[EM] Rouse reply II

[MIKE OSSIPOFF]

I'd said:

 >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.

Craig replied:

Obviously there would need to be some provision for pairwise ties or equal
defeats.

I reply:

Not for pairwise ties. The method's method for dealing with more
than one winner in the count covers the situations caused by
pairwise ties.

As for equal defeats, yes something has to be said about how to
deal with that situation. For public elections, there's no reason
to propose other than this simple, obvious, & natural solution:

If 2 or more defeats are equal, and are equally the weakest defeats
in the Schwartz set, then drop them all simultaneously. The situation
won't occur anyway in public elections, or will practically never
occur.

In small committees it can happen, and that's why Markus suggested
this:

When 2 defeats share the least defeat-support, among the defeats
between Schwartz set members, drop the one that has the most
defeat-opposition. If 2 or more that share the least defeat-support
also have the same defeat-oppostion, then drop them simultaneously.

Whether you want to propose that more elaborate solution for a
small committee of course depends on whether the committee-members
will tolerate the complication. No harm is done with the simpler
procedure; if someone objects that decisiveness could be better, then
that might be the time to suggest Markus's improvement.

Craig continued:

For Cloneproof SSD, you can write the counting proceedure much
more simply with the Smith set

I reply:

No, the Smith set won't do at all for SSD. You don't want
Smith Sequential Dropping. Dropping defeats reduces the Schwartz
set, but it increases the Smith set. I don't know what Smith
Sequential Dropping's properties would be. Does it have good
properties? It sounds somewhere between SSD & PC.

Craig continued:

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.

I reply:

Though there are no pairwise ties in public elections, the dropping
of a defeat is effectively like a pairwise tie. So the Smith &
Schwartz sets are no longer the same once the dropping begins, even
in public elections.

Mike Ossipoff

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