[EM] Multiwinner participation rule. Reply to M. Schulze

[David Catchpole]

On Tue, 14 Dec 1999, Craig Carey wrote:

> I read Mr Cachpole's  response. The connection between the
>  "regularity" definition and the "probability" idea is nearly no
>  connection at all. You just happen to be have them in mind at the same
>  time, plus they were written about at the same time. You did not prove
>  a connection and none exists. It is a weak form of rebuttal: to connect
>  on failing idea to another when they are in truth separate.

You're using that awful circular logic again. Please stop.(more further
down)

> 
> If AV and FPTP and Condorcet and Borda and IFPP and would have
>  candidate A win, then what are the probabilities for candidate A
>  winning in your method: 0.96?. Just how small do those numbers (that
>  ought be 1) get?.

AV, FPTP, etc. as they are usually expressed are _deterministic_ election
systems- they all share the same two-candidate system probability function

f(x)=	{ 0	if	x<1/2
	{ 1/2	if	x=1/2
	{ 1	if	x>1/2

Maybe you're getting the drift now? I'm going to go through the slog of
sending the introduction of "Distribution of Power Under Stochastic Social
Choice Rules" by Pattanaik and Peleg, Econometrica Vol. 54 No. 4 to you.
Hopefully then you'll understand-

(i)	what a probabilistic election method is
(ii) 	what regularity is
(iii)	the simple fact that regularity relates specifically to a
	probabilistic formalism for election methods.

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Nothing is foolproof given a talented fool.