[EM] IIA Theory

[Craig Carey]

At 16:54 08.10.99 , David Catchpole wrote:

...
>Non passarin. I don't get the reference to Iraq and you should already see
>that Schultz-IIA per se also fails the same example.




It was not just your IIA and Schulze's rules that were failed by the
 IIA rule, but also my proof that the rule passed IFPP with 3 candidates.



Correction:  My 3 candidate IFPP is failed by Schulze's IIA rule.
----------   The proof is the example below. The error in my previous
 6-7 October 1999 proof was the 2 terms on both sides of the inequality
 that was supposed to be the solution to the 2 [two] candidate smaller
 election.


>I've already said that for many examples the rule may not possibly be 
>satisfied.


The situation is probably going to be that both your IIA rule and
 Mr Schulze's fails ALL practical preferential voting methods that it
 is imposed against. 



AN EXAMPLE SHOWS IIA FAILS METHOD(S) WHEN IT OUGHT NOT


>IIA's not a general criterion -- the criterion which it applies to an
>electoral system is that _where_ it may be satisfied, it should be. For ye
>olde paradox of voting, we can't find an IIA (neither Schultz nor
>otherwise) result without completely subverting majority rule.

... [Omitted: W is the method. So writing W'...]


The method that has a proven record at failing IIA
 (found this week using a small REDUCE program)


>> Here's an example which both STV & IFPP agree, and which the rule
>>  fails:
>> 
>> A. 2
>> BC 2
>> CA 1
>

: Apply the rule: since B is a loser the removal of all preferences
:  for B (i.e. removal of candidate B) should not cause A to flip from
:  being a winner to a loser. Unfortunately for the rule, it does.

: A. 2
: C. 3

About all methods: C wins.

...

>This will always fail to satisfy "Schultz-IIA" too. Say A won A vs. B vs.
>C? "Schulze-IIA" says that because A wouldn't have won had B not stood, A
>should not win. What about B winning the 3 candidate race? No, "S-IIA"
>says that because B wouldn't have won had C not stood, B should not win.
>Okay, how about C? Same problem.
>
>Just because IIA as a specific rule on an election schema may not be
>satisfied does not mean that it is not a useful principle where it may be.
>This has been the point of my past umpteen e-mails.

All the 2 submitted of IIA tested have failed IFPP

How are you going to modify it. To make it not apply in those regions
 where it fails IFPP, for example, would lead to a complex formula.

To partially apply an unmodified IIA rule, can be the same a strictly
 applying a improved version.

However, I presume it would be wanted to the have vote alteration
 effects constraints rule(s) simple. Such rules ought not cover tens of
 pages of paper at any time, as the number of candidates tends towards
 being infinite.

It seems to me that the rejection of IIA indicates that preferential
 voting theory is not in any true and broad sense, a part of
 'social decision theory' (or whatever that realm of ideas is called).

[IIA might now be uninteresting (like pairwise comparing)


====================================================================

At 18:09 08.10.99 , Bart Ingles wrote:
>DEMOREP1 at aol.com wrote: 
>[...]
>> I mention again that (A) an election is held for a time period using the
...
>(A) Proponents of systems which break the field of candidates into pairs
>(or larger subsets) for comparison, i.e. ranked systems, seem to try to
>avoid any assumptions whatever about the overall field, instead relying
>on criteria such as IIA to make sure the method is not overly
>self-contradictory.  Any comparisons between candidates or groups of
>candidates are considered relative.

Which IIA passes Condorcet?. Is it the same as the other two?.
Pairwise comparison of candidates in "groups" of candidates is not
 "obviously desirable" (referring to Condorcet).

.....
>Bart


PS. Correction: 5/6 = 1.6666... (no e-mailed me over that).


This message was delayed in my e-mail reader.

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Mr G. A. Craig Carey                   E-mail: research at ijs.co.nz
Auckland, Nth Island, New Zealand
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