[EM] IC-Smith//Plurality

[Michael Ossipoff]

I recently asked someone about the practical value of the Smith Criterion.
IRV dramatizes the desirability of choosing the CW. Presumably there could
be situations in which not choosing from the Smith set could cause a
problem similar to one caused by not choosing the CW.

I've suggested some advantages of the familiar Condocet-IRV,  in a few
different forms. (where "Condorcet" could mean improved Condorcet (IC) or
traditional unimproved Condorcet (TUC). In one version the IRV count is
done among all of the candidates In another, beaten candidates are deleted
from the ballots before doing the IRV count.

The latter version seems preferable, because a pair or other set of
unbeaten candidates should be entitled to the same win that a single
unbeaten candidates is entitled to.

There are various other methods that could be substituted, before or after
the hyphen, allowing various additional method-combinations that might have
similar properties.

I haven't thoroughly checked verified the properties of some of the
promising-seeming ones.

Here's one that seems promising. I hesitate to say what properties it seems
to have, because the combination of properties that it appears to have
seems more than what I would have expected to be attainable:

IC-Smith//Plurality:

Using the IC definition of "beat", determine the Smith set. From the Smith
set, choose the Plurality winner.

The IC definition of "beat":

(X>Y) means the number of ballots ranking X over Y.

(Y>X) means the number of ballots ranking Y over X

(X=Y)T means the number of ballots voting X and Y at top
(not voting anyone over X or over Y, and voting X and Y over someone)

X beats Y iff (X>Y) > (Y>X) + (X=Y)T

[end of IC definition of "beat"}

Symmetrical IC-Smith//Plurality would be the same, except for, instead,
using the Symmetrical IC definition of "beat":

Same as the IC definition of "beat", except that:

(X=Y)B means the number of ballots voting X and Y at bottom.
(not voting X over anyone, or Y over anyone, and voting someone over X and
voting someone over Y)

X beats Y iff (X>Y) + (X=Y)B > (Y>X) + (X=Y)T

...unless two candidates beat eachother, in which case only one beats the
other. The one that beats the other is the one who is ranked over the other
by more ballots.

[end of Symmetrical IC definition of "beat"]

IC-Smith//IRV might bring a different set of criterion compliances, trading
one for another.

Michael Ossipoff
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