Normative principles of elections- Condorcet and Irrelevance of Alternatives (plus a brief hello and an STV clarification)

[Blake Cretney]

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On Thu, 27 Aug 1998 09:17:34   David Catchpole wrote:
>On Wed, 26 Aug 1998, Mike Ositoff wrote:
>
>I guess it's hard to always have everyone agreeing, but I believe the
>criterion of irrelevant alternatives actually does allow for the criteria
>below.
>
>The fact is that if a Condorcet winner exists, that winner
>satisfies IA, and vice versa. This is a good point about Condorcet,
>in case people are just being defensive without provocation.
>
>I personally disagree with the vagueness of just plain "majority rule", 
>believing that more focused principles of majority rule need to be
>developed. As for the concept of strategy- IA has a large-scale
>positive effect on the behaviour of actors in an election.
>
>I would appreciate it if you gave me examples of IA contradicting other
>ubiquitous criteria, as I am a relative newcomer to the "field"; however, I
>believe that the concept of IA itself is a particularly dominant one- that
>the outcome of the election reflects the values of the electorate 
>independent of the presence of any losing candidates.
>
IA, which I will call IIAC, is not possible.
Consider this example.

Ballots cast
45 A B C
35 B C A
20 C A B

Let's assume your favorite method chooses A as the winner.
This means that B should be irrelevant.  So let's take it
out and see what the result is.
45 A C
35 C A
20 C A

That is 45 A>C 55 C>A.  Based only on these votes, it would
be absurd to choose A as the winner over C.  So we have to
conclude that any method that would choose A, does not
satisfy IIAC.

But what about systems that would choose B.  That means C is
irrelevant.

45 A B
35 B A
20 A B

So 65 A>B 35 B>A.  A is the obvious winner.  So we have to
conclude that any method that would choose C, does not
satisfy IIAC.

But what about systems that would choose C.  That means A is
irrelevant.

45 B C
35 B C
20 C B

So 80 B>C 20 C>B.  B is the obvious winner.  So we have to
conclude that any method that would choose C, does not
satisfy IIAC.

So in fact no method will satisfy IIAC.
By the way, the criterion I was relying on which
contradicted IIAC was that if there are only two candidates,
the one with the most votes should win.  I think that's
called Paretto.  In fact, I suspect assuming Paretto is not
really necessary, and that it would be possible to construct
examples that showed that for a method that gives a victory
to certain levels of minority, it would have to give a
different answer to the same level of minority in a
different case.  The only real assumption is that you're
doing something that can be reasonably called voting.

I think the best you can do is MIIAC, the Modified
Independence from Irrelevant Alternatives Criterion, which
says that a candidate is irrelevant if it is not in the
Smith set.  This will likely make the bulk of candidates,
especially unpopular ones, irrelevant.  As a result, your
chances of losing out because you vote sincerely are low,
and even if you wanted to vote insincerely it would be hard
to predict how to do this effectively.



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