# [EM] Cycles and subgroups

DEMOREP1 at aol.com DEMOREP1 at aol.com
Sun Jul 16 13:46:15 PDT 2000

```A few observations about cycles and subgroups --

The very simple circular tie-

N1 ABC
N2 BCA
N3 CAB

Assume the N amounts produce A>B>C>A.

The AB, BC and CA combinations are each in 2 of the 3 vote groups.

By reversing the groups there is

N4 CBA
N5 ACB
N6 BAC

The AB/BA, BC/CB, CA/AC combinations are now in 4 of the 6 vote groups.

In a larger example each choice (A, B, C) might be 2 or more subchoices--
such as A might be a D/E subgroup (especially simple clone subgroups); B
might be a F/G/H subgroup, etc.

It would appear that with 3 or more choices ALL election methods fail to meet
one or more test standards (aka criteria) due to possible cycles and
subgroups.

What to do ???

How many test standards (if not ALL of them) regarding cycles and subgroups
are irrelevant in getting a majority rule winner (for single winner
elections) ???

How many test standards are in effect chicken-egg type standards ??? That is,
certain cycle/subgroup data produces the test standard.  Such test standard
then causes other cycle/subgroup data to fail the test standard.

I note again for the simple 3 choice case (with 3 or 6 vote groups), that if
no choice gets a first choice majority and is not a Condorcet winner, then
one of the choices will get a majority if the first plus second choice votes
are combined (ignoring ties and truncated votes).

The same tiebreaker can be used if there are 4 or more choices with no first
choice majority and no Condorcet winner.

```