[EM] Condorcet methods - should the cycle order always determine the result order? (Toby Pereira)

Kristofer Munsterhjelm km_elmet at t-online.de
Tue Nov 4 23:56:41 PST 2014

On 11/04/2014 11:46 PM, Forest Simmons wrote:
> Toby,
> You mentioned Kemeny.  The very purpose of Kemeny is to determine a
> "social order," namely the one that minimizes the average "distance"
> from that order to the ballot orders..
> The trouble with Kemeny is that the choice of metric for the "distance:"
> is clone dependent: changing the size of a clone set changes the number
> of transpositions of order to move a candidate past that set.

If you change "sum" (or average) to leximax, then that problem goes away 
and you get Ranked Pairs, right?

Can River also be formulated as an optimization problem?

> However, if cardinal ratings (e.g. score ballots) are used, then clone
> independent metrics can be substituted for the Kemeny distance. I once
> posted a message to this list describing a clone free technique for
> converting a set of ordinal ballots into a set of ratings  Then based on
> those ratings it was possible to define "Kemeny Done Right,"  Dodgson
> Done Right," and "Borda Done Right."  Of these three "done right"
> methods, only the latter fails the Condorcet Criterion.

Does altering Kemeny in this way fix its vulnerability to cloning? I'd 
imagine that any way of turning rankings into ratings would make the 
ratings depend on the candidates in some way; otherwise, you could bolt 
that onto, say, Range, and get a deterministic ranked method that passes 
IIA (which we know is impossible).

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