[EM] Discover Magazine article

[Markus Schulze]

Dear Mike,

you wrote (25 Oct 2000):
> An example: Steve said that, when Tideman(wv) and BeatpathWinner
> give different results, the Tideman(wv) winner pairbeats the
> BeatpathWinner winner in the vast majority of cases. So if the
> people could choose between those winners, they'd choose the
> Tideman winner, and so the use of Tideman is more democratic.
>
> Markus replied that there could be a cycle of such relationships
> among methods, and that that invalidates the idea. But that's an
> IRVie argument against Condorcet.

The Schulze winner is usually identical to the PC winner. The
Copeland score of the PC winner is usually very low compared to
the Copeland Score of the winner of most other Condorcet methods.
Therefore, in those cases where the Schulze winner resp. the PC
winner X differs from the winner Y of a given other Condorcet
method (e.g. Tideman), winner Y usually pairwise beats winner X.
Because of these reasons Steve concludes that Tideman was
more "democratic" than Schulze. I disagree with Steve
(1) because I don't consider the Copeland score to be important
and (2) because in so far as PC has many desirable properties
--e.g.: PC meets Saari's Positive Involvement Criterion and
Fishburn's No-Show Criterion; PC isn't vulnerable to "indirect
strategies"-- I consider it to be very advantageous that
Schulze doesn't differ unnecessarily from PC.

Norman wrote about Steve's argumentation (27 May 2000):
> If we thought this was an important factor in selecting a
> method, we would probably choose Copeland, since its results
> are even superior to those of IBCM.  It is likely that a method
> has to sacrifice some of the desireable properties of Schulze's
> method in order to do better here. Copeland, for example almost
> certainly violates clone criteria, whereas Schulze's method is
> the only method (that I'm aware of) that has been proven to
> satisfy one strong formulation of Clone Independence criteria.
> Tideman satisfies a weaker definition of clone independence,
> SD is 'mostly' clone independent, but fails in rare cases;
> IBCM and Tideman both violate Beatpath GMC, etc.

Markus Schulze