[EM] Does the 'Independence of Irrelevant Alternatives Criterion' Imply a

Forest Simmons fsimmons at pcc.edu
Mon Apr 5 15:27:02 PDT 2004

On Fri, 2 Apr 2004, James Green-Armytage wrote:

> Forest wrote:
> >If you look up the recent thread on the neural network approach to
> >democracy, you will see that not all list members subscribe to your
> >transitive preference axiom.
> >It's perfectly possible for a brain to be wired or programmed by genetics
> >or experience so that someone prefers red to green, green to blue, and
> >blue to red.  To over simplify, suppose that two thirds of your neurons
> >prefer red to green, a different two thirds of your neurons prefer green
> >to blue, and yet a different two thirds of your neurons prefer blue to
> >red.
> >Human individuals are composites, not atoms.
> >Your axiom might be a useful approximation to reality, but like most
> >axioms, it isn't an absolute truth.
> James replies:
> 	Agreed. But basically there is no reason for a voting system to
> accommodate people with intransitive preferences, since a person
> expressing such preferences is either very poorly informed and forgetful
> or strategically motivated. If anyone really takes the time to think about
> their preferences between a set of options, they can be expected to come
> up with a transitive ranking. So yes, it is an axiom which we should
> accept for the purpose of voting methods design.

Mostly agreed.  The main benefit of assuming transitivity of preferences
is in allowing Condorcet to be done with an ordinary ranked ballot instead
of requiring voters to indicate their preference in all N*(N-1)/2 pairs of

This is a convenience that is probably worth the cost of not allowing full
expressivity of non-transitive preferences.

If requiring individuals to submit transitive ballots were sufficient to
preclude Condorcet Cycles, then the requirement would have a more solid
justification. But, as we know, that "If" clause is not satisfied.


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