Arrow/IA/IIAC

[DEMOREP1 at aol.com]

s349436 at student.uq.edu.au wrote in part-

A voting paradox will still exist in several cases in which, at least, the
addition of a close clone will punish its voters.
----
D- A clone is a clone is a clone to varying degrees in ANY matrix (2 x 2 to N 
x N). 

Examples

100 AB
0 BA
net 100 AB

99 CD
1  DC
net 98 CD

98 EF
2 FE
net 96 EF

etc.

51 YZ
49 ZY
net 2 YZ

(with odd number variations)

I note again that a minority will choose the lesser perceived evil(s) in 
number voting if its earliest choice(s) cannot win (especially in  smaller 
minority cases).

40 AB
35 BA
25 CX

X will likely be A or B (otherwise plurality prevails).
----
s349436 at student.uq.edu.au wrote in part later

'Ere dooz- the simple "confused and irrational voters" system-

2   3   4
A   B   C
B   C   A
C   A   B

Now, let's expect that when a new candidate enters the race, it should
benefit or at least have no effect on the people who preferred the new
candidate to both the "old" and the "new" winner- that is, it genuinely
benefited these voters to support this new option.
--
D-  See the above clones example and my comments on the 40-25-35 Cretney 
example. New clone candidates cause divisions to different degrees.

When there is initially 

M  AB
N  BA

and C is added there obviously can be 

M CAB or
M ACB or
M BAC

and

N CBA or
N BCA or
N BAC

Both M and N may obviously be divided among the added C variations (with 
possible very different AC, CA  and BC, CB numbers).

Thus it should come as no surprise that there may be some apparently strange 
results in a confused and irrational voters case with a small number of 
voters (as in a 2-3-4 voters case or for that matter ANY  V-1, V, V+1 voters 
case).