[EM] Favorite Betrayal and Condorcet

Kevin Venzke stepjak at yahoo.fr
Fri Apr 15 21:59:38 PDT 2022


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.

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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