, roughly 2230 UT

[Michael Ossipoff]

Juho:

You said:

I'll add one additional question right away in order not to delay the
discussion by one more round.

On 25.5.2012, at 0.17, Michael Ossipoff wrote:

Juho says:
 
I assume that the strategy applies at least to all typical winning votes
based Condorcet methods.
 
Am I on the correct track so far?
 
[endauote]
 
Yes, I’d say that, under the conditions I described, favorite-burial is
optimal in all Condorcet(wv) versions. But the sometime optimality of
favorite-burial is, by definition, a property of all FBC-failing methods.
I’m not trying to single-out Condorcet(wv). It’s just one of many
FBC-failing methods.

You said:

The definition of term "Condorcet(wv)" is not fully straight forward. 

[endquote]

Yes. It covers a broad set of methods that are loosely united as Condorcet
methods. I don't claim to give a precise definition of that term.

At least one of Condorcet's suggestions involved solving circular ties by
comparing defeat-strength. Every method called a Condorcet version must do
that, and must also elect the voted CW if there is one. I don't claim to
have a more precise definition of Condorcet versions. Anyway, Condorcet(wv)
versions compare the strength of pairwise defeats by votes-against. In other
words, if X pairbeats Y, then the strength of that defeat is measured by the
number of voters who voted X over Y.

You said:

I assume that the definition covers at least the case where we have a top
loop of three candidates, and one of those looped candidates has
the smallest worst loss of all candidates when measured as winning votes,
and that candidate shall win. 

[endquote]

Yes. I'd say that that, if there are only 3 candidates in the top cycle,
then every Condorcet(wv) version that I'm aware of would elect the top-cycle
candidate with the weakest defeat, as measured by wv.

But remember, I'm no longer advocating Condorcet, and so it is no longer my
responsibility to define it.   Well, yes, I've been saying things about
Condorcet's strategy problems, and so you can use the definition that I gave
above to determine what I mean by "Condorcet".

But remember that those who say that Condorcet is better than Approval
likewise have a responsibility to define Condorcet, if I do.

You said:

Is the strategy valid in this special case only or maybe in all situations
in all methods that meet the definition of Condorcet(wv) that I gave above?

[endquote]

That question is answered in my text that you quoted earlier in this e-mail
that I'm replying to:

I'd say that surely or almost surely, the Condorcet favorite-burial strategy
that I described is also optimal with any method that fails FBC, provided
that your information about how others will vote isn't better than it is in
our actual elections, and provided that it's all-important to you that you
maximally help the Democrat against the Republican, and provided that you
believe that the Democrat is the only candidate who can beat the Republican.

For more generality, you can replace "rank Democrat alone in 1st place" with
"Vote Democrat alone at top", or "Vote Democrat over everyone else".

Mike Ossipoff