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Re: RFD: Reviving Constitutional amendment: Smith/Condorcet vote tallying

On Tue, Oct 22, 2002 at 03:03:37PM +1000, Anthony Towns wrote:
> Well, you just said a message ago that you didn't like using terms that'd
> been used before either, so that's a bit contradictory. It's weird
> to think that x can be "preferred" over y while y is also "preferred"
> over x, but probably not much more so than "masters" or "dominates" etc.

I think you're overgeneralizing.

I'm only trying to avoid terms which would lead to pointless discussions.
I think that "dominates" is such a term, because it has a specific yet
ambiguous definition in the current constitution.  Other terms, such as
"vote" or "preferred" are not in this category.

In any event, as I stated before, I had dropped the use of "preferred"
in favor of "beat path" because "beat path" is used in the technical
literature on voting systems and seems to have a precise definition
which agrees with the definition I'm using.

> > > ATM the quorum is done last ("check the winner meets quorum, if not,
> > > the default option wins").
> > In this proposal, I'm not concerned with precisely matching the sequence
> > of events in the current mechanism.
> When I said "atm" I meant with the current draft -- the quoted phrase
> was from that draft.

This whole issue warrants a seperate message.  At the moment we're
discussing tangential issues and not focussing on the heart of the
message.  [I'll compose that message after I get done with this

> > If any of the options presented were good ideas, why would nobody vote
> > for them?
> Huh? *You* just said you were concerned with the case where no one votes.

We're focussing on tangential issues, I'll write up a seperate 
message on this topic.

> > Perhaps step 9 should be phrased:
> >     9. If all options in the schultz set, in each pairwise comparison,
>                                ^^^^^^^
> Schwartz?

Yeah, sorry.

> >        have both the same number of votes for the option as against the
> >        option, a tie exists and the elector with the casting vote picks
> >        the winner from the options in the schultz set.
> > That seems to eliminate the ambiguity you've described.
> I would still be inclined to require the default option to win if it's
> part of the tie. But yes, it clears up the ambiguity nicely, afaics.

I propose we eliminate all options which don't beat the default option
before we get to this step.  [I know I've made statements which don't
agree with this proposal.  Anyways, this topic is the subject of my
planned next message.]

> > Here's my definitions:
> > 
> > Option A is defeated by option B if option B beats option A.
> "A `defeat' exists between option A and option B (and A is said to defeat
> B) if A beats B, and the pairwise comparison between A and B has not
> already been eliminated from consideration."

Good point.

> > Given a set of candidates and a vote, the weakest defeat is the defeat
> > which has the fewest opposing vote.  If there's more than one pair
> > of options which has this many opposing votes, the weakest defeat is
> > the one where the defeated option also has the most votes in favor.
> > If there's more than one pair of options which has the fewest opposing
> > votes and (for that many opposing votes) the most options in favor,
> > then all of these defeats are considered instances of the weakest defeat.
> "A defeat, D, is said to be weaker than another defeat, E, (and thus E
> is said to be stronger than D) if it has fewer opposing votes, or it has
> the same number of opposing votes and more supporting votes. Two defeats,
> D and E, are said to be equal if the number of opposing votes are equal,
> and the number of supporting votes are equal. The weakest defeats of a set
> are the ones which are equal to each other, and weaker than all others."

I like this.

> It might be better to recast the calculation of the "Schwartz set"
> in terms of "defeats" rather than "beats".

The definition of schwartz set I used requires transitive closure, and is
thus tied to the term "beat path".  Other than that, I suspect you
could be right.



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