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 <[email protected]> > > > 2012/2/16 MIKE OSSIPOFF <[email protected]> > >> 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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