[EM] A four bit (sixteen slot) range style ballot

[Kevin Venzke]

Hi Abd,

The best way to decide how to apply rank ballot criteria to Approval is to
have a framework for all methods into which you can translate Approval.
People may not agree with you but at least it's clear what you have done.

--- En date de : Ven 11.6.10, Abd ul-Rahman Lomax <abd at lomaxdesign.com> a écrit :
> My contention there was that Approval Voting satisfies the
> Majority Criterion if Plurality satisfies the criterion.

But you say this and then quote Woodall's Majority criterion, which
Plurality fails?

> The contrary argument, if I can summarize it, is that if a
> majority of voters prefer A to B, but actually vote for both
> A and B, then it is possible that B wins if some other
> voters only vote for B. The wording of the criterion by
> Woodall is
> 
> > * Majority. If more than half the voters put the same
> set of
> > candidates (not necessarily in the same order) at the
> top of their
> > preference listings, then at least one of those
> candidates should be elected.
> 
> The way this criterion is worded, Approval satisfies the
> criterion based on actual votes, but not necessarily based
> on internal preferences, for that majority might, for
> example, all prefer A to B but actually vote for A and B.

But within Woodall's framework, all methods have to be interpreted as
rank. Woodall uses an interpretation of Approval so that it will fit in
his framework. You don't have to use that interpretation. But arguing 
about whether a method satisfies a Woodall criterion without any attempt
to stay within Woodall's framework seems futile.

Kevin Venzke