Re: Condorcet Voting and Supermajorities (Re: [CONSTITUTIONAL AMENDMENT] Disambiguation of 4.1.5)
At 10:07 AM 11-29-2000 -0500, Raul Miller wrote:
>That's one question. Another question is: what problem are we trying
to solve?
Last things first... This is a -very- important question that I don't know
the full answer to.
The main problem: The current "Standard Resolution Procedure" as written
in Appendix A of the Debian Constitution is confusing and ambiguous.
There are (at least) two ways of addressing this issue. The first way is
to amend Appendix A so that the current procedure is made unambiguous and
clear. The advantage of this is that it causes the minimal amount of
change to the actual process. The disadvantage is that if the main problem
is real, there are multiple interpretations as to what the proper
unambiguous method is.
The second way is to look for what the faults are in the current process
are, and amend Appendix A with a better procedure that is also unambiguous
and clear. I think I prefer this way.
What I would consider ideally unambiguous for a replacement for A.6 would
be pseudocode for determining the election, rather than the poorly-written
english we have now. Something that most of the Debian Developers could
probably be able to sit down, code in their favorite language, and get all
get the same answers.
On Wed, Nov 29, 2000 at 07:28:44AM -0500, Buddha Buck wrote:
> Whether one criteria is better than another is of course a matter of
> opinion.
Agreed. Still, consensus is possible.
> Above, you prefer Single Transferable Vote (which also appears to be
> called "Instant Runoff Voting" or "IRV" on most of the voting method
> websites) because it "biases selection in favor of first preferences
> at the expense of other preferences". Obviously, you think this is a
> good thing.
Sure -- but logically, if I'm a voter, and I indicate a second and third
preference on a ballot, that shouldn't weaken the strength of my first
preference.
I was going to say that I would consider that a valid criteria to consider
for a voting system, but then I realized that I don't understand what you
mean. Could you elaborate?
I don't know if IRV has the problem that your 2nd or 3rd choice votes could
cause your 1st vote choice to lose, but IRV does have the problem that in
certain cases, your 2nd choice vote could cause your 3rd choice to
win. The http://www.electionmethods.org/ site describes this.
> Others may prefer other methods because they reverse the preferences of
> the fewest number of voters. This is a different criteria. Is it
> better? I think so, and so do others. You may not. Most of the
> "traditional" Condorcet resolution methods favor this criteria.
Sure -- mediocracy tends to be easy to agree on.
Again, I don't understand what you mean...
Here's what I meant...
In a Condorcet vote, if there is one choice which pairwise defeats all
other choices, then that choice wins. That's a pretty good indication that
that choice is well supported. However, if there is no choice that
pairwise defeats all other choices, then you must have a cycle(s) of some
sort: More people prefer A to B, more B to C, more C to A, in the simplest
of cycles. To claim an absolute victor, the cycle(s) needs to be broken,
effectively reversing one or more of the pair-wise contests. Such a
reversal is effectively overriding voters expressed preferences.
Methods of choosing a winner in the presence of such cycles can be judged
based on how few voters preferences are overridden. That is a standard
criteria which is used to judge.
> I think the best we can do is list a bunch of alternatives, with
> explanations and descriptions of their advantages and disadvantages,
> and discuss from there.
I'm willing (see above :).
OK, here are some choices:
Definitions from http://www.barnsdle.demon.co.uk/vote/vote.html
Defn: An "unbeaten set" is a set of options none of which is beaten [in a
pairwise contest] by anyone outside that set.
Defn: A "small unbeaten set" is an unbeaten set that doesn't contain a
smaller unbeaten set.
Defn: The "Schwartz set" is the set of options which are in small unbeaten
sets.
Defn: The "Smith set" is the smallest set of options such that every option
in the set beats every option outside the set. Note: In some cases, the
Smith Set can contain the entire set of options.
Given: A set of preferential ballots, modifed by eliminating all options
that are not in the Smith set.
Option: Plurality
Examine the 1st choice on all ballots. The choice with the highest vote
total wins.
Advantages: Easy to understand.
Disadvantages: Does not take into account complete knowledge of voters
preferences. Requires re-examination of the ballots after the initial tally.
Other factors: Strongly favors first choice preferences. Plurality
encourages "strategic voting" when used as a general voting method and can
choose an option that is disliked by a majority; I am uncertain how
limiting it to the Smith Set affects this.
