[EM] Arrow's axioms

[Ernest Prabhakar]

On Mar 5, 2004, at 5:45 PM, Philippe Errembault wrote:

> Arrow's axioms do NOT apply to real world, since he wants to make 
> ranked results from ranked individual choices, while strict ranking of 
> preferences is incompatible with human nature.

Hi Philippe,

I'm not sure I understand your point.  My impression was that Arrow's 
theorem also applied to systems with partial orderings, i.e., where I 
could say A > B = C > D.

> We all would find very difficult to make a strict and fixed order of 
> preference between different choices. All preference are based on 
> multidimensionnal criterions, and to order them you must choose 
> a ponderation, which are by the human nature NOT fixed. In those 
> conditions, making an election is not more than multiplying the number 
> of dimensions by the number of voters. So, I see no reason why we 
> should restrict to a strict preference order in the community choice, 
> if we are not able to make it in an indiviual choice.

Umm, I'm not sure I agree with that, at least assuming we allow 
equal-ranking.  While our overall impressions and feelings about 
something are indeed complex and multi-dimensional, we are usually able 
to collapse that into a single dimension given a sufficiently 
well-defined questions.   My feelings about different types of cuisines 
is fairly complex, but when asked at a particular time (like now) I can 
rank them as Chinese > Indian > Mexican = Thai  > American.  I do find 
the dyadic (?) approach (A > B >> C) interesting, though.

In fact, I see the role of elections as precisely to generate that kind 
of concrete result from various fuzzy issues.

It is rather like quantum wave functions.  By themselves, they're very 
fuzzy and indeterminate.   However, as soon as you force a decision, 
you end up with a linear list of probabilities (in fact, some 
scientists like Roger Penrose argue that this is actually what a human 
decision is).

> I'm currently working on a fully different way of implementing 
> democracy. This idea is not based on a vote system as we know it, and 
> is much more repectful of human nature. There are still a few problems 
> with it, but it would solve many of the problems with the election 
> systems. (it works a little like a neural structure)

Sounds interesting, but my suspicion is that neural systems are 
notoriously non-deterministic.  At some point, we have to have a binary 
decision: Yes or No for a particular candidate.  I'd rather keep my 
non-determinism in the human brain, and have my election method as 
deterministic as possible [save for random-factors needed to ensure 
clone independence when breaking ties].

Or, are you in fact not arguing against the *method* of elections, but 
against the very idea of a single unambiguous winner?  Is the goal to 
create some sort of gestalt of public opinion, which authorizes a 
particular individual to perform a specific function based on their 
accordance with expressed ideals?

-- Ernie P.


>  
> Philippe Errembault
> ----- Original Message -----
>  From: Ken Johnson
> To: election-methods-electorama.com at electorama.com
> Sent: Friday, March 05, 2004 7:34 PM
> Subject: [EM] Arrow's axioms
>
>
>
> Date: Thu, 4 Mar 2004 23:27:06 +0100 (CET)
> From: =?iso-8859-1?q?Kevin=20Venzke?= <stepjak at yahoo.fr>
>
> Arrow's axioms could well be justifiable, but his proof doesn't provide
> the justification. There may be good reasons why CR 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 cardinal
> methods, its conclusion would be that rank methods cannot satisfy the
> axioms whereas CR can.
>
>
> 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.
>
> Kevin Venzke
>
>
> Kevin,
>
> 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. 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.
>
> Ken Johnson
>