[EM] Arrow's Theorem.

[Craig Carey]

At 2003-07-15 00:33 -0400 Tuesday, Eric Gorr wrote:
>At 6:39 PM -0400 7/14/03, Rob Speer wrote:
...
>Borrowing the defintion of IIA from:
>
>http://www.wikipedia.org/wiki/Independence_of_irrelevant_alternatives
>if one option (X) wins the election, and a new alternative (Y) is 
>added, only X or Y will win the election.
>
   http://www.condorcet.org/emr/criteria.shtml
...
>
>So, where did I go wrong?
>

Snooping around in false beliefs of Blake. Unlike lobbyists he
had a liking for untruth before that of publicity for the same,
to say an idea roughly.

A "candidate" is called both an "option" and an "alternative".
A first suspicions is that Mr Cretney wants to promote some untruth
by having that thing be a preference too, and he does exactly that
in the definition of monotonicity which has other defects too.

Has Mr Gorr got any other ideas that Dan Keshet and Blake Cretney
wanted him to know about, that he has some questions on ?. None
of those definitions can be improved: a fraction are contrary to
the truth that interested the Marquis de Condorcet (1745-1794)
and to only one Massachusetts Green party (of Sommervill and
Cambridge) [they never have true good reasoning]:
   http://www.massgreens.org/mrg

Evidently Mr Cretney can't be a person who actually jots down his
ideas on how he made a mistake in wording by confusing a
preference on a ballot paper with a politician.

It seems simple: Cretney has a mess advancing things that are
undefined and undesirable. What is Mr Gorr's problem: anonymity
stopping him finding out more ?. Mr Gorr was brighter and more
pro-IRV then he would not ask me question about principles for
mankind that are available from Green dominated publicity
operations.

This is full of false statements including the hard to remove
false claim that Approval is passed by Monotonicity: lies
throughout the whole webpage:

   http://www.condorcet.org/emr/criteria.shtml

I shall unsubscribe after writing this.


Regarding the useless rules of Blake that provide no light to
man or beast or historian:

 Cut The Gordian Knot; the knot of king Gordius of Phrygia was
 cut with the sword of Alexander the Great, so dictionaries say.

--------------------------------------------------------------------

Also I have some draft scribbles on the Arrow Theorem in reply
to Mr Shulze. I am going to unsubscribe now, so the great
thinkers here could track me down at
   http://groups.yahoo.com/group/single-transferable-vote


At 2003-07-15 09:51 +0200 Tuesday, Markus Schulze wrote:
>> I really want Approval to fail a condition of Arrow's
>> Theorem somewhere.
>
>Arrow's Theorem says that there is no preferential paretian
>non-dictatorial single-winner method that meets IIA.
>
>Approval Voting, Average Rating, Median Rating, etc. are no
>preferential methods.
>
>To be a preferential method, the method must be defined
>on every possible set of orders of merit and must not
>take more into consideration than just the orders of
>merit.
>
>Markus Schulze


* "Dictatorial[ness]" is not worded well at least in the derived
 definitions I've seen. The principle seems to be too weak and
 inconsistent with proportionality.

 If any used patch in the 'theorem' is not defined then the whole
 thing is not a theorem. A theorem is reasonable and in that
 inferences from premises are made.
 
 According to the e-mail of Mr Gorr, Mr K Arrow said at no date
 that Mr Gorr disclosed, which properly raises a question of whether
 the text allegedly by Arrow was forged) that it was a theorem
 ("the proof of the theorem"). Witness:

--------------------------------------------------------------------
At 2003-07-14 13:47 -0400 Monday, Eric Gorr wrote:
>At 10:20 AM -0400 7/14/03, Eric Gorr wrote:
>>At 10:18 PM -0700 7/13/03, Alex Small wrote:
...
>I decided to write to Dr. Arrow concerning this and got the following 
>message back:
>
>--
>Dear Mr. Gorr,
>
>Both statements are correct. The "monotonicity" condition together 
>with Independence of Irrelevant Alternatives, implies the Pareto 
>condition, which is the sufficient condition used in the "Vanderbilt" 
>version.  Actually, the monotonicity condition is used in the first 
>statement of the theorem (first edition of my book, SOCIAL CHOICE AND 
>INDIVIDUAL VALUES, 1951), while I used the Pareto condition in the 
>second edition (1963).  If one looks at the proof of the theorem in 
>the first edition, I showed that the monotonicity condition implied 
>the Pareto condition and then, in effect, derived the theorem from 
>the Pareto condition. The difference is, therefore, not very large.
>--
--------------------------------------------------------------------

 My argument would need to be done better than that, It may get
 rejected here is a place where people lie to each other on
 whether something is defined (to a usable state) or not. If Mr
 Lanphier distributed REDLOG programs then presumably that would
 change into Mr Lanphier complaining that no member but me would
 run the voting problem solving software.

* The Pareto rule malfunctions when there are 0 winners or the
number of winners is the number of candidates, and it does so
over the multiwinner First Past the Post method. Pareto is a
type of defective replacement for monotonicity and it seems to be
unable to pass even first past the post. Pareto is inconsistent
with itself since if it is AND-ed with itself and FOR-ALL-ed then
a False value results. 

* IIA is undesirable. It seems to be more that it stands against
 a needed meta-rule instead of being similar to some needed axiom.

* The idea that the theorem is important, would require the absence
 of that particular detail.

* Mr Schulze wrote vaguely:


>To be a preferential method, the method must be defined
>on every possible set of orders of merit and must not
>take more into consideration than just the orders of
>merit.

The word "more" would stand in for "less than" ("<") if there was
not that "not". A better idea might be list all the cases, whith
a new case for each new type of ballot paper, and have a new
wording for each. The Soc Choice definition creators may want to
cover up rules that sink and vanish under 8 vote elections, but
it is especially those that critics would want to have a look
at.

* It does not match up with STV ?
  + linearity: ruling out curves. (rule P2)
  + more refined decisions (an appended preference) does not upset
    what was done. A need to keep the decision making simple.
    (rule of truncation resistance).
  + etc.
Note that they are not in the theorem but are things of political
choosers of preferential methods.
 
Thus the Imposs theorem has got nothing to do with politics.
Thus a lack of results that politicians can use are not due to the
theorem.

They are aiming to be vague and then derive nothing so it is more
a topic that would interest the Election Methods List any of
mine.




Craig Carey
New Zealand
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