[EM] Relevance of Consistency

[Forest Simmons]

Some Condorcet devotees disparage the Consistency Criterion only because
no Condorcet method can satisfy it.  Others do not disparage it, but
reluctantly let go of it for the same reason.

But Condorcet (unlike IRV) methods are very close to the boundary of the
set of methods that do satisfy the Consistency Criterion.

Here's what I mean:

The Consistency Criterion is of the form

If (hypothesis), then (conclusion),

where the two main clauses are

(1) hypothesis: the method picks candidate A when restricted to either set
of ballots B1 or B2,

and

(2) conclusion: the method picks candidate A when applied to the combined
set of ballots B1 union B2.

Now suppose that candidate A is the CW in both subsets B1 and B2.  Then
candidate A is the CW of the union.  So Condorcet methods have a kind of
partial consistency in the spirit of the Consistency Criterion.

Only in those cases where at least one of the subsets (of the CC
hypothesis) has no CW is (the conclusion of) the Consistency Criterion
violated.

But when one or more subsets is indecisive, i.e. does not give definite
support to any opinion as to which candidate should win, we should not be
surprised if the over all outcome disagrees with a common subset outcome
whose commonality was just a statistical fluke.

Condorcet methods are "borderline consistent" while (as the examples show)
IRV is not.

Forest


On Mon, 4 Nov 2002, Blake Cretney wrote:

> On Sun, 2002-11-03 at 21:28, MIKE OSSIPOFF wrote:
>
> > Consistency, like a number of other criteria, is relevant to how
> > well a voting system reflects the electorate's wishes. Say a candidate
> > wins in each district. If he wins in each district, there's a
> > meaningful sense in which he can be called the people's choice in
> > each district. One hopes that the result, when a set of ballots is
> > counted, in some way represents what those people want. So then
> > we count the whole set of ballots systemwide, and that candidate
> > loses. If there's some way in which the outcome in the districts
> > can be called the people's choice, representative of what they want,
> > then how can we say that about the systemwide result? The voting
> > system has acted inconsistently. That's all the criterion is saying.
>
> The argument seems to be that if X wins a district under method M, than
> method M says that X is the choice of the district.  It makes sense to
> think of districts as having choices, and method M says that it is
> candidate X.  If X wins in every district, then we can look at X as the
> unanimous choice of the districts (according to M), and therefore X
> should win (if M is being consistent).
>
> The argument takes the convenient phrasing (that a group chooses a
> candidate) and interprets this as if it were literally true that groups
> have choices.  They don't.  Neither do districts.  Nor is there really a
> people's choice in a district.  Some people choose one thing, some
> another.  Of course, you could define people's choice so that it means
> the winner under a particular method.  But that doesn't mean that you
> can treat the voters as if they were all just participants in a group
> opinion.
>
> ---
> Blake Cretney (http://condorcet.org)
>
>
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