[EM] Favorite Betrayal and Condorcet

[Forest Simmons]

El vie., 15 de abr. de 2022 10:10 p. m., Kevin Venzke <stepjak at yahoo.fr>
escribió:

> Hi Forest,
>
> > The FBC (Favorite Betrayal Criterion) has long been thought (at least by
> me) to be
> > incompatible with the Condorcet Criterion when restricted to Universal
> Domain election methods.
>
> In 2005 I purported to show that Condorcet and FBC were incompatible,
> although
> it does rely on a symmetric tie. I modified Woodall's proof regarding
> Condorcet
> and LNHarm to get it.
>
> You raise an interesting possibility of making them compatible by giving
> up UD.
> But it seems to me the best we could do is find a format of voting under
> which
> we can't determine how the definitions should apply.
>
> I think you proposed two methods here, which are identical unless there are
> pairwise ties.
>
> The second one:
> > elect the candidate that, on the fewest ballots (if at all) is defeated
> > head-to-head by any candidate ranked ahead of it.
>
> ...seems to be the same as BTP, from Dec 2020.
>
> This is a good FBC method but it's not compliant:
>
> 0.383: A>B>C
> 0.343: C=B>A  -->  C>A=B
> 0.179: A=C>B
> 0.092: B>C>A
>
> A>B>C>A cycle, A wins, scoring off the two A-top factions.
>
> But when the .343 lower B, C wins as CW with 100% score.
>

Or looking at it in reverse, when B is raised to equal top with C,  it
makes C lose because it no longer beats B pairwise, which makes it lose
points in the first and last factions ... which would have been OK had B
gained enough points to win.

>
> Kevin
>
> (end)
>
>
>
> Le vendredi 15 avril 2022, 19:51:08 UTC−5, Forest Simmons <
> forest.simmons21 at gmail.com> a écrit :
> The FBC (Favorite Betrayal Criterion) has long been thought (at least by
> me) to be incompatible with the Condorcet Criterion when restricted to
> Universal Domain election methods.
>
> But today while contemplating how to propose DMC as it's own Condorcet
> completion method [lacking a CW, elect the most truncated candidate that
> pairwise beats every candidate with fewer truncations], my mind reverted
> back to a related DSV approval method that I had rejected because it was
> not precinct summable, sometimes requiring a second pass through the
> ballots to compactly summarize the necessary information:
>
> Lacking an outright "True Majority Winner", elect the candidate that, on
> the most ballots, pairwise defeats every candidate ranked above it.
>
> As I wracked my brain for a clever one-pass data compression idea, it
> suddenly hit me that this two pass DSV Approval method is both Condorcet
> and FBC compliant!
>
> Suppose you raise your favorite F to equal rank with your compromise C on
> some ballot B. This move cannot decrease C's approval count, because C
> still pairwise defeats every candidate ranked above it on ballot B that it
> beat before. So the method passes the FBC.
>
> How about the Condorcet Criterion? Well, the CW will always get a perfect
> 100 percent score, and will be ranked ahead of any other candidate X on at
> least one ballot, giving X a less than perfect Approval score.
>
> Can a similar result be achieved by a one pass method?
>
> For now let's call this method Two Pass FBC Condorcet (2PFBCC).
>
> IRV routinely requires more than two passes thhrough the ballots, so
> 2PFBCC is better in this regard, since it only requires more than one pass
> when lacking a CW, i.e. extremely rarely, and never more than two
> ...soundly dominating IRV in summability ... not to mention monotonicity,
> Condorcet compliance and Compromise immunity (FBC) ... while of course
> retaining clone independence, etc.
>
> And one more biggy ... simplicity and succinctness of definition: elect
> the candidate that, on the fewest ballots (if at all) is defeated
> head-to-head by any candidate ranked ahead of it.
>
> Of course, for the lay person this definition must be supplemented by a
> definition of "head-to-head defeat" ... but that should not be too painful
> for a lover of democracy!
>
> However, just for fun let's incorporate the head-to-head defeat definition
> into one complete definition for the entire method:
>
> Candidate X gets a point from ballot B if (and only if) every candidate Y
> ranked ahead of X on ballot B is merely an exception to the rule ...i.e
> more often than not X is ranked ahead of Y, even though on this particular
> ballot, candidate X is not ranked over Y.
>
> It goes without saying that the candidate to be elected is the point
> winner.
>
> This definition is self-contained including the heuristic that inspired it.
>
> Heuristic: we can forgive X for being ranked below Y on ballot B, as long
> as that is more the exception than the rule when it comes to ballots in
> general.
>
> A nagging question:
>
> Should a point granted to X by ballot B be considered to be actual for X
> by the voter of ballot B even when B did not rank X at all, as long as X
> pairwise defeated all of the ranked candidates?
>
> No, we withdraw the word "approval" originally used for this method in the
> DSV context ... but reserve the right to use the word consent:
>
> Which is worse? ... that stretch of the word "consent" ? ... or the one
> that counts IRV voters as consenting to the IRV winner Y that they left
> unranked even though their favorite X defeated every other candidate
> pairwise, including Y.
>
> In any case, here is my current proposal for 2PFBCC that skirts this
> issue:
>
> Lacking a CW ... for each ballot B, give a point to each candidate X that
> is ranked on ballot B, unless some candidate Y ranked above X on ballot B
> is also mostly (i.e. more often than not) ranked above X on other ballots,
> too.
>
> Finally, elect the point winner.
>
> Is that a method most EM readers and their friends could live with?
>
> How about the VoteFair and STAR vote people?
>
> How about RCV proponents in general?
>
> And how about Range/Score enthusiasts?
>
> [Among whom I count myself ... especially for Score Sorted Margins]
>
> How about Majority Judgment supporters? ... to whom I am highly
> sympathetic, also.
>
> I know we had our hearts set on a one pass method for Burlington, Vermont,
> But this method is de-facto one-pass (according to FairVote data) more than
> 99 percent of the time, and only 2-pass the rest of the time ... nothing
> compared to IRV's obligatorty multiple passes through the entire ballot set
> almost every election.
>
> Try it, test it, and spread the word!
>
> [or show me the simple bubble popping fact that I have over-looked]
>
> -Forest
>
>
>
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