[EM] Markus' goal is attainable, & Dave had a point, but....

[MIKE OSSIPOFF]

Dave suggested that one criterion could replace the 4 majority defensive 
strategy criteria. Actually there is one criterion such that any methods 
complying with that criterion complies with all 4 majorilty defensive 
strategy crtiterion. Steve Eppley defined such a criterion around the 
beginning of 2000. It's called the Beatpath Criterion (BC).

But there are 2 reasons why I don't replace the majority defensive strategy 
criteria with BC:

1. PC only meets 2 of the majority defensive strategy criteria. Approval 
only meets one of the majority defensive strategy criteria (But Approval & 
CR meet FBC, met by no other method).
Therefore BC doesn't judge finely enough, since it doesn't show the 
accomplishments of methods that meet some of the majority defensive strategy 
criteria.

2. BC doesn't speak to the concerns that the 4 majority defensive strategy 
criteria speak to. The majority defensive criteria directly address certain 
strategy concerns. If they were replaced with BC, a motivation statement 
would be needed to accompany BC, whose motivation and strategic purpose 
isn't obvious at all.

I challenged Markus to write a votes-only criterion equivalent to my CC or 
SDSC. Actually that's possible. I haven't checked the postings yet, but I 
hope that I've beat Markus to it by saying now that it can be done.

Actually this isn't something new. It's come up in previous discussion. I 
knew earlier that such votes-only equivalent criteria can be written, but in 
this discussion I forgot it.

In fact, SFC & GSFC were initially defined votes-only. Not because I 
preferred that, but simply because that was the first way that occurred to 
Steve & me.

But I wasn't entirely comfortable with the way that SFC & GSFC were written, 
because they needed a stipulation of rank-balloting, something that too me 
seemed inelegant and arbitrary.
So, when it occurred to me that SFC & GSFC could be written in terms of 
sincere preferences, to get rid of the arbitrary rules-stipulation, I 
improved SFC & GSFC in that way, because I prefer mention of preferences to 
having an arbitrary rules-stipulation.

Likewise, BC was defined votes-only. It too has the same arbitrary 
rules-stipulation. I say "has", because I never changed BC to get rid of 
that. That's because I don't use BC to tell why methods are better--I've 
only used BC as a convenient quick way to find out if a method meets the 4 
majority defensive strategy criteria. BC is used for that purpose, not 
directly for method advocacy. Again, that's because BC doesn't speak 
directly to voters' concerns.

Now, let me use CC as an example to show how these criteria can all be 
written votes-only.

First let me re-state my CC. I've recently posted its supporting 
definitions, so won't write them here.

My Condorcet Criterion (CC):

If there's a CC and if everyone votes sincerely, then the CC should win.

[end of my CC definition]

Votes-only CC definition:

A pairwise comparison is the voting of one candidate over another.

A method's balloting should allow the voter to make  pairwise comparisons 
between any number of candidates, up to all the candidates.

If a candidate pairwise-beats each one of the other candidates, then s/he 
should win.

[end of votes-only CC equivalent to my CC]

I don't like that rules-stipulation that it needs. To me, mentioning the 
arbitrary-sounding, discriminatory-sounding rule-stipulation is more 
inelegant and awkward than the mention of sincere preferences.

Additionally, my sincere preferences version speaks more directly to the 
concerns of voters.

All the majority defensive strategy criteria could be written votes-only, 
but I prefer the sincere-preferences approach.

Likewise, as I said, BC is written votes-only.

Now, hopefully I'm posting this before Markus posts a votes-only CC 
equivalent to my CC. When I've more or less implied that something can't be 
done, I like to be the one who shows that it can be done.

Mike Ossipoff

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