[EM] Clones in Circular Ties

[DEMOREP1 at aol.com]

The below assumes that each choice gets a YES majority of all of the voters 
on a YES/NO vote.

A simple circular tie in a single winner case --

35 ABC
34 BCA
31 CAB

100

66 A > 34 B
69 B > 31 C
65 C > 35 A

A>B, B>C, C>A

If D is made a 100 percent clone of B, then there is

35 ABDC
34 BDCA
31 CABD

100

A > B and D, B and D > C, C > A, 100 B > 0 D

Going backwards, even the 2 or 3 choice cases can be deemed to have an 
element of cloneness.  Namely, the largest head to head defeat shows the 
largest clone (noting that head to head comparisons may involve direct 
opposites or real clones).

With 3 or more choices, eliminating one choice at a time may, of course, 
cause a bad defeat (by such losing choice) to be removed.

Example

27 ABCD
26 BCDA
25 CDAB
23 DABC
101

75 AB 26
50 AC 51
27 AD 74
76 BC 25
53 BD 48
78 CD 23

A > B, B > C, C > D, D > A
--
Rearranging--

Highest defeat

78 CD 23
76 BC 25
75 AB 26
74 DA 27 lowest worst defeat
53 BD 48
51 CA 50

Lowest defeat

407    199   Totals  606

Is D the largest clone ?

Note the DA line.

If D is eliminated, then there is

76 BC 25
75 AB 26
51 CA 50

202    101  Totals  303

If C is eliminated, then A beats B.

Would a circular tie winner always be near the median in a vertical 
arrangement if the highest defeated clones lose ???

Another somewhat obvious tiebreaker would have the highest YES votes choice 
be the winner (if there is no Condorcet winner).

I note again that any tiebreaker must be rather obvious to get adopted into 
law for real public elections.