[EM] Is "Inverse Nanson" better than standard Nanson?

[Blake Cretney]

Dear Markus,

> Dear participants,
> 
> due to Condorcet, a "proposition" is a statement of the
> form: "X is better than Y." An "opinion" is a set of
> n*(n-1)/2 propositions (one for each pair of candidates).
> A "possible opinion" is a set of n*(n-1)/2 propositions
> (one for each pair of candidates) that is compatible to
> a ranking. An "impossible opinion" is a set of n*(n-1)/2
> propositions (one for each pair of candidates) that is
> incompatible to every ranking.
> 
> Due to Condorcet, when one "eliminates" a proposition of
> an opinion then one still has an opinion. Therefore, it
> is clear that "eliminating" can only mean "inverting".
> 
> Markus Schulze
> 

Here's the Condorcet quote,

> Create an opinion of those n*(n-1)/2 propositions which win
> most of the votes. 

I have to agree with Mike.

Condorcet says to "create" an opinion of the n*(n-1)/2 propositions. 
I take this as a description of how to find the initial opinion, not a
definion of what an opinion is.  What Condorcet means by "opinion" can
only be pieced together in context.  So, I don't view the n*(n-1)/2 as
a fixed part of the definition of an opinion.  

Otherwise, we have to read both "eliminate" and "remaining" in a
surprising way.  Normally, "eliminate" means remove, and "remaining"
means those that haven't been removed.  We would expect that Condorcet
would have said, "reverse" and "resulting" if this is what he meant.

Of course, it would be somewhat awkward to write "the resulting
opinion of the resulting propositions," but the phrase could be
rewritten, for example, "the opinion of the resulting propositions". 
So, if Condorcet wanted to express this idea, he could have done so
easily.

Note that Condorcet seems to like giving the number of various
entities.  Telling us the number of possible and impossible opinions
doesn't really add much.  It certainly doesn't define them.  So, it
seems natural that Condorcet would have mentioned the number of
propositions in the initial opinion without meaning anything
particularly significant by it.  

As well, if we take his initial statement as a definition, and are
truly rigorous:

> Create an opinion of those n*(n-1)/2 propositions which win
> most of the votes. 

An opinion would be n*(n-1)/2 propositions WHICH WIN MOST OF THE VOTES
(emphasis, not shouting).  Nothing the procedure does can change which
propositions win most of the votes.  Inverting should be impossible,
since this would result in an opinion of propositions, some of which
did not win most of the votes.

> If this opinion is one of the n*(n-1)*...*2
> possible, then consider as elected that subject to which this
> opinion agrees with its preference. If this opinion is one of the
> (2^(n*(n-1)/2))-n*(n-1)*...*2 impossible opinions, then eliminate
> of this impossible opinion successively those propositions that
> have a smaller plurality & accept the resulting opinion of the
> remaining propositions.

---
Blake Cretney