[EM] Responses to some of Forest's ideas

[Rob LeGrand]

Forest wrote:
> Here's an example of this (zero info):
>
> 45 A >> B > C
> 45 C >> B > A
> 2  C > A >> B
> 4  B > A >> C
> 4  B > C >> A
>
> B is the low utility CW that gets eliminated, having only 8 percent
> approval. Demorep's method gives C the win because it is the CW among the
> candidates satisfying the minimum approval standard.
>
> Does it bother you that after the results are announced, the first faction
> (A's supporters) might regret not having (insincerely) approved B ?

Absolutely.  That effect is avoidable.  Picking B won't cause anyone to regret
his vote.

Demorep wrote:
> Forest well knows that with 3 or more choices, ALL sorts of sincere/insincere
> games can and will be played.    The election results are based on the votes
> cast.  There is always the next election for more game playing.

But isn't it important to minimize the opportunity for strategy?  In
particular, when a sincere Condorcet candidate exists, the only way to make
sure no one can benefit from using strategy is to make sure a voted Condorcet
winner wins, no matter how low his utility.  Otherwise insincere voters can
force the sincere Condorcet candidate's victory, even if only a small number of
sincere voters would have "approved" of him.

Obviously there's something of a tradeoff between picking the "best winner" and
discouraging strategy.  At one end of the spectrum are Cardinal Ratings and
Borda; at the other are Random Dictator and Random Pairwise.  I'm interested in
finding an entirely deterministic method that discourages strategy as much as
possible.  That's the only reason I consider the Smith (and Condorcet)
criterion important.

I can understand if some would prefer to sacrifice strategy-proofness to try to
pick a better candidate.  I'd just rather assume the voters are devious and use
as stable a method as possible.  (The only reason I support Approval as the
best practical method is its simplicity; unfortunately, voters must depend on
accurate approval polls to cast an effective vote.  The best ranked-ballot
Condorcet methods make strategic voting difficult enough that casting a sincere
ballot is almost always the best strategy, but I think it might be hard to
convince most voters, at least initially, that insincerely ranking their less
favorite frontrunner last won't help them.)

By the way, after some more simulations, I can confidently say that Black is
the best Condorcet method for SU given sincere ballots, for whatever that's
worth.

Thanks for your responses, guys.  Tell me what you think.

--
Rob LeGrand
honky98 at aggies.org
http://www.aggies.org/honky98/

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