3-valued Booleans inside rules, passing Condorcet (Re: [EM] "More often" (was: IRV and Condorcet operating identically)

[Craig Carey]

At 03\03\02 02:38 -0500 Sunday, Dave Ketchum wrote:
 >On Sun, 02 Mar 2003 09:58:47 +1300 Craig Carey wrote in part:
 >> At 03\03\01 09:49 -0500 Saturday, Stephane Rouillon wrote:
...
 >> about an election having only the papers (AB), (B), and (C). For
 >> that election, the Condorcet method has an undefined region of
 >> quite a big size.
 >
 >Seems like "undefined region" is an unfortunate label.  Agreed that
 >Condorcet has cycles, and that its basic definition allows these to exist
 >but does not provide a resolution for them.
 >
 >STILL, this problem is recognized and I do not hear anyone being dumb
 >enough to propose actual use of Condorcet without completing the
 >definition of the method by specifying how to process cycles (while it is
 >true that there is debate as to exactly what to do with them).
...

It is not OK to say that
    it would be dumb to use Condorcet because: it can't always return the
    right number of winners.

Condorcet could be quite good under fairness testing that got weakened
to forgive it for whenever the rule probed into its region that got the
wrong number of winners.

Fixing it is a no gain situation. I myself weaken tests so that
Condorcet slumps if fixed.



 >IRV also has an undefined region, while smaller - what to do when two weak
 >candidates are equal, and thus neither can be discarded as weakest.
...

IRV is Mr Ritchie's method isn't it?.

Doesn't USA clean up its nuclear wastes by trucking them to steel refinery
factories. Wasn't that how the CVD's Mr Ritchie who was planning that??.


A rule testing a method can overlook the ties.

Here is 2 solutions for ties in the space of the weights of the ballot
papers:

(1) say all ties are mishandled at the top of the analysis.
   I.e. most of the "<"s might actually mean "<=". That seems OK

(2) A computer does not accept that. So my lax, stri, strieq functions
  can expand and contract solids to  include or exclude their surfaces and
  cuts.


What is the best way (for this topic), to define a function (named
"stri", say ("stri" is for "strict"), that cuts out the surface of its
argument ?.

Question:
What should "stri (x=0) or ((y=0) and (z=0))" equal ?:

    (a): False [since the space is 3-D and R is the union of polytopes of
         a lower dimension (ie. x=0 is a plane)].

    (b): False [since all equalities. (It is known that x,y,z are free
         rather than, say, equal to 0)]

    (c): "(x=0)' [since that is all the highest dimensional part of the
         polytope]

My REDLOG code uses (b); I presume that the (c) is the best choice.
Because I use "(b)", I have two "stri" functions: one contracts solids
but leaves the x=y flats, and the other deletes those.

This whole topic of ties is so easy.




Craig Carey 

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