[EM] Markus' request

[Markus Schulze]

Dear Forest Simmons,

I wrote (16 Feb 2005):
> 1. Please post an authoritative definition for the
>    "Dutta set"! (Please post one that doesn't presume
>    that there are no pairwise ties!)
>
> 2. Please post an authoritative definition for
>    "Condorcet lottery"! (As far as I remember correctly,
>    Jobst Heitzig wrote that "Condorcet lottery" is not
>    monotonic. So it seems that Jobst Heitzig and you
>    are talking about slightly different things.)

You wrote (16 Feb 2005):
> Markus asked me to define the Dutta Set, the Condorcet
> Lottery method, and clarify whether or not this lottery
> method is monotonic.
> 
> I think the best I can do is to include a copy of Jobst's
> posting of 5 Jan 2005, which answers all of these questions
> to one degree or another.
> 
> In particular, the monotonic nature of the method is
> described in properties 11 and 12 below.

Thank you for forwarding Jobst's mail. As far as I understand
his mail correctly, then Condorcet lottery is not monotonic
in the general case. He wrote: "Although the method is
monotonic in the sense of 11. and 12., the probability p(x)
can still decrease when x is reinforced and there are more
than 5 candidates."

Also Jobst's mail doesn't contain a definition for Dutta's
minimal covering set.

Markus Schulze