[EM] SSD & BeatpathWinner

[MIKE OSSIPOFF]

If you explain SSD to someone by giving them a written definition
of the Schwartz set, many people will probably refuse to
read it. But I defined SSD, using a diagram, and it was
understood & liked by the person to whom I explained it.
I made dots, representing candidates. I enclosed some in a
closed curve and said that these are unbeaten by anything outside
this set. After getting agreement that the winner should come
from that unbeaten set, I drew another closed curve inside it,
saying that that's a smaller unbeaten set, inside the first one.
I said that, for the same reason,
the winner should come from in there. So the winner should come
from the innermost unbeaten set.

Then I said SSD's rule:

Drop the weakest defeat among the innermost unbeaten set.
Repeat till there's an unbeaten candidate.

(At some point it would have to be clarified that the dropping
of a defeat can change who is in the innermost unbeaten set, but
one needn't add that when talking on a sidewalk).

***

All that is quite plausible. The motivation for it and
justification of it is obvious & natural. That can't be said
for BeatpathWinner. When you start talking about beatpaths, and
how to measure their strength, your listener will feel that
it's all arbitrary. Sure, it makes sense its own way, but would
he have any reason to believe that the count should be done by
that rule, out of all the possible rules? Dropping the weakest
defeat from among those that are in conflict is obvious & natural.

***

The person to whom I defined SSD had never had a voting system
defined to her, had no prior exposure to the subject of voting
systems, except for a brief mention of Approval.

***

Under many-voter conditions (no pairwise ties or equal defeats),
SD, SSD, & BeatpathWinner all choose the same winner.

***

Mike Ossipoff

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