[EM] Markus: Demonstration that Benham & Woodall meet CD

[Michael Ossipoff]

Kevin and Markus--

Kevin--

The definition below is what I now mean by CD.

Markus--

You asked me to precisely define the chicken dilemma, and to demonstrate
that Benham and Woodall don't have the chicken dilemma.

I've defined a criterion that I call the Chicken Dilemma Criterion. It's
intended as a precisely-defined criterion. I'll state it below in this
post. But, if it isn't precise, then you should feel free to say so.

In a subsequent post, I'll tell why Benham and Woodall pass CD.

*Supporting definitions:*

1. The A voters are the voters who prefer candidate A to everyone else. The
B voters are the voters who prefer candidate B to everyone else. The C
voters are the voters who prefer C to everyone else.

2. A particular voter votes sincerely if s/he doesn't falsify a preference,
or fail to vote a felt preference that the balloting system in use would
have allowed hir to vote in addition to the preferences that s/he actually
votes.

*Premise:*

1. There are 3 candidates: A, B, and C.

2. The A voters and the B voters, combined, add up to more than half of the
voters in the election.

3. The A voters and the B voters all prefer both A and B to C.

4. The A voters are more numerous than are the B voters.

5. Voting is sincere, except that the B voters refuse to vote A over anyone.

6. Candidate A would be the unique winner under sincere voting (...in other
words, if the B voters voted sincerely, as do all the other voters).

7. The C voters are indifferent between A and B, and vote neither over the
other.

*Requirement:*

B doesn't win.

[end of CD definition]


------------------------------

In the chicken dilemma scenario described in the premise of the Chicken
Dilemma Criterion (CD) defined above, if B won, then the B voters would
have successfully taken advantage of the A voters' co-operativeness. The A
voters wanted to vote both A and B over the candidates disliked by both the
A voters and B voters. Thereby they helped {A,B} against worse candidates.
But, with methods that fail CD, the message is "You help, you lose".
------------------------------

*Some methods that pass the Chicken Dilemma Criterion:*

ICT, Symmetrical ICT
<http://wiki.electorama.com/wiki/Symmetrical_ICT>,
MMPO<http://wiki.electorama.com/wiki/MMPO>,
MDDTR, IRV <http://wiki.electorama.com/wiki/IRV>, Benham's
method<http://wiki.electorama.com/w/index.php?title=Benham%27s_method&action=edit&redlink=1>,
Woodall's method <http://wiki.electorama.com/wiki/Woodall%27s_method>
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