[EM] Adding Choices

[DEMOREP1 at aol.com]

Some of the criteria floating around make a big deal about what happens if 
choices are added or removed.

I suggest that such criteria are irrelevant due to the possible/actual 
dividing of votes when choices are added.

The simple case-

N1  AB
N2  BA

Assume N1 > N2

Choice C is added

There may be

N1A CAB
N1B ACB
N1C ABC

N2A CBA
N2B BCA
N2C BAC

N1= N1A + N1B + N1C
N2= N2A + N2B + N2C

Truncated votes ignored for simple case purposes.

Thus, with C added there may or may not be a

(1) Condorcet Winner (who beats each other choice),
(2) Condorcet Loser (who is beaten by each other choice), 
(3) circular tie (each beats or ties at least 1 other choice).

The only certain thing is that there is still N1 A > N2 B.

Note- the 6 group may be turned inside out by making the AC/CA or BC/CB 
pairings as the original pairings (which regroups parts of the original N1 
and N2)

With 4 or more choices complexity really multiplies due to possible multiple 
overlapping cycles and subcycles (e.g. Smith sets, etc.).

Little wonder that there is some rather major confusion in election methods 
(due to the math combinations of added choices).

I mention again (especially in connection with public office and issue 
elections) - an election method in the real world must operate on (A) the 
real votes for the choices on the ballots (plus write-ins, if allowed) and 
NOT on (B) some added or removed votes and added or removed choices (noting 
the possibility of candidate deaths after the ballots are prepared).