[EM] Of course, when no one is beaten, choose among unbeaten by top-count. A Schwartz-set variation.

[Michael Ossipoff]

It occurs to me that maybe Symmetrical IC-Beatpath(lv) and Symmetrical
IC-Ranked-Pairs(lv) might meet FBC, and fail Smith. That would be a
lot better the reverse.

I don't know if they meet FBC. But, at this time, I don't know that
they don't meet FBC, CD, Condorcet, 0-info LNHe, MMC, and
Clone-Independence.

Of course neither do I know that they do.

"Ranked-Pairs" is abbreviated "RP". I'll abbreviate  "Beatpath" as
"B". So it's Symmetrical IC-RP(lv) and Symmetrical IC-B(lv).

Or, abbreviating more, SICRC(lv) and SICB(lv).

Of course Beatpath and Ranked-Pairs are only for when everyone is
beaten. Otherwise, a top-count should choose among the unbeaten
candidates, as in Symmetrical ICT.

Someone could object that, in SICRC(lv) and SICB(lv), a defeat of 2 to
1 counts for more than a defeat of a million to 2.

But remember that Ranked-Pairs and Beatpath are only used when the
defeats nonsensicially, paradoxically, contradict eachother. The
electorate choose A over B, and B over C, and C over A.

If people object to 2 to 1 being more than a million to 2, then might
not they also object to defeats that can form nonsensical cycles?

And, non-defeats don't do that. Only defeats do that. So wouldn't it
make sense for non-defeats to have "default" status, and for the
number of objectors to a defeat to matter more than te number of
advocates of a defeat? The defeat-objectors are the ones who are
voting against something potentially nonsensical. So maybe they should
be listened to with higher priority.

Isn't this an alternative definition of the Schwartz set?:

A candidate is beatpath-trounced if there is an unreturned beatpath to
him. The Schwarz set is the set of un-beatpath-trounced candidates.

Well, how would Symmettical IC-Schwartz-Top do?  If no one is
unbeaten, by Symmetrical ICT, then choose, from the Schwartz set
(based on Symmetrtcal IC), the candidate with highest top-count.
Symmetrical IC-Schwartz-Top could be abbreviated "SICST"

That has more recently occurred to me, and I haven't had the
opportunity to evaluate it. I haven't had the opportunity to evaluate
SICRC(lv) or SICB(lv) either. I have no idea if any of those 3 methods
would be any good, or would even work.

The only IC methods that I make any claims about are ICT and Symmetrical ICT.

SICRC(lv), SICB(lv), and Symmetrical IC-Schwartz-Top (SICST) are pure
speculation at this point, and I don't claim to know their properties,
of if they'd be any good at all.

SICST occurred to me as a possible way to avoid need for losing-votes.
Maybe using the Schwartz-set is good enough, and it isn't necessary to
use Ranked-Pairs or Beatpath. I don't know.

In voting systems, speculation has its place.

Mike Ossipoff