[EM] My Favorite Deterministic Condorcet Efficient Method: TACC

[fsimmons at pcc.edu]

> I'm not fond of the minimal defense failure... It seems to me the
> "train wreck" disincentive to defect is more likely to lead to
> favoritebetrayal (and nomination disincentive) than cooperation.
>
> That is:
>
> 49 Bush
> 24 Gore
> 27 Nader>Gore
>
> If this is a Bush win, and people think the votes might actually
> look like
> this, it takes much less convincing to make the Nader voters
> create a
> Gore win via compromising, than to make Gore voters add tons of
> Nader
> second preferences. It's not even clear here that Gore voters are
> interested in Nader, in which case a Bush win is purely a
> favorite
> betrayal incentive.
>
> One might argue that Nader voters won't compromise when Nader seems
> stronger. But if Gore voters are reluctant to vote for Nader (no
> matterwhat the reason is), Nader isn't stronger in any
> meaningful way. He can't
> win the election.

Forest Replies:

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.  

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).  

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.

But the following probabilities are consistent with all three:

Prob(Bush)=38.5%
Prob(Gore)=35.5%
Prob(Nader)=26%

These probabilities came from the stochastic analog of TACC that I call RBOCC
for Random Ballot Order Chain Climbing.

Forest