Weak Independence of Irrelevant Alternatives

[DEMOREP1 at aol.com]

Once again --- on the addition (or subtraction) of alternatives and resulting 
math complications.

N1  A>B
N2  B>A

N1 or N2 is a majority.

Choice C comes along.

New possible types of votes (ignoring truncated votes) ---

CAB
ACB
ABC
N1 Total

CBA
BCA
BAC
N2 Total

C may (in head to head pairings -- ignoring ties) ---

1. beat both A and B, or 
2. beat A, lose to B, or
3. beat B, lose to A, or
4. lose to both A and B.

How often would the election result change from the original result with the 
addition of the 3rd choice ???  (noting the 1, 2 or 3 possible results)

Which of the three choices then becomes the most clone like (since 100 
percent clones are not likely in larger elections) ???

If the 3 choices suddenly appear to a stranger (with the 6 types of A,B,C 
votes) , could such stranger know which 2 of them was in the original pairing 
??? (i.e. know which of them to eliminate to reproduce such original pairing)

Expand the above to 4 or more choices for additional complexities.

I beat the dead political horse some more ---- any election method in real 
public elections operates on the actual choices and the actual votes cast --- 
NOT with some mythical election with added or removed choices and/or added or 
removed votes (unless one is dealing with election law felons -- vote 
robbers, ballot box stuffers, etc.). 

Many, if not ALL, of the criteria which complain about *strange* things 
happening with such mythical additions or removals are quite *irrelevant* 
(because they miss the elementary point of having possible divided majorities 
if there are 3 or more choices).

In particular for a single winner office, one obvious way to get rid of 
plurality is to require that the winner get a majority in order to be elected.

Obviously if he/she cannot get such majority with first choice votes, then 
the needed additional votes will have to come from 2nd or lower place votes.