[EM] Arrow's axioms
Philippe Errembault
phil.errembault@skynet.be
Fri Mar 5 15:02:05 2004
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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.
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.
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)
Philippe Errembault
----- Original Message -----=20
From: Ken Johnson=20
To: election-methods-electorama.com@electorama.com=20
Sent: Friday, March 05, 2004 7:34 PM
Subject: [EM] Arrow's axioms
Date: Thu, 4 Mar 2004 23:27:06 +0100 (CET)
From: =3D?iso-8859-1?q?Kevin=3D20Venzke?=3D <stepjak@yahoo.fr>
Arrow's axioms could well be justifiable, but his proof doesn't =
provide=20
the justification. There may be good reasons why CR should be rejected=20
as a viable election method, but Arrow's premises don't elucidate those=20
reasons because if the theorem were generalized to encompass cardinal=20
methods, its conclusion would be that rank methods cannot satisfy the=20
axioms whereas CR can.
=20
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
=20
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
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<DIV><FONT face=3DArial size=3D2>Arrow's axioms do NOT apply to real =
world,=20
since he wants to make ranked results from ranked individual =
choices, while=20
strict ranking of preferences is incompatible with human=20
nature.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>We all would find very difficult to =
make a strict=20
and fixed order of preference between different choices. All =
preference are=20
based on multidimensionnal criterions, and to order them you must =
choose=20
a ponderation, which are by the human nature NOT fixed. In those=20
conditions, making an election is not more than multiplying the number =
of=20
dimensions by the number of voters. So, I see no reason why we should =
restrict=20
to a strict preference order in the community choice, if we are not =
able to=20
make it in an indiviual choice.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT><FONT face=3DArial =
size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>I'm currently working on a fully =
different way of=20
implementing democracy. This idea is not based on a vote system as we =
know it,=20
and is much more repectful of human nature. There are still a few =
problems with=20
it, but it would solve many of the problems with the election =
systems.=20
(it works a little like a neural structure)</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>Philippe Errembault</FONT></DIV>
<BLOCKQUOTE=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style=3D"FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV=20
style=3D"BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>=20
<A title=3Dkjinnovation@earthlink.net=20
href=3D"mailto:kjinnovation@earthlink.net">Ken Johnson</A> </DIV>
<DIV style=3D"FONT: 10pt arial"><B>To:</B> <A=20
title=3Delection-methods-electorama.com@electorama.com=20
=
href=3D"mailto:election-methods-electorama.com@electorama.com">election-m=
ethods-electorama.com@electorama.com</A>=20
</DIV>
<DIV style=3D"FONT: 10pt arial"><B>Sent:</B> Friday, March 05, 2004 =
7:34=20
PM</DIV>
<DIV style=3D"FONT: 10pt arial"><B>Subject:</B> [EM] Arrow's =
axioms</DIV>
<DIV><BR></DIV><BR>
<BLOCKQUOTE =
cite=3Dmid20040305072505.10481.79506.Mailman@geronimo.dreamhost.com=20
type=3D"cite"><PRE wrap=3D"">Date: Thu, 4 Mar 2004 23:27:06 +0100 =
(CET)
From: =3D?iso-8859-1?q?Kevin=3D20Venzke?=3D <A =
class=3Dmoz-txt-link-rfc2396E =
href=3D"mailto:stepjak@yahoo.fr>"><stepjak@yahoo.fr></A>
</PRE>
<BLOCKQUOTE type=3D"cite"><PRE wrap=3D"">Arrow's axioms could well =
be justifiable, but his proof doesn't provide=20
the justification. There may be good reasons why CR should be rejected=20
as a viable election method, but Arrow's premises don't elucidate those=20
reasons because if the theorem were generalized to encompass cardinal=20
methods, its conclusion would be that rank methods cannot satisfy the=20
axioms whereas CR can.
</PRE></BLOCKQUOTE><PRE wrap=3D""><!---->
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
</PRE></BLOCKQUOTE><BR>Kevin,<BR><BR>It isn't evident. It is =
reasonable to=20
stipulate non-dictatorship axiomatically because this principle is=20
non-controversial and nobody is championing dictatorship as a viable =
election=20
method. On the other hand, if the objective of elections is to =
maximize=20
"social utility", then CR probably represents the simplest and most =
natural=20
way to measure (or at least define) social utility, and it should not =
be=20
excluded from consideration axiomatically.<BR><BR>Ken=20
Johnson<BR><BR></BLOCKQUOTE></BODY></HTML>
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