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

Michael Ossipoff email9648742 at gmail.com
Thu Jan 9 12:46:54 PST 2014

```On Thu, Jan 9, 2014 at 3:05 PM, Markus Schulze <
markus.schulze at alumni.tu-berlin.de> wrote:

> Dear Mike Ossipoff,
>
>
> > It merely means that an example in which method M wouldn't
> > elect candidate A under sincere voting is an example to
> > which CD doesn't apply. It's an example that says nothing
> > about whether  M meets CD.
>
> But then also plurality voting satisfies the Chicken Dilemma
> Criterion.
>
>
>
No, Plurality doesn't satisfy CD.  CD doesn't apply to Plurality. Plurality
neither passes nor fails CD, because it isn't possible to write a Plurality
example that satisfies CD's premise. Here's why

Say the method is Plurality.

Everyone votes sincerely, except that the B voters refuse to vote A over
anyone. But, sincere voting in Plurality doesn't require the B voters to
vote A over anyone. The balloting system in use wouldn't allow them to do
preferences for B over everyone). So far, so good. No problem yet.

More A voters than B voters. More C voters than A voters, A voters and B
voters all prefer A and B to C. C voters not voting between A and B (That's
not insincere in Plurality)--We can write an example in which all of the
above condtions are met. I don't have a copy of the criterion in front of
me, it appear, so far, that all of CD's premise conditions can be met in a
Plurality example.

Can we write an example in which A would win under sincere voting. No. Not
if we want to meet the other premise conditions. With sincere voting (and B
voters refusing to vote A over anyone, which isn't insincere in Plurality,
everyone gives their Plurality vote to their favorite, and so C must win.

So CD doen't apply to Plurality. Plurality neither passes nor fails CD.

That's ok with me.

Could CD be reworded so that Plurality would fail? Without making the
criterion wordier or more complicated? If so, Ii wouldn't object.
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