[EM] Concluding comments re: deterministic Ranked-Pairs
email9648742 at gmail.com
Sat Dec 21 05:25:52 PST 2013
Two things have occurred to me about the deterministic Ranked-Pairs
(DRP)versions that I've been posting about:
1. The two-paragraph DRP definition that I first proposed when Anders
Kaseorg suggested giving precedence to discards that result from
contradictings sets of stronger defeats,, is really just another equivalent
wording of the 1-paragraph DRP definition that I'd posted just before that,
when Anders first posted about Prabhakar's MMV.
So my 2-paragarph definition was really equivalent to my 1-paragraph
definition, which, it seems to me, was the same as the 1-paragsraph DRP
definition at Eric Gore's website.
This was what that definition said:
A defeat, D, is a discarded defeat if it contradicts a set of defeats that
contains a defeat stronger than D, and no defeats weaker than D.
[end of 1-paragraph definition]
That's the DRP version that I called Greater & Equal DRP, or GEDRP.
Another way of saying what has occurred to me about that is:
Speaking of sets of stronger defeats, and mixed stronger-&-equal defeats in
two paragraphs instead of one doesn't make any change in the method--only
in its wording.
Maybe saying it in two paragraphs adds some clarity, at the expense of some
2. My latest Hierarchial Deterministic Ranked-Pairs (HDRP) proposal
consists of GEDRP plus a 3rd paragraph which has the conditional clause and
the weaker-preferring clause. I'd correctly mentioned that those clauses
lose some desirable criterion-compliances. It has occurred to me that,
without them, DRP has the problem that Markus brought up immediately after
Anders' first post about MMV.
You could leave out the 3rd paragraph (the one about cycles of equal
defeats), and that, too, would sacrifice those criterion-compliances (such
as MMC and Clone-Independence).
Of you could have that 3rd paragraph, with the conditonal and
weak-preferring clauses, to try to avoid the problem Markus spoke of. If,
as might as well be done, the first 2 paragraphs are combined into 1
paragraph, then of course the 3rd paragaraph becomes a 2nd one instead.
So, it seems to me that DRP can't have MMC & Clone-Independence, and still
avoid Markus' criticism.
Maybe the simpest, strongest and most important conclusion from all this is
that DRP, in any version, falls far short of MAM.
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