[EM] Losing Votes (ERABW)

[Chris Benham]

I propose the following as a reasonably practical, "summable", Condorcet method:

*Voters rank from the top however many candidates they wish. Equal-ranking is allowed.

The result is determined from a pairwise matrix. On that matrix, ballots that rank above bottom
any X=Y contribute one whole vote to X>Y and another to Y>X.

Ballots that truncate both X and Y  have no effect on the X>Y and Y>X entries in the pairwise
matrix.

With the thus created pairwise matrix, decide the winner with Schulze (Losing Votes).*

It isn't a big deal if  Ranked Pairs or River are used instead of  Schulze.  "Losing Votes" means 
that the pairwise results are weighed purely by the number of votes on the losing side. The "weakest
defeats" are those with the most votes on the losing side, and of course conversely the "strongest
victories" are those with the fewest votes on the losing side.

This has these advantages over Winning Votes: it appears to meet the "Approval Bad Example" 
defection-related criterion, it can't fail to elect a positionally dominant Smith-set member, and it
doesn't have any zero-info random-fill incentive.

Instead, in the "acceptables versus unacceptables" situation it has the more natural zero-info 
strategy of just equal-top ranking the acceptables and truncating the unacceptables.

It doesn't share Winning Votes' compliance with Minimal Defense  (incompatible, or effectively so,
with ABE compliance).

It has these advantages over Margins: it meets the Plurality criterion and it meets Steve Eppley's old
"Non-Drastic Defense"  criterion.

That says that if  more than half the voters rank X above Y and X no lower than equal top, then Y
can't win.

46: A>C ("sincere" may be A>B)
10: B>A
10: B>C
34: C=B ("sincere" may be C>B)

More than half the voters rank B above A and B no lower than equal-top, but Margins elects A.
If the method were Bucklin, B would be the only candidate with a majority score in the first round.

Using the rules of my suggested method, the pairwise comparisons go:

 B>A 54>46,    A>C 56-44,    C>B 80-54  (the 34 C=B have been added to both sides).

The weakest defeat (as measured by Losing Votes) is B's, so B wins. Or in terms of Ranked Pairs,
the strongest pairwise result is A>C so that is locked and the next strongest is B>A so that is locked
and then C>B is skipped because it's incompatible with an already locked result; so the final order is
B>A>C.


Enough for the time being.

Chris Benham
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