[EM] Smith set/IIAC/GSFC

[MIKE OSSIPOFF]

The Smith candidate admits anyone who draws a Smith set member.

When you don't, that's the Schwartz set:

1. An unbeaten set is a set of candidates unbeaten from 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 candidates who are in innermost
   unbeaten sets.

[end of definition]

With pair-ties, there can be more than 1 innermost unbeaten set.
In public elections there won't be. It's because of the possibility
of more than 1 innermost unbeaten set that we can't just define the
Schwartz set as the smallest unbeaten set, along the lines of the
Smith set definition.

In public elections the Smith & Schwartz sets will be the same.
In small committees they might not be the same.

The current Schwartz set, recalculated at each stage of the count,
is used in SSD (Schwartz Sequential Dropping).

SSD & BeatpathWinner always choose from the Schwartz set. In a small
committee, Tideman can choose outside the Schwartz set, but it won't
happen in public elections.

Mike Ossipoff


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