Option: Instant Runoff
Examine the 1st choice on all ballots. If a single choice has more than
half the total votes cast, it wins. If not, eliminate from all ballots the
choice that has the fewest number of 1st choice votes, and repeat until
there is a winner.
Advantages: Current system in place.
Disadvantages: Does not take into accout complete knowledge of voters
preferences. Requires re-examination of the ballots after the initial tally.
Other factors: When used as a general voting method, can cause an option
to win that would have lost if voted higher, and vice versa. Does not meet
-any- of the "academic criteria" espoused by Condorcet-favorable
experts. I am uncertain how limiting it to the Smith Set affects this.
Option: Runoff-Pairwise
Conduct a second vote using Approval Voting, with the options chosen solely
from the Smith set.
Advantages: Allows voters to compromise and readjust their voting after
seeing the outcome of the initial balloting.
Disadvantages: Requires second vote. May encourage strategic voting in
second vote.
Option: Smith/Condorcet
Of the n options in the Smith set, order the n*(n-1) pairwise results by
number of votes for the winning choice, strongest to weakest. (e.g., if A
beat B by 100:50, and B beat C by 76:74, order them as AB first, BC second,
because 100 is bigger than 76).
Drop the weakest defeat iteratively until one option is unbeaten. That
unbeaten option is the winner.
Advantages: Variants have been studied for 200+ years.
Disadvantages
Option: Sequential Dropping
Order the pairwise results as in the Smith/Condorcet option. Drop the
weakest defeat that is part of a cycle until one option is unbeaten. That
option wins.
Option: Schwartz Sequential Dropping
Order as in Smith/Condorcet
Drop the weakest defeat among members of the current Schwartz Set. Repeat
until one option is unbeaten.
Option: Tideman's Method
Order the results as in Smith/Condorcet.
From strongest to weakest, drop defeats which form a cycle with remaining
stronger defeats. The remaining undefeated candidate will win.
Apparantly, Tideman's is considered the best method among people who have
studied voting methods. David Barnsdale's site above lists some criteria
that people feel are important.
> > I'll note that the URL you cited doesn't have anything equivalent to
> > Single Transferrable Vote. [So it's not comprehensive.] I don't think
> > "my favorite web site doesn't mention this system" somehow makes the
> > systems it proposes to be somehow superior.
>
> The URL I'm looking at does not discuss IRV under Condorcet resolution
> methods, but it does discuss IRV as a technique for general elections
> (i.e., an alternative to Condorcet). I'm looking at http://
> www.electionmethods.org/, which does have some faults (it has an
> -extreme- bias towards Condorcet and against plurality and IRV, for
> instance).
Turns out I'd missed the cite.
> > The nice thing about Single Transferrable Vote is that it
> > automatically makes first preference votes more important than
> > second preference votes (and so on). There are few systems at the
> > URL you cited which even attempt this.
>
> Most of the Condorcet resolution methods I've seen don't attempt that
> because they don't see it as a valid criteria. They see overruling the
> fewest number of votes to be a valid criteria.
Right, but that's method, and not a reason why.
> Actually, I did find one description of a voting concern that does
> severely impact IRV. IRV requires the multiple examination of every
> ballot, which can be prohibitive if the number of ballots is huge,
> or fragile, etc. Since most voting reform sites are concerned with
> reform of real-world elections, where there may be millions of voters,
> this is a bigger concern for them than it is for us. And this is a
> valid criteria for them to consider. The Condorcet resolution methods
> normally discussed can all be computed solely from the aggregate
> voting data, not needing to further examine individual ballots.
In other words: it requires computerization of the voting process.
And: rankings actually indicate preference, as they represent more than
the ability to cast multiple votes.
> > > This sort of situation happens no matter how you resolve a cyclic
> > > tie, though. You pretty much have to be "unfair" in some sense to
> > > choose a winner. As I said, I'm inclined to suspect that there
> > > other means are likely to be more optimal, although I'm not clear
> > > exactly how.
> >
> > It really sounds more as if you want to find faults in the
> > constitution than you've thought this through and have a better
> > alternative to propose.
>
> No voting system is going to be 100% "fair" to all voters. The
> question remains, however: How do we determine "fairness" to evaluate
> different methods?
--
Raul
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