[EM] Does the 'Independence of Irrelevant Alternatives Criterion' Imply...

[Ken Johnson]

>Date: Fri, 02 Apr 2004 21:39:43 -0800
>From: Richard Moore <moore3t1 at cox.net>
>...
>
>But what did you think of INI?
>
>  -- Richard
>  
>
In your earlier post (Election-methods digest, Vol 1 #576, Message 7) 
you defined INI ("Independence of Non-supporting Information") as
"If X wins and Y loses, and margin(X,Z) <= margin(Y,Z), then removing 
candidate Z from the election shall not cause Y to win and X to lose."
This sounds like a reasonable criterion, but as stated above I don't 
think it has relevance to Arrow's IIA criterion because IIA relates to 
how the election result might change when you remove a candidate from 
the vote count, not from the election. (In the former case, the votes 
don't change; in the latter case voters may strategically change their 
voting preferences based on which alternative candidates are running.) A 
more concise statement of INI (if this is what you meant) might be:
"If X wins and Y loses, and margin(X,Z) <= margin(Y,Z), then removing 
candidate Z from the COUNT shall not cause Y to win and X to lose."
In the case of CR and Approval all of Arrow's criteria, including the 
following interpretation of IIA, hold:
"If X wins and Y loses then removing candidate Z from the count shall 
not cause Y to win and X to lose."
- Ken