[EM] Rouse reply II

[LAYTON Craig]

Mike wrote:

>The Schwartz set:
>
>1. An unbeaten set is a set of candidates none of whom are beaten by
>   anyone 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. (In other words, the Schwartz set is the union
>   of the innermost unbeaten sets).
>
>[end of definition]
>
>In public elections, where there are no pairwise ties or equal
>defeats, the Schwartz & Smith sets are indentical. Of course the
>Smith set is briefer to define, and so it should be the one used
>when definiing public proposals.

Obviously there would need to be some provision for pairwise ties or equal
defeats.  For Cloneproof SSD, you can write the counting proceedure much
more simply with the Smith set and have a special part of the legislation
"where there are any ties or equal defeats, use the following proceedure:"
where you set out the entire cloneproof SSD proceedure.  No one will comment
or report on this section, because it's just an obscure contingency (and
most people won't understand it).  You don't need to have a simpler counting
proceedure for a public proposal, you just need to explain a simpler
counting proceedure.