[EM] Re: Arrow's axioms

[Gervase Lam]

> From: "Steve Eppley"
> Date: Wed, 03 Mar 2004 06:58:22 -0800
> Subject: Arrow's axioms (was Re: [EM] Re: [Fwd: Election-methods digest,
> Vol 1 #525 - 9 msgs])

> By Arrow's
> time, they'd learned that, lacking mind-reading
> technologies, they couldn't elicit cardinal utilities that
> could be compared between individuals, for instance to
> compare the utility difference between your "100" candidate
> and your "0" candidate to the utility difference between my
> "100" candidate and my "0" candidate.  Simply summing our
> reported numbers, which don't have units (such as dollars)
> attached, would not help them find which alternative had
> the greatest utility.  If each voter is constrained to
> assign numbers within a given range, such as 0 to 100, then
> the sum would not be the utilitarian sum.

OK.  This makes me understand why it says in Wikipedia that 'economists' 
abandoned Cardinal Utility in favour of Ordinal Utility (i.e. ranking).  
Nevertheless, some of the information that you get from Cardinal Utility 
disappears when it is converted to a ranking.

So, couldn't the shortcoming with Cardinal Utility be alleviated by using 
a "mark out of 100" instead of a Cardinal Rating out of 100?  That is, 
only a candidate who is perfect in EVERY way to a voter would be given a 
mark of 100.  Basically, only an omnipotent candidate could achieve this.  
At the other extreme, only a candidate of EXTREME badness in EVERY way to 
a voter would be given a mark of 0.

I suppose what I am saying here is may be a Cardinal Rating method should 
be used.  However, each voter's best candidate is not given 100.  Nor is 
each voter's worst candidate given 0.  The best and worst candidates are 
given a mark that depends on how good they are.  (This is why I personally 
think that somehow a distinction should be made between Cardinal Ratings 
and Cardinal Utilities).

Thanks,
Gervase.