# [EM] RE: MMPO

Simmons, Forest simmonfo at up.edu
Thu May 26 12:44:40 PDT 2005

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I don't have much time right now, but here are a few brief replies to Mike's comments and questions.

>From: "MIKE OSSIPOFF" <nkklrp at hotmail.com>
Subject: [EM] MMPO

....

As you know, MMPO can be introduced to people very briefly:

Voters rank as many or as few candidates as they want to. Equal ranking is
allowed.

Elect the candidate over whom fewest people prefer someone else.

[end of suggested public MMPO introduction]

Forest replies:  That's a great introductive definition.

Mike continued ...

>Before BeatpathWinner/CSSD, Ranked-Pairs, or SSD were posted to EM, or at
least before I understood their advantages, I wanted to try to make PC
(easily shown to) comply with SDSC, and I tried something that I called the
"subcycle rule", which involved collapsing cycles. It had problems. Maybe
cycles can be collapsed in a way that doesen't have the problems that the
subcycle rules had.

When you refer to collapsing cycles, you mean the way that it's done in the
sprucing-up procedure, right?

Forest replies:  right?  We'll have to compare notes on this.  Basically, I think what you call a "subcycle" is what I call a "beat clone set."   A beat clone set C is a set of alternatives such that if alternative X is outside of C and X is beaten by one member of C then X is beaten by all members of C.

So clone cycles qualify as beat clone sets.

I proposed collapsing C by removing the members of C from each ballot and introducing a new candidate [C] at the position formerly occupied by the median member of C on that ballot, i.e. on each ballot collapse C to its central position on that ballot.

If the ballots were CR style ballots, then on each ballot C should be collapsed to its mean CR on that ballot.

Mike continued ...

Sprucing up is complicated, isn't it? Too complicated for a public proposal?
I don't want to ask you to write a long description of its advantages, if
you don't have a lot of time to, but, just summarizing briefly, what's the
nature of it's gain?

I reply:

It is too complicated for public proposal.  Its purpose was to spruce up any method by forcing it to satisfy the Condorcet Criterion and Clone Independence.

The first step was to eliminate all alternatives except those that had a chance of being chosen by sophisticated players of the game "on the count of three we both pick an alternative, and if my alternative is the one that beats yours pairwise, then you owe me a dollar."

The second step was to collapse beat clones.

After these two steps the election would be reduced to a singleton or a cycle of three (at least in public elections). The singleton could be a collapsed cycle.

The cycle or collapsed cycle is resolved by the method being spruced up.  If the winner is a collapsed cycle, then the method is used again to resolve that cycle, etc.

I'll dig up an archives posting if you really want it, but I don't think the details will make that much difference to you.

Forest

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