From: David Stretch
Newsgroups: sci.math
Subject: Re: Voting theorem
Date: 24 Nov 1997 21:42:09 -0000
In article <19971124205800.PAA12003@ladder02.news.aol.com>,
AHPep wrote:
>[request for info on Arrow's work om voting]
You may like to try to get hold of the following books:
Kelly, J.S. (1978). _Arrow impossibility theorems._ NY: Academic
Press. ISBN: 0-12-403350-4.
MacKay, A.F. (1980). _Arrow's theorem: the paradoc of social choice: a
case-study in the philosophy of economics._ New Haven, NY: Yale
University Press. ISBN: 0-300-02450-9.
Colman, A.M. (1995). _Game theory and its application in the social
and biological sciences._ Oxford: Butterworth Heinemann. (2nd
Edition). ISBN: 0-7506-2369-1.
I can't recall the details of the theorem, and my books dealing with
the issue are not easily to hand, nor will be for a few days. However,
I do know that Andrew Colman's book deals with the theorem at a very
practical level, as well as describing voting paradoxes in a wider
context (The weak and strong Borda effect, Condorcet effects,
etc)---particularly the issues of transferable votes, and similar. It
might be useful for you. I hope this helps.
--
David D Stretch: Greenwood Institute of Child Health, Univ. of Leicester, UK.
Lecturer in Mathematical Psychology. Phone:+44 (0)116-254-6100
dds@leicester.ac.uk http://www.leicester.ac.uk/CWIS/AD/GWINST/greenwood.html
==============================================================================
From: Scott Vaughen
Newsgroups: sci.math
Subject: Re: Voting theorem
Date: Tue, 25 Nov 1997 18:58:35 -0800
Ken Arrow wrote the "Impossibility Theorem" in the the 50s or 60s.
It says that if there are 3 or more choices there is no way to guarantee
the population will be able to elect their "true" preference.
I learned a lot on this from a book called Excursions in Modern
Mathematics by Peter Tannenbaum and Robert Arnold from Prentice Hall.
Another very closely related topic would be apportionment . I wrote some
extra credit material for my high school students to use on both Arrow's
theorem and on apportionment. You will find lots of info on the
"paradoxes in apportionment" on my website.
http://www.gate.net/~svaughen
One of these days, I want to put info on the voting theorem on the page,
too.
The section on my webpage on apportionment paradoxes has to do with
strange things that have happened as the government has tried to
appropriately apportion the number of seats in the House of
Representatives.
It seems this would be very appropriate to your discussion on
"proportional representation"
-Scott
AHPep wrote:
>
> I am preparing for a discussion on proportional representation and remember
> vaguely a theorem by (Ken Arrow?) in the 1950s(?) stating that no system
> of voting can be devised that complies with a small set of reasonable
> constraints.
> I would appreciate pointers to this, especially a statement of the constraints.
>
> Thanks in advance.
>
> Andy Pepperdine
> ahpep@aol.com
==============================================================================
From: NoJunkMail@this.address (Gerry Myerson)
Newsgroups: sci.math
Subject: Re: Voting theorem
Date: Tue, 25 Nov 1997 09:27:32 +1100
In article <19971124205800.PAA12003@ladder02.news.aol.com>, ahpep@aol.com
(AHPep) wrote:
=> I am preparing for a discussion on proportional representation and remember
=> vaguely a theorem by (Ken Arrow?) in the 1950s(?) stating that no system
=> of voting can be devised that complies with a small set of reasonable
=> constraints.
=> I would appreciate pointers to this, especially a statement of the
=> constraints.
See the textbook by Alan D Taylor, Mathematics and Politics, Springer 1995.
Gerry Myerson (gerry@mpce.mq.edu.au)