[EM] My Favorite Deterministic Condorcet Efficient Method: TACC

[Kevin Venzke]

Hi Forest,

--- En date de : Mar 9.11.10, fsimmons at pcc.edu <fsimmons at pcc.edu> a écrit :
> As we know, in the above scenario the result that is best
> assuming sincere votes
> is not the same as the result that is best assuming that
> the Gore faction
> truncated in order to create the cycle.
> 
> Assuming sincere votes giving Bush the win encourges
> favorite betrayal. 
> Assuming insincere truncation of Nader in the second
> faction and giving Gore the
> win rewards that truncation.  Nader cannot be given
> the win because of the
> Plurality criterion.
> 
> So there is no completely satisfactory deterministic
> solution.  

I agree technically, but on these ballots I don't think it's likely that
any special incentive is operating on the Gore voters, or that one can
be found that would make them completely stop their truncation.

In my opinion this unpleasant situation will tend to be solved prior to
election day. As I've said before, there is too little to gain and 
everything to lose in one "side" running two strong candidates. So, 
nomination disincentive is actually unavoidable, I think.

I don't usually regard truncation as insincere in the same way that
burial or compromise is insincere, but it seems particularly unusual to
call it insincere in the context of an approval-based method.

> However, on the whole, if we want determinism and Condorcet
> efficiency,  it
> seems more important to prevent insincere cycle producing
> truncation than
> worrying about lack of FBC compliance, since (1) the FBC
> and Condorcet
> efficiency are incompatible, any way, and (2) sincere
> Condorcet cycles are rare
> (in my opinion).

Well for (1), also burial resistance and LNHarm are incompatible with
Condorcet. I'm also not talking about strict FBC compliance, but just
minimal defense, which is basically a weak form of FBC for majorities.

For (2) I am not sure what all you include in "sincere." For strictly
ranked sincere ballots, I agree that cycles should be rare. If truncation
(as under an approval-based method) isn't considered insincere then I
think sincere cycles need not be uncommon. If they are, I would guess it's
because in practice not enough viable candidates are nominated to see the
problem.

> Now consider the following propositions (relative to the
> above scenario):
> 
> (1) Woodall's Plurality Criterion says that Nader should
> have less probability
> than Bush.  
> 
> (2) It seems that Gore and Nader together should have more
> probability than Bush.
> 
> (3) Gore should not have more probability than Bush,
> because that would
> encourage truncation in another case where the sincere
> ballots of the middle
> faction turn out to be Gore>Nader .
> 
> No deterministic method can satisfy these three
> conditions.

The way I phrase this problem with this scenario is that no method can
simultaneously satisfy Plurality, Minimal Defense, and LNHarm. Which one
to lose (with 3 candidates) depends on what you're going for...

Personally, the methods I'm interested in all either satisfy MD or LNHarm.
I don't really care about Condorcet except as it can service MD or other
criteria that protect literal majorities.

Kevin