# [EM] Condorcet How?

robert bristow-johnson rbj at audioimagination.com
Sat Mar 20 22:30:42 PDT 2010

```On Mar 20, 2010, at 5:04 PM, Markus Schulze wrote:

> Here are the proposed statutory rules:
>
> http://m-schulze.webhop.net/propstat.pdf

thanks Markus.  this is nice.  and more concise than the Wikipedia
procedure.

__________________
Suppose d[V,W] is the number of valid ballots on which candidate V is
strictly preferred to candidate W. ...

A Òpath from candidate X to candidate Y of strength zÓ is a sequence
of candidates C(1),...,C(n) with the following four properties:

1. C(1) is identical to X.
2. C(n) is identical to Y.
3. For all i = 1,...,(nÐ1): d[C(i),C(i+1)] > d[C(i+1),C(i)].
4. For all i = 1,...,(nÐ1): d[C(i),C(i+1)] ³ z.

p[A,B] is the maximum value such that there is a path from candidate
A to candidate B of that strength. If there is no path from candidate
A to candidate B at all, then p[A,B] : = 0.
__________________

might we add a line after (4.) that says "z is the largest such z so
that all four of the above conditions are satisfied."?  or else, we
could say that any path from candidate X to candidate Y has strength
of zero.  perhaps just including "z" in this statement:

"p[A,B] is the maximum path strength, z, such that there is a path
from candidate A to candidate B of that strength."

Markus, the language is concise, i think that your method is the most
bullet-proof against anomalies and resistant to tactical voting.  But
the obstacle to get over is this "Keep Voting Simple" philosophy:
http://repealirv.blogspot.com/ .  even with nice and concise
legalistic language, i don't see how your proposed statutory rules
get past people's need for transparency (and most people will need
simplicity to support accessibility to support transparency).

i know that some laws (especially tax laws and quota and distribution
laws in the U.S.) are far more arcane, but i don't see many election
laws that have the vote counting method as inaccessible to most non-
technical readers.  (the reason is, of course, that plurality needs
few words to describe it.)

also, at some point, you have to move from "potential winner" to the
unambiguous "elected candidate".  is Candidate F identified as
*elected* (not just a "potential winner") if and only if p[F,G] ³ p
[G,F] for every other candidate G?

just my initial thoughts.  but i really like seeing the Schulze
method expressed in such compact language.

--

r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."

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