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

Juho Laatu juho4880 at yahoo.co.uk
Thu Jan 9 11:21:00 PST 2014

Few requests to make the definition precise.

1) You should define what "falsifying a preference" means. I have seen different uses on that term on the EM list. If the voter feels "A>B" but votes "A=B" or if the voter feels "A=B" but votes "A>B" a falsification, or are all differences in preferences and voted rankings falsifications? I note that you excluded the case where the elecion does not allow the voter to express all hies/her preferences. Here I thus mean the case where the voter can express all his/her preferences.

2) What does "B voters refuse to vote A over anyone" mean? Does that mean not ranking A at all (=not mentioning A in the ballot) if that possibility exists, and otherwise ranking A last (on the ballot)? Is it ok to rank A tied last (on the ballot) when it would be possible to rank also A last alone (on the ballot)? Is it ok to rank A last (on the ballot) even if one could leave A unranked (=not mentioned in the ballot)?

3) What does "C voters are indifferent between A and B, and vote neither over the other" mean? Does that allow e.g. votes 100: C>A>B, 100: C>B>A?

Juho

On 9.1.2014, at 18.39, Michael Ossipoff <email9648742 at gmail.com> wrote:

> 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, MMPO, MDDTR, IRV, Benham's method, Woodall's method
>
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info

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