[EM] Elisabeth's questions

[MIKE OSSIPOFF]

Stephane asked:

Would you have a web reference for a precise description
of the BeatpathWinner method...

Is it like Ranked Pairs ?

I reply:

BeatpathWinner and Ranked Pairs are both considered Condorcet
versions. BeatpathWinner is regarded as a Condorcet version because
it's equivalent to a method (Cloneproof SSD) that's an interpretation of one 
of Condorcet's proposals.

Ranked Pairs is the best interpretation of
one of Condorcet's proposals.

BeatpathWinner/Cloneproof SSD and Ranked Pairs are the best rank
counts, if we value the standard of getting rid of the lesser-of-2-evils 
problem.

They meet all the criteria that Condorcet is listed as meeting
in the criteria compliance table at the top of the technical
evaluation page at the website http://www.electionmethods.org
, and they're both nonfalsifying, expressive, and conditionally
completely expressive, as I've defined those terms here.

I don't have a web reference, but I'll give precise definitions
here:

BeatpathWinner:

1. X beats Y if more people rank X over Y than vice-versa.
2. The strength of X's defeat of Y is measured by the number of
   people who rank X over Y.
3. There's a beatpath from X to Y if either X beats Y, or if X
   beats someone who has a beatpath to Y.
4. A sequence of defeats that makes it possible to accurately say
   that X has a beatpath from X to Y is called a beatpath from
   X to Y.
5. The strength of a beatpath is measured by the strength of its
   weakest defeat.
6. If the strongest beatpath from X to Y is stronger than the strongest
   beatpath from Y to X, then X has a beatpath win against Y.
7. A candidate is winner if no one has a beatpath win against him/her.

[end of definition]

In other words, a beatpath is a sequence of defeats, so, for example, if A 
beats B, B beats C, and C beats D, then A has a beatpath to D.

Ranked Pairs:

1. In order of strongest defeats first, consider each defeat as
   follows: Keep it if it doesn't conflict with already-kept defeats.
2. When all of the defeats have been considered in that way, a candidate
   wins if he has no kept defeats.

(Defeats conflict if they form a cycle)

[end of definition]

Obviously, the strongest 2 defeats will be kept, because there
won't be enough already-kept defeats to form a cycle.

Let me know if there are any questions about these definitions or
about single-winner voting systems in general.

Mike Ossipoff









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