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. <div><br></div><div>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.<div>
<br></div><div>If Bad prefers F to G, then the chances that G can win are reduced.</div><div><br></div><div>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.</div>
<div><br></div><div>Jameson<br><br><div class="gmail_quote">2012/2/16 Jameson Quinn <span dir="ltr"><<a href="mailto:jameson.quinn@gmail.com">jameson.quinn@gmail.com</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br><br><div class="gmail_quote"><div><div class="h5">2012/2/16 MIKE OSSIPOFF <span dir="ltr"><<a href="mailto:nkklrp@hotmail.com" target="_blank">nkklrp@hotmail.com</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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Say the method is SODA.<br><br>Say your favorite, F, is going to win the initial, ballots-only, Approval count, under sincere voting. <br><br>The runner-up, G, has some (from your viewpoint) not-as-good-as-G candidates at the top of hir ranking for delegated approvals.<br>
<br>(There's nothing unusual or unlikely about that. A big-votegetting compromise can have some preferences that<br>many don't like as much)<br><br>Because F wins, G doesn't win. Therefore, s/he gives hir delegated approvals to some of hir higher-ranked candidates.<br>
<br>One of them wins as a result.<br><br>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.<br><br>If you'd buried your favorite, you would have gotten a better outcome, not gettable by you in any other way.</div>
</div></blockquote><div><br></div></div></div><div>No. FBC holds.</div><div><br></div><div>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.</div>
<div><br></div><div>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.</div>
<div><br></div><div>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. </div>
<span class="HOEnZb"><font color="#888888">
<div><br></div><div>Jameson</div></font></span></div>
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