[EM] Arrow/IA/IIAC

[DEMOREP1 at aol.com]

Mr. Cretney's FAQ at
http://www.fortunecity.com/meltingpot/harrow/124/singfaq.html
has in part-
-----
What is an Irrelevant Alternative? 

According to Arrow, an irrelevant alternative is any that does not 
win. For example, in the following example, 
40 A B C 
25 B C A 
35 C B A
If A is declared the winner, then B and C are both Irrelevant 
Alternatives. Arrow suggested that irrelevant alternatives should not 
affect the result of the election. So, if A is the winner, A should 
still have been the winner, even if C did not participate. However, such 
an election would be 
40 A B 
60 B A 
A's winning is a very counter-intuitive result here. If, however, the 
method chooses B as the winner in the two-candidate case, then it has 
been affected by an irrelevant alternative. It should be pointed out 
that "irrelevant alternative" is a very loaded word, and it is not 
universally agreed that such candidates are irrelevant. 

***
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What is Arrow's Theorem? 

Using the above definition of an Irrelevant Alternative, Arrow suggested 
the criterion that no Irrelevant Alternative should affect the result of 
an election. This is called the Independence from Irrelevant 
Alternatives Criterion. 
In short, Arrow proved that no method can satisfy all of a number of 
reasonable sounding criteria. In particular no method can: 

1. Allow voters to rank candidates. 
2. Always choose the majority winner in a two-candidate race. 
3. Meet the Independence from Irrelevant Alternatives Criterion. 

This can be easily proven from the following example 
40 A B C 
35 B C A 
25 C A B 

The pair-wise results are: 
A over B, 65-35 
B over C, 75-25 
C over A, 60-40
It is clear that no matter which candidate we choose as winner, IIAC 
should allow us to hold a pair-wise election between this and any other 
single candidate, and this candidate should still be the winner. Since 
each candidate is the majority loser of one of these pair-wise contests, 
we cannot satisfy both 2 and 3. 

end of FAQ excerpt
----
Based on what I have written about clones in circular ties, I suggest that 
Mr. Arrow's Theorem is highly defective and is itself irrelevent.

Namely, the 
3. Meet the Independence from Irrelevant Alternatives Criterion. 
item is itself circular (based on a circular tie).