[EM] New clones definition?

[Joe Weinstein]

Rob's proposal sounds familiar, as well as maybe even plausible.  Let's try 
it out on a very simple election:

100:  A>B

(A and B are the only candidates, everyone loves A and detests B.)

Delete B from ballots, you get:  100:  A
Delete A from ballots, rename B as A, you get:  100:  A

The proposal makes A and B 'clones'!

Well, if you don't like an example which starts with just two candidates and 
therefore will reduce to no-contest when one is deleted, let's try again 
with a third candidate, e.g. start with:   100:  A>B>C.
Either way - deleting B, or deleting A and then renaming B as A - you end up 
with:   A>C.  So again, A and B are 'clones'.

More generally, the proposal will make 'clones' out of any two candidates A 
and B which are adjacent in preference for all voters - no matter how voters 
distribute among the alternatives A>B, B>A, A=B.

As the first example illustrates clearly, such 'clonehood' lacks one 
property that some people (including me) find essential.  Namely, suppose 
voters learn that the winner is some (unspecified) member of a given set of 
'clones'.  Then there should be overall indifference as to WHICH of the 
'clones' has won!

Joe Weinstein
Long Beach CA USA


----Original Message Follows----
From: Rob LeGrand <honky1998 at yahoo.com>
Reply-To: honky98 at aggies.org
To: election-methods-list at eskimo.com
Subject: [EM] New clones definition?
Date: Tue, 2 Apr 2002 21:55:37 -0800 (PST)

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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