[EM] Something that can happen in SODA

[Jameson Quinn]

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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