[EM] Something that can happen in SODA

[Jameson Quinn]

My main backstop argument for why FBC holds (that you can approve F and G)
is still just as valid. But I missed even more reasons that you might not
have to.

If Bad prefers G to F, then G probably does not have to approve Bad,
because if Bad can win with G's delegated votes, then probably G can win
with Bad's delegated votes.

If Bad prefers F to G, then the chances that G can win are reduced.

So all in all, the chances that you can only avoid Bad by approving both F
and G are very, very slim. F must have declared indifference between G and
Bad, and then hold to that indifference when push comes to shove; G must
prefer Bad; and Bad almost certainly must be indifferent between F and G.
If every stance (x, y, or indifference) of each candidate on any other
pairwise choice is 1/3 probable, then this combination is a 1/27 chance;
and in fact, it's probably less than that, because there is more than a 1/3
chance that your favorite F will agree with you that G is better than Bad.

Jameson

2012/2/16 Jameson Quinn <jameson.quinn at gmail.com>

>
>
> 2012/2/16 MIKE OSSIPOFF <nkklrp at hotmail.com>
>
>>  Say the method is SODA.
>>
>> Say your favorite, F, is going to win the initial, ballots-only, Approval
>> count, under sincere voting.
>>
>> The runner-up, G, has some (from your viewpoint) not-as-good-as-G
>> candidates at the top of hir ranking for delegated approvals.
>>
>> (There's nothing unusual or unlikely about that. A big-votegetting
>> compromise can have some preferences that
>> many don't like as much)
>>
>> Because F wins, G doesn't win. Therefore, s/he gives hir delegated
>> approvals to some of hir higher-ranked candidates.
>>
>> One of them wins as a result.
>>
>> But if you had voted for G, but but not for F, then G would have won,
>> instead of the worse candidates in hir ranking.
>>
>> If you'd buried your favorite, you would have gotten a better outcome,
>> not gettable by you in any other way.
>>
>
> No. FBC holds.
>
> First off, if F prefers G to Bad, then you can just delegate to F.
> Although F will be in the lead when it's time to assign their delegated
> votes, they will be able to see that if G approves Bad, then Bad will win;
> so F will approve G. So most of the time (since you'll more often than not
> agree with your favorite on any given pairwise choice such as that between
> G and Bad) you can simply delegate to F.
>
> And in fact, the chances for this dilemma to come up are even slimmer. If
> F prefers Bad to G, then Bad is almost certainly the Condorcet winner, and
> will win with either F's or G's delegated votes, so you have no reason to
> vote for G. And even if F has declared indifference between G and Bad, they
> will have the option to approve G and not Bad (as you prefer) because you
> can approve the current winner among your equally-preferred preferences.
> Why would they do this, if they're predeclared as indifferent? Perhaps G
> promises to carry out some portion of F's program; or perhaps F simply
> prefers that Bad, with few first-choice votes, doesn't win.
>
> But of course, although one of the above cases will be true most of the
> time, it's not the guarantee that FBC requires. So you have the option of
> approving F and G in this case, instead of delegating. If your vote was the
> reason F beat G, then approving both keeps G ahead; if it was not, then
> your vote changes nothing.
>
> Jameson
>
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