[EM] Arrow's axioms

[Kevin Venzke]

Ken,

 --- Ken Johnson <kjinnovation at earthlink.net> a écrit : > 
> >This is like saying "There may be good reasons why Random Ballot should be
> >rejected as a viable election method, but Arrow's premises don't elucidate
> >those reasons because if the theorem were generalized to encompass dictatorship
> >methods, its conclusion would be that non-dictatorial methods cannot satisfy
> >the axioms whereas Random Ballot can."
> >
> >I hope it's evident why this is a strange way of speaking.
> >
> 
> It isn't evident. It is reasonable to stipulate non-dictatorship 
> axiomatically because this principle is non-controversial and nobody is 
> championing dictatorship as a viable election method.

I should have been clearer.  You said that "if the theorem were generalized 
to encompass cardinal methods, its conclusion would be that rank methods cannot 
satisfy the axioms whereas CR can."  This is strange because Arrow's conclusion
*already* includes that non-rank methods could meet all of *the other three*
axioms.

That's what I was getting at with my response.  Arrow's conclusion already says
that dictatorial methods can meet *the other three* axioms, and non-paretian
methods can meet the other three, and IIA-failing methods can meet the other
three...

So it's not clear what you mean by "if the theorem were generalized to encompass
cardinal methods."

> On the other hand, 
> if the objective of elections is to maximize "social utility", then CR 
> probably represents the simplest and most natural way to measure (or at 
> least define) social utility, and it should not be excluded from 
> consideration axiomatically.

Do you think Arrow has "excluded [CR] from consideration axiomatically" by showing 
that a ranked method can't meet the other three axioms?  What methods do you think he 
has not excluded axiomatically?


Kevin Venzke
stepjak at yahoo.fr



	

	
		
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