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

Vidar Wahlberg canidae at exent.net
Thu Jan 9 09:24:42 PST 2014

On Thu, Jan 09, 2014 at 11:39:38AM -0500, Michael Ossipoff wrote:
> *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]

What's the difference between this and the later-no-harm criterion?

"The criterion is satisfied if, in any election, a voter giving an
additional ranking or positive rating to a less-preferred candidate
cannot cause a more-preferred candidate to lose".

Vidar Wahlberg

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