[EM] Cloneproof SSD definition wordings

[MIKE OSSIPOFF]

I agree that Cloneproof SSD's problem as a proposal, is the need
to define the Schwartz set. One could avoid scaring people, by
avoiding nameing the Schwartz set, and just incorporating it in the
Cloneproof SSD definition, the way we, at the website, incorporated
it in the ordinary SSD definition.

But, if people are actually willing to listen, and don't write it
off unfairly, the Schwartz set definition isn't something that they
can say is really difficult or lacking in plausibility:

1. An unbeaten set is a set of alternatives none of which are beaten
   by anything outside the set.
2. An innermost unbeaten set is an unbeaten set that doesn't contain
   a smaller unbeaten set.
3. The Schwartz set is the set of alternatives that are in innermost
   unbeaten sets.

[end of definition]


People understand that there's something special about the Schwartz
set alternatives. Right after introducing the idea of pairwise counts,
bring up unbeaten sets & innermost unbeaten sets, and the Schwartz set.

I've successfully used a diagram, where dots represent candidates,
and an ellipse drawn around some of the dots represents an unbeaten
set. A smaller ellipse drawn inside that obviously bears the same
relation to the rest of the big ellipse as the big ellipse beats to
the completely outside dots, and so it's clear that that innermost
unbeaten set is the one that means something.

My girlfriend immediately liked SSD, explained that way, though she'd
rejected SD because of its cycles. She wasn't just being polite, because
she didn't pretend to understand or like SD. She'd had absolutely no
prior exposure to voting systems or rank balloting counts.

Cloneproof SSD definition:

Here's the clear, explicit definition that I use now:

1. Calculate the Schwartz set, based only on undropped defeats.
2. If there are no defeats among that set's members, then they all win,
   and the count is concluded.
3. Otherwise, drop the weakest defeat that's among that set's members.
4. Go to 1.

[end of definition]

For such a 1st class voting system, Cloneproof SSD is easy to explain
and get acceptance for.

Mike Ossipoff

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