[EM] The Strong Favorite Betrayal Criterion at Last!

[Forest Simmons]

This is the first day of April, but I'm really serious about the subject
line.

If I am not mistaken, it is indeed possible to satisfy the strong FBC with
the right kind of ballot, though it seems impossible with any ballot type
that has been proposed previously.

The ballot has two parts.  The first part is an ordinary ranked preference
ballot or a Cardinal Ratings ballot with enough resolution to distinguish
all of the candidates.

The second part must provide a way for each voter to mark (or leave
unmarked) as many pairs of candidates as desired.

The candidate pair receiving the most marks is the finalist pair.

The winner is the head-to-head winner of the finalist pair, i.e. the
member of the pair which is ranked or rated above the other on (the first
part of) the greatest number of ballots.

In summary, this method uses approval of pairs to pick the finalist pair,
and then uses the pairwise matrix compiled from the rankings or ratings to
determine which member of that pair is the method winner.

Since the first part of the ballot (the ranking or rating part) has no
influence on which pair of candidates is the finalist pair, there is
nothing to gain from insincere ranking or rating on that part of the
ballot.

All of the strategy is limited to the second part of the ballot.

In this strategy usually it would be to your advantage to approve the pair
consisting of the two candidates that you rated tops on part one of your
ballot.

The only exception would be a case in which this pair shared top
popularity with another pair in which your favorite had a better chance of
being the preferred member of the pair.

In any case you would be wise to approve at least one pair that included
your favorite.

So in part one of the ballot your favorite has strict priority, and in
part two of the ballot your favorite is not betrayed.

Like ordinary Approval, this method fails the Majority Criterion (as does
any method satisfying the FBC) but does satisfy it strategically in the
perfect information case.

Since all of the strategy is in the second part of the ballot, voters who
don't want to worry about strategy can leave that part blank.

It could be a feature of the method to automatically approve the pair
consisting of the top two rated candidates from part one, unless this
default configuration were intentionally crossed out.

Another feature of the second part of the ballot could be some check boxes
allowing you to support the approval strategy of some party or candidate.

If you supported the approval strategy of some candidate other than your
favorite, would that be considered betrayal?

Here's an example of what the second part of the ballot might look like
(without the optional features just mentioned above) in a four way race:


         | Joan | John | Jane |
_________|______|______|______|
Jean     |  X   |      |  X   |
_________|______|______|______|
Jane     |      |  X   |
_________|______|______|
John     |      |
_________|______|

The X's indicate that on this marked ballot the approved pairs are
{Jean,Joan}, {Jean,Jane}, and {Jane,John}.

What should we call this method?

How about Rated Pairs?

Is there any simpler method that factors all of the strategy away from the
rankings or ratings of the candidates?

Forest