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Re: Request for comments [voting amendment]

Matthias Urlichs wrote:

So who did come up with the mistake "Schultz", and did they eat too many
peanuts? ;-)

Anthony Towns:

The correct restatement is something more like:

	{ x | forall y: y >> x --> x >>> y }

Or, in understandable language: The Schwartz set is the innermost unbeaten
set, or the smallest set of candidates such that none are beaten by any
candidate outside the set.

I think we need to come up with better, understandable, language.

Let me make sure I understand the Schwartz set.

Is it accurate to say that if x is in the Set, and y>>x, then y is in the set?

Is it accurate to say that if there is no y such that x>>y (i.e., x defeats nothing), then x is NOT in the set?

If we have options A, B, C, D, an A>>B,C,D, B>>C>>D>>B, then {B,C,D} is not the Schwartz Set because A>>B? A is in the Schwartz Set because there is no x such that x>>A?

I'm trying to figure out where x>>>y comes into play with the Schwartz set.

What is the Schwartz set for:

A==B; A>>C,D,E; B>>C,D,E; C>>D>>E>>C?

I coul make an argument that {A} is the Schwartz set. It's an unbeaten set, and the smallest of all possible unbeaten sets (tied with {B}, etc. The same argument could be made for {B}. I think the answer is {A, B}, but I don't have any real justification for it.

As for resolution, I'd adopt the SSD method, which states
1- Determine the Schwartz set.
2- Drop the smallest defeat(s) within the set.
3- Repeat 1-3 until there's a winner.

See http://electionmethods.org/CondorcetEx.htm.
It explains all of this in reasonably easy-to-understand language.

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