[EM] Re: [Fwd: Election-methods digest, Vol 1 #520 - 13 msgs]

[Ken Johnson]

> --__--__--
>
> Message: 9
> Date: Fri, 27 Feb 2004 01:56:49 -0500 (EST)
> Subject: Re: [EM] Re: EM] There's nothing wrong with Average Rating.
> From: "wclark at xoom.org" <wclark at xoom.org>
> To: election-methods at electorama.com
> Reply-To: wclark at xoom.org
>
>
>> It was my understanding that Arrow's theorum does apply to CR.  Actually
>> it applies to Approval as well, it's just that Approval meets all of the
>> conditions except allowing voters to rank three or more choices in
>> order.
>
>
> It was my understanding that Arrow's theorem only applies to ordinal
> methods, and not to cardinal methods.  At least, I've never seen a proof
> that didn't require ordinal-only ranking.
>
> I believe Arrow's own formulation was restricted to dealing only with
> social choice functions over preference *orderings*, without any 
> reference
> to the intensity of preference (i.e. cardinality.)  It's been a while
> since I actually looked at his (1951) though.
>
> I'm sure somebody else on the list will know for certain what the facts
> are here... I'll start digging through the archives to see if this has
> come up before.
>
> -Bill
>
>
I get a little irritated of hearing this mantra over and over - "Arrow 
proved that no voting system is 'perfect'". Usually the statement is 
made categorically, with no qualification regarding "ranked preferences" 
or anything (e.g., see the March Scientific American article).

I wish someone would put this issue to rest once and for all: Is CR (or 
Approval) an "ideal" voting method according to Arrow's criteria or is 
it not? If it is, then the "Arrow proved ..." assertion is patently 
false and should be recognized as such. Although Arrow limited his 
analysis to ranked preference methods, it certainly makes sense to ask 
the question in the broader context of CR and Approval, and I'd like to 
see some clarification on this issue.

Ken Johnson