# [EM] RE: FBC, Clone-Winner, and pairwise components seem incompatible

Simmons, Forest simmonfo at up.edu
Sat Jun 25 17:30:34 PDT 2005

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Forest replies:

Suppose that you modify MDDA by specifying a three slot, MCA style ballot, i.e. allowing voters to rank as many alternatives as they like in first and second place, but all other candidates are considered equally ranked and unapproved.

Call the resulting method MDDA3.

It seems to me that MDDA3 satisfies Clone-Winner, because you have to cram cloned alternatives into at most two slots per ballot, which makes it impossible to have a 51%  majority cycle in a clone set.

I would prefer what I we might call "67%MDDA3" where the disqualifications are made by two-thirds majorities, and the ballots are three slot style.

With three slot ballots it is not possible to disqualify all candidates with a 67% majority, so the description is ...

1.  Rank as many alternatives as you like with either a 1 (highly approved) or a 2 (also approved).

2.  For each pair of alternatives X and Y, if X is ranked above Y on more than two thirds of the ballots, then disqualify Y.

3.  The winner is the remaining alternative with the most approval, i.e. the remaining qualified alternative that is ranked on the greatest number of ballots.

Here's another reason I like the two thirds plus or 67% rule:

Consider the ballot set

x:  A>B
y:  C>B

If the respective values of x and y are 67 and 33, then I think that A should win, even though B has 100 percent approval.

But if  the respective values of x and y are 51 and 49, I think that B should win; in my opinion a mere 51% "high approval" shouldn't trump 100% mere approval.

Both of these parameters are satisfied by 67%MDDA.

Whether or not we restrict to a three slot ballot, I think we should go with the 67% disqualification rule, since that would make the method satisfy clone-winner for all practical purposes, since it is impossible to have a beat cycle of three candidates in which each defeat is of more than two thirds strength (assuming that the individual ballots rank the alternatives transitively).

In summary, the compliances Kevin asked about seem to be compatible, but perhaps not in the way that he was hoping for.

Forest

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