[EM] Ultimate SPE Agenda Processing: Sink Swap Bubble

[Forest Simmons]

I've been thinking that the ballot set

49 C
26 A>B
25 B

could have come from truncation of sincere 25 B>A ...

Or ... it could have come from truncation of sincere 49 C>B ...

Or even burial of C under B from sincere 26 A>C.

So the sincere CW could have been A,B,or C.

So how do we know which two candidates to involve in the sincere runoff
match?

It seems that with all of this strategizing there must be enough
information floating around to know that some particular candidate X was
very likely not the sincere CW.

If X was C, then the runoff should be between A and B. In general, the
fresh ballot runoff should be between the two non-X candidates.

But how to officially decide the identity of X is not clear to me.

Suppose the basic method is agenda processing by Sink Swap Bubble.

Why not apply DMC Benham to the final list with the defeat matrix derived
from a fresh set of ballots?

It may not be a totally sincere solution, but it seems to me that it would
be adequate ... better than anything else we've got going now:

Suppose for the ballot set
49 C
26 A>B
25 B
The agenda is based on minPairwise Support from minmin to Maxmin...
unfavorable to favorable ... so
B<A<C is the starting agenda.

After one round of Sink Swap Bubble we have  C<B<A.  DMC Benham elects the
least favorable candidate on the list that defeats every more favorable
one.

So elect C if it defeats both A and B, else elect the pairwise winner
between A and B.

If C wins it is the fresh ballot CW ... so quite likely the sincere CW.

If A wins, then quite likely the sincere preference that was truncated to
give us our ballot set was the 25 B>A faction's.

If B got elected, the most likely explanation is that sincere 49 C>B got
truncated to 49 C.

Does this seem reasonable?

If Robert Bristow-Johnson's assessment is valid, it would be rare to lack a
ballot CW ... so this fresh set of ballots requirement would be a rare cost.

I think it would be worth it in a high stakes election ... as well as
highly informative ... and perhaps entertaining.

Am I way off base?

My main point is that we cannot expect the method by itself to discern from
the first ballot set alone who should win.

The three subversion of sincere CW scenarios were by simple unilateral
action.

Anybody have a better idea for a reasonably sincere completion?

Forest


On Tue, Apr 11, 2023, 1:52 PM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> On 11.04.2023 19:55, Forest Simmons wrote:
> > Suppose someone provides a list of candidates already sorted pairwise.
> >
> > Now do Benham elimination ... start at the loser end of the list and
> > eliminate candidates one by one until there is (according to a fresh set
> > of ballots) a CW among the uneliminated.
> >
> > How much incentive if any to rank insincerely?
>
> Since Condorcet is incompatible with LNH, there will be some incentive
> to either truncate or random-fill (depending on the situation). I would
> also imagine that if the strategists know the list ahead of time, and
> they know that it's A>B>C>D, then if C is the CW, A is their favorite,
> and A beats B pairwise, they'll have an incentive to engineer a false
> cycle by burying C under B.
>
> If they don't know the list, it's much harder to do. It reminds me of
> the Conitzer and Sandholm preround, which makes strategy harder to
> devise in practice, and just how hard depends on what information the
> strategists have (see
> https://www.cs.cmu.edu/~sandholm/voting_tweaks.ijcai03.pdf). (In
> practice, this doesn't matter, because most elections have relatively
> few candidates; it's just the "it depends on information" aspect that's
> similar.)
>
> -km
>
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