On Sat, May 24, 2003 at 09:24:34PM -0400, Nathanael Nerode wrote:
> Consider if all the people who, in my original example, ranked A=D,
> instead ranked A *below* D.
> 19x ADB
> 19x ABD
> 1x BDA
>
> A vs. B
> 38 to 1
>
> D vs. A
> 20 to 19
Huh? YM A vs D: 38:1.
> B vs. D
> 20 to 19
>
> There's no Condorcet winner.
And A meets quorum and wins.
If you meant:
19x DAB
19x ABD
1x BDA
You have:
A beats B, 38:1
B beats D, 20:19
D beats A, 20:19
and under the proposed system, A is dropped for lack of support, and B wins.
What are the possible outcomes?
A wins, in spite of not having a quorum of support
B wins, in spite of A being preferred by a vast majority.
D wins, in spite of B being preferred by a clear majority.
A is unacceptable, but could easily have been made acceptable by the people
who support A getting a single additional vote. This has never been a problem
in the past.
As A is unacceptable, the qualification against choosing B as the winner
is fairly weak. Further choosing D is unacceptable, since that causes
process problems in the future: what do we do instead? So choosing B is
the least objectionable, which is to say best, course of action.
Note that without quorum, A is dropped any way, since it doesn't defeat
the default option by its majority requirement, and B wins then too. The
way the proposal is constructed, the elector with a casting vote can
never choose to void the election if any options are acceptable.
> With Manoj's quorum, A is eliminated and B wins by a hair, same as with
> the equal rankings. But 38 people prefer A to B and only 1 person
> prefers B to A. Now B is implemented. Some people may think that this
> is desirable, of course. I certainly don't.
A majority of 20:19 think it's more desirable than doing nothing,
by assumption.
> Consider my original example:
> 19x A=DB
> 19x ABD
> 1x BA=D
>
> Under Manoj's system, B wins! B is implemented!
> A new ballot ("Fix the results of the stupid ballot we just had!")
> proposes A vs. "Keep the present system" (B) vs. "more discussion" (D).
> The first set of voters hated B and want to get rid of it before
> discussing things further, so they change their votes:
> 19x ADB
> 19x ABD
> 1x BA=D
So, if the first set of voters find A acceptable, why didn't they vote
that way originally? They could have, quite easily.
> ---
> The problems are not really present for the Technical Committee, since
> the quorum is 2. For technical reasons, this cannot cause any odd
> behavior.
Not due to quorum perhaps, but you can still get:
3 ABD
3 DAB
2 BDA
A beats B, 6:2; B beats D 5:3; D beats A 5:3. A doesn't make its majority
requirement, and is eliminated, so B wins. Cloneproof SSD alone would
have eliminated B beats D and D beats A, leaving A or D as the winner.
> --
> It also seems unlikely for the aforementioned problems to happen in a GR
> when the number of voters is >=2*R, where R is the quorum requirement.
>
> Unfortunately, it *can* happen with an arbitrarily large number of
> voters.
Yes, and it's possible for a meteorite to hit master.debian.org just as
the vote's closing and for D to thus win by default, even if _everyone_
voted for A!
It's not a likely thing to happen both historically, and because in
the balance, it's beneficial for you to express full preferences,
wherever possible.
I don't think you can actually get any problems with quorum with more
than 12R voters, actually. That's 570 of 1000 developers voting, so isn't
particularly unbelievable. You also need a linearly increasing number of
options to manage this, afaict; I think you need at least 7 options to
have a vote where an option beats the winner, but doesn't make quorum,
with 12R voters, as well as an utterly unbelievable distribution of
preferences.
> How? When there are lots of options and lots of rankings equal to
> the default option, as well as a highly splintered electorate