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Margin Schulze method

RV
Robert Verron
Fri, Apr 30, 2021 7:08 PM

Hello,

In the Schulze method, the strength of a path is defined in terms of an
absolute number of voters. Specifically, if we consider a link between A
and B (that is, a direct path from A to B) and write d[A, B] for the
number of voters strictly preferring A to B (and d[B, A] in a similar
way), why is the strength of the link defined as max(d[A, B], d[B, A]) ?
(I'll call this the "max version")

Schulze [1] allows several definitions of the strength of a link,
including the margin. That is, the strength of a link between A and B
could be |d[A, B] - d[B, A]| (the "margin version").

I've also noticed that, unlike the max version, the margin version
satisfies the chicken dilemma criterion.

So, I don't know why the max version was picked. Is there an actual
reason ? Could someone please explain or link to a
discussion/paper/whatever about it ?

Thanks !

Robert Verron.

[1] Schulze, M. A new monotonic, clone-independent, reversal symmetric,
and condorcet-consistent single-winner election method. Soc Choice Welf
36, 267–303 (2011). https://doi.org/10.1007/s00355-010-0475-4

Hello, In the Schulze method, the strength of a path is defined in terms of an absolute number of voters. Specifically, if we consider a link between A and B (that is, a direct path from A to B) and write d[A, B] for the number of voters strictly preferring A to B (and d[B, A] in a similar way), why is the strength of the link defined as max(d[A, B], d[B, A]) ? (I'll call this the "max version") Schulze [1] allows several definitions of the strength of a link, including the margin. That is, the strength of a link between A and B could be |d[A, B] - d[B, A]| (the "margin version"). I've also noticed that, unlike the max version, the margin version satisfies the chicken dilemma criterion. So, I don't know why the max version was picked. Is there an actual reason ? Could someone please explain or link to a discussion/paper/whatever about it ? Thanks ! Robert Verron. [1] Schulze, M. A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method. Soc Choice Welf 36, 267–303 (2011). https://doi.org/10.1007/s00355-010-0475-4