# Reverse Symmetry Criterion

DEMOREP1 at aol.com DEMOREP1 at aol.com
Sun Mar 25 09:33:31 PST 2001

```Mr. Simmons wrote in part-

Consider the following summary of 90 preference ballots:

40 C > A > B
20 A > B > C
30 B > C > A

IRV gives the win to B.  Reverse all of the preferences and IRV still
gives the win to B.  However, we cannot fault IRV in this case because
the candidates form a Condorcet cycle: C beats A beats B beats C, and are
therefore in some sense tied.
----
D- As usual I note that such rankings are only relative and NOT absolute.

How many YES votes could each choice get ???

With 3 choices especially, there is also the question of how to treat the 2nd

A 60
B 50
C 70

Does C win ???

A 70
B 60
C 50

Does A lose ???
B 50, C 40.  Does B win ???

Do the votes that cause the circular tie cancel each other (as with ordinary
YES or NO votes cancelling each other) ???

That is dropping 20 ABC, 20 BCA and 20 CAB leaves ----

20 CAB
10 BCA

Does C win ???

Another option - who gets (or is most likely to get) 46 votes first
---forward or backward) ???

Are the *other* 2nd place votes used (as if votes were drawn randomly for
each choice among the second choice votes) ---

20 A needs 26 of 70 -- 37.1 pct
30 B needs 16 of 60 -- 26.7 pct
40 C needs 6 of 50 -- 12.0 pct

Does C win the odds race ???

Would using such odds percentages cause more truncated votes (tending towards
plurality type resultsS) ???

Are ties different with 3 or more choices (that are NOT in an *exact* tie
---- i.e. an *unbalanced* tie) ???

Does the above odds race apply to 4 or more choices in a circular tie ???

26 ABCD
25 BCDA
24 CDAB
23 DABC

98

Who is the most likely to get 50 votes first ???

```