[EM] "Leader of the Free World" Project

[Forest Simmons]

Perhaps Tengvall thinks of penalizing clones as a form of discouraging or
repelling clones, so that his clone punishing method has more of a
tendency to get rid of clones than a clone independent method, and
therefore more deserving of the description "clone free."

Forest



On Mon, 13 Oct 2003, Markus Schulze wrote:

> Hallo,
>
> there was a discussion between Arto Tengvall (the specialist
> on election methods of the "Leader of the Free World"
> project) and me about which election method should be used
> at the LFW project. I posted my paper "A New Monotonic
> and Clone-Independent Single-Winner Election Method"
> (http://groups.yahoo.com/group/election-methods-list/files/nmciswem.pdf)
> to him. Arto Tengvall replied (10 Oct 2003):
>
> > About the Leader of the World - project.
> >
> > There will be one official electoral result, counted by the very
> > best method known so far. Today, it is my method, but if someone
> > can show that there is another method still better (judged by
> > essential mathematical and logical criteria), I would have no
> > objection against changing the method. Here is a short and easy
> > definition of my method. As you can see, it also satisfies the
> > criteria you have used yourself. It satisfies some extra criteria,
> > too, which I have no time to write now.
> >
> > 1. Count votes in all pairwise comparisons, according to this:
> > Count a vote to X from every ballot where X is given better or
> > equal preference than Y, and to Y from every ballot where Y is
> > given better or equal preference than X. X beats Y if the former
> > score is bigger than the latter, and vice-versa.
> >
> > 2. The vote minimum of each X is the smallest score of X in any
> > of X:s comparisons.
> >
> > 3. There is a beatpath from X to Y if X beats Y (in pairwise
> > comparison between these two) or X beats some Z that beats Y.
> >
> > 4. Eliminate every candidate X such that there is a beatpath
> > from some Y to X but not vice-versa.
> >
> > 5. Check the vote minimum of each non-eliminated. The winner
> > is the one with the biggest vote minimum. (A tie is possible.)
>
> In short: The Tengvall winner is that Schwartz winner A whose
> worst pairwise comparison with another candidate B (measured
> by the absolute number of voters who strictly prefer candidate B
> to candidate A) is minimal.
>
> When every voter casts a complete ranking then Tengvall's method
> is identical with Schwartz//MinMax.
>
> On first view, Tengvall's method seems to be identical with
> Schwartz//MinMax(VotesAgainst). But when the strength of a
> pairwise comparison is measured by the absolute number of
> voters who strictly prefer candidate B to candidate A then
> it isn't guaranteed that the worst pairwise comparison
> of the Schwartz winner A with another candidate is necessarily
> with another Schwartz winner. Therefore, Tengvall's method
> isn't quite Schwartz//MinMax(VotesAgainst).
>
> I wrote to Tengvall, that his method violates independence of
> clones and reversal symmetry. And I asked him which criteria
> he uses to conclude that his method is the very best method
> known so far judged by essential mathematical and logical
> criteria. Arto Tengvall replied (13 Oct 2003):
>
> > My method has similarities with Schwartz//Minmax, however one
> > defines that method. I have seen many different definitions
> > but my method is a little bit different. Maybe you should
> > look again, without thinking Schwartz method, so without any
> > pre-opinions. Then you can see, withaout any deeper analysis,
> > that my method easily fullfills clone-independency and reversal
> > symmetry.
>
> Can somebody tell me where I have made a mistake?
>
> Markus Schulze
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