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

[David Catchpole]

My point exactly- you fail to acknowledge that no Condorcet winner exists
for the following system (and therefore that IA is not satisfied for
any outcome from that case). To say that it does not exist for all cases
is a bit silly.

I actually stated that where Condorcet winners do not
exist, IA cannot be satisfied; but that where they do, it does where they
are elected.

See below for the Condorcet bit.

(PS from now on I'll stay on with convention and call this IIA. I already
stuffed up calling monotonicity homogeneity or something like that)


On Wed, 26 Aug 1998, Blake Cretney wrote:

>  
> --
> 
> 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.
> >w
> >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

 A to B- A
 A to C- C
 B to C- B

A paradox of voting exists- No Condorcet winner exists in this case and
therefore IA is not satisfied: QED. My point exactly.

That one can say from this one anecdote that IA NEVER exists for any
other elections is fanciful.

> 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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