[EM] The Strong Favorite Betrayal Criterion at Last!

Forest Simmons fsimmons at pcc.edu
Fri Apr 4 17:53:02 PST 2003

Thinking more about the method described below.  Would FBC compliance
dissolve if pairs were locked in place in order of decreasing approval,
skipping over contradictory victories as in Ranked Pairs?

It seems like the order on the second part of the ballot might be
manipulated to create a contradiction where none naturally existed, which
might give some voter or faction of voters a strategic advantage.

I started thinking along these lines as a way to ensure Pareto compliance.

It could be that every ballot ranked three of the ten candidates in
exactly the same order, say A>B>C, and that, because of neglect, the pair
{A,B} received only 99.999% approval, while {B,C} received 100% approval,
so the final match was B versus C, making B the winner.

One solution would be to extend the social order as far as possible
before generating a cyclic contradiction.  In this example the next pair
locked in would be A>B.

I suppose another solution would be to simply force compliance with Pareto
at the outset by removing all candidates that are strictly dominated by
some other candidate.

Would this destroy compliance with the FBC?


On Tue, 1 Apr 2003, Forest Simmons wrote:

> 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
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