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

On Fri, Oct 18, 2002 at 03:42:26PM +1000, Anthony Towns wrote:
> Sorry, there's a "Smith set", not a Schulze set. So presumably we mean the
> Schwartz set.


> *shrug* Then how about "An option A is said to master an option, B,
> if A beats B, or if there is some other option, C, where A beats C and
> C masters B." ? Or "transitively beats" ?

In my first draft, I used "Option j is PREFERRED over option k if ...",
but that has the disadvantage of not being tied to the technical
nomenclature which has in the past been used to discuss this kind of

> > > Shouldn't the quorom be counted at the same time the supermajority is?
> Sorry, I don't mean at the _exact_ same time, I just mean before the counting
> method is applied. ie:
> 	1. Collate votes.
> 	2. Remove options that don't meet the supermajority requirement.
> 	3. Remove options that don't meet the quorum requirement.
> 	4. Count votes, according to cloneproof SSD.
> 	5. Break ties, if necessary.
> 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.

> > > >     7. If no option beats the default option, the default option wins.
> > > Why this special case? The Perl program I wrote for this uses the
> > > following system:
> > To deal with the case of no votes and on a ballot with no quorum
> > requirement.
> In which case every option will be listed as tied, and the tie-breaking
> rules can come into play.

If any of the options presented were good ideas, why would nobody vote
for them?

> Huh? The weakest defeats are part of 3 -- 2(a,b,c) are just alternative
> versions of 2(a,b,c) from above.

Looking at the quoted material, I think I misread what you were originally

> > > >     8. If only one option remains in the schultz set, that option is
> > > >        the winner.
> > > >     9. If all options in the schultz set are tied with each other,
> > > >        the elector with the casting vote picks the winner from the
> > > >        schultz set.
> > > "tied with each other" doesn't seem particularly well defined, IMO.
> > > Every single pairwise comparison has to be exactly balanced, or already
> > > discarded.
> > I'm not at all clear what you're objecting to, here.  Is there something
> > ambiguous about that phrasing?
> It's reasonable to consider all the options in the Scwartz set to be
> "tied with each other" -- dropping the weakest defeats is an automatic
> tie breaker, casting votes are a manual tie breaker. I'd be inclined
> to swap 10 and 9, and say "If there are any pairwise defeats, drop the
> weakest...", and "If there are no pairwise defeats, then either there
> are no pairs and we have a winner, or we break the tie by...".

I disagree with your assertion: 

	 It's reasonable to consider all the options in the Scwartz set
	 to be "tied with each other"

Tied has a specific meaning (same number of votes or as against).

The case where the schwartz set has more than one member and at least
one pair of options is not tied is noteworthy.  Here, we have a somewhat
ambiguous expression of preference.

Were there any other reasons (besides the concept that 'schwartz set'
"must" be the same thing as 'tied') for you to prefer another phrasing?

Perhaps step 9 should be phrased:

    9. If all options in the schultz set, in each pairwise comparison,
       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.

> > > >           c. The schultz set is then refigured with the Beats of the
> > > >              weakest defeats eliminated. 
> > > "refigured" isn't well defined.
> > I'm having trouble understanding this objection as well.
> It's not well defined -- you have to use context and intuition to make
> a guess at what it means, and what you're meant to do.

I see nothing wrong with having to use context.

I'm somewhat concerned with a need to use intuition, but I think
it's relevant that any attempt at understanding requires some use of

> > Hmm.. can you propose some alternate interpretations of "refigured"?
> Not really, but I wouldn't've been able to propose any of the alternate
> interpretations of any of the voting stuff in the constitution when it
> was proposed, either -- and that didn't stop it from decaying into an
> ambiguous incomprehensible mess within a couple of years.

I understand this issue.

> I'd suggest we be completely clear about what's going on. Something like:
> 	We define the "Current Schwartz Set" initially as the Schwartz
> 	Set calculated from the defeats of all options that have not been
> 	eliminated (This set is non-empty, since the default option is
> 	never eliminated by supermajority or quorum requirements)
> 	At this point we:
> 		1. Eliminate all options not in the Current Schwartz Set
> 		   from consideration.
> 		2. If there are any pairwise defeats amongst members of
> 		   the Current Schwartz Set, we:
> 			2a. Choose the weakest such defeat(s) [define]
> 			2b. Eliminate them from consideration [define]
> 			2c. Recalculate the Current Schwartz Set, ignoring
> 			    any options that have been eliminated, and
> 			    ignoring any pairwise comparisons that have
> 			    been eliminated, and return to step 1.
> 		3. If there were no pairwise defeats, then:
> 			3a. If there was only a single option in the Current
> 			    Schwartz Set, it is the winner.
> 			3b. If the default option is in the Current Schwartz
> 			    Set, it is the winner.
> 			3c. Otherwise, the vote is considered a tie,
> 			    and the elector with a casting vote may choose
> 			    to declare any of the tied options the winner,
> 			    or may declare the default option the winner.
> Apart from the two lines marked [define], I think that's fairly
> unambiguous. (3b) replaces "7" in the draft, (3c) might be being too
> generous to whoever gets a casting vote?

Overall, I think I like this.  However, I think we also need to define

Here's my definitions:

Option A is defeated by option B if option B beats option A.

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.

The vote count in opposing the losing option in the weakest defeat is
treated as if 0 votes had been cast for this specific vote pair.

Or: I think the hard part of this is coming up with good definitions.


Given a set of candidates and a vote, the weakest defeat is the defeat
which has the fewest opposing vote.

The option opposing the weakest defeat which also have the most
votes in favor of the defeated option.

But that feels too sloppy.

Suggestions, anyone?


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