[EM] Markus: Demonstration that Benham & Woodall meet CD
email9648742 at gmail.com
Thu Jan 9 11:15:29 PST 2014
CD can be regarded as a weaker special case of Later-No-Harm (LNHa).
LNHa can be regarded as a stronger generaliztion of CD.
All methods that meet LNHa meet CD. The reverse isn't true.
IRV meets LNHa, in addition to CD.
IRV, Benham, and Woodall meet CD.
On Thu, Jan 9, 2014 at 12:24 PM, Vidar Wahlberg <canidae at exent.net> wrote:
> 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.
> > 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
> > 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
> > 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
> > 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
> > 6. Candidate A would be the unique winner under sincere voting (...in
> > 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
> > 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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