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

[Kevin Venzke]

Hi Abd,

--- En date de : Sam 12.6.10, Abd ul-Rahman Lomax <abd at lomaxdesign.com> a écrit :
> > 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?
> 
> Plurality allows voters to place a candidate at the "top of
> their preference listings." 

That is inadequate to satisfy the criterion, which refers to candidates
plural. Woodall's Majority is equal to what has been called "Mutual 
Majority" on this list.

>Does Plurality fail Woodall's
> Majority Criterion? That depends on interpretations. 

Again, is there any reason to try to use Woodall's criteria if you won't
try to use it within Woodall's framework?

>The
> criterion was not designed and defined well enough to be
> sure. 

The criterion is unambiguous if you apply it in the context intended,
which defines the terms the criterion is using. If you're trying to use
this criterion when making a sandwich or fixing your car then you can't
expect that the definition will be clear as written.

>What is a "preference listing"?

A quote? Ok:

>As is usual in the Social Choice literature, I shall use lower-case 
>letters a, b, c,... to denote candidates (or choices). Each voter casts a 
>ballot containing a preference listing of the candidates, which is written 
>as (for example) abc, to denote that the voter places a first, b second 
>and c third, with no fourth choice being expressed. A preference listing 
>is complete if all candidates are included in it and truncated if some are 
>left out. (A preference listing that leaves out just one candidate will be 
>treated by most election rules, including STV, as if it were complete; but 
>one should not call it complete, since some election rules may not treat 
>it as such.) A profile is a set of preference listings, such as might 
>represent the ballots cast in an election. Profiles may be represented in 
>either of the forms shown for Elections 1 and 2 below, indicating either 
>the proportion, or the absolute number, of ballots of each type cast. 

> > > 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.
> 
> Basically, the term "Majority Criterion" went on to be used
> by others in various ways, with various definitions and
> interpretations.

Is it the *definition* or the *term* which matters to you? If I were
writing to any other person I would just assume it must be the definition,
in which case Woodall's criterion is not relevant, because it's equal
to "Mutual Majority," not what we usually call "Majority."

> I think you may know that my position on "voting systems
> criteria" in general is that they are a failed attempt to
> create objective standards for comparing voting systems.

Yes, I know that.

Kevin Venzke