[EM] New clones definition?

[Rob LeGrand]

I just thought of a possible definition of clones:

Candidates A and B are clones in a ranked-ballot election if and only if
deleting A from the ballots and renaming B as A is equivalent to deleting B
from the ballots.

Example:

49:Reagan>Anderson>Carter
33:Carter>Anderson>Reagan
18:Anderson>Carter>Reagan

Deleting Carter gives:

49:Reagan>Anderson
33:Anderson>Reagan
18:Anderson>Reagan

Deleting Anderson gives:

49:Reagan>Carter
33:Carter>Reagan
18:Carter>Reagan

Now the sets of ballots are identical except for the name of Anderson/Carter,
so Anderson and Carter are clones in this election.  On the other hand,
deleting Reagan gives:

49:Anderson>Carter
33:Carter>Anderson
18:Anderson>Carter

Which isn't identical to either of the other sets of ballots, so Reagan isn't a
clone of either of them.  Can this definition ever fail?  Has it been suggested
before?

--
Rob LeGrand
honky98 at aggies.org
http://www.onr.com/user/honky98/rbvote/calc.html

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