[EM] Re: realization on method equivalence

[Chris Benham]

Russ,
You wrote (Tue.Apr.12):
"I just realized that two Condorcet-Approval hybrid
methods that I had thought were distinct are actually
equivalent. This may have been pointed out already,
and it may even be obvious to some, but it was a
significant realization to me nonetheless. (If it
*has* been pointed out, please don't hesitate to tell
me where.)

Method 1: The winner is the most-approved member of
the Smith set.

Method 2: If no CW exists, repeatedly drop the
least-approved candidate
until a CW is found."

CB: An example in an  Adam Tarr (April,2002) post
demonstrates that you are mistaken:

49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush

Bush>Nader>Gore>Bush, so all the candidates are in the
Smith set.
Approval scores: Bush 55,  Gore 51, Nader 33.

Your "method 1" above elects Bush, while "method 2"
elects Gore.

http://lists.electorama.com/pipermail/election-methods-electorama.com/2002-April/008013.html


Chris  Benham











Find local movie times and trailers on Yahoo! Movies.
http://au.movies.yahoo.com