[EM] Favorite Betrayal and Condorcet

[Forest Simmons]

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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