Erratum Re: [EM] (P1) and monotonicity for single-winner election systems and Condorcet.

[David Catchpole]

On Wed, 27 Oct 1999, Craig Carey wrote:

> 
> Mr Catpole's theorem is far from being as bad I had written.
> I said the rule failed to pass 2 candidate FPTP. However, the
>  W(V)<>W(V') is the left of the "implies".

Thank Erdos's SF for that... (more further down)

> I wrote a REDUCE program to see what 3 candidate methods were 
>  passed and failed by the rule Mr Catchpole wrote and which
>  is immediately below. The problem was solved using symbolic
>  algebra. REDUCE is much slow when doing 19 for loops.
> What I found was that the rule failed FPTP, IFPP, and Borda,
>  for both 1 & 2 winners. The rule passed Condorcet (1 and 2
>  winners) with the regions where Condorcet picks the wrong number
>  of winners, being made regions where the rule held (and
>  similarly for ties, in all methods). To get that result, I had
>  made Pi be Condorcet pairwise comparison. Doing the created
>  a rule that failed methods including FPTP, and passed Condorcet.

Um... what do you mean by "Condorcet picks the wrong number of winners?"
I've been talking about single-winner election systems, SF-dammit!

Again, Pi is not Condorcet pairwise comparison. It's an individual
comparison with respect to voter i, not an aggregate comparison. (more
further down)

> 
> 
> 
> 
> At 11:46 26.10.99 , Craig Carey wrote:
> >
> >A method of Mr Catchpole that falls apart over two candidate election
> > is studied here.
> It didn't. I apologise to Mr Catchpole. It needs 3 candidates before
>  the rule to be found to be be of no great value. The rule seems to be
>  a way to test if the method Pi-like nature if a pairwise comparison is
>  done. There is no need to write "not Pi(c2,c1,V)" instead of "Pi(c1,c2,V)"
>  presumably. 

There is, because a voter may be indifferent between c2 and c1, meaning
not Pi(c2,c1,V) AND not Pi(c1,c2,V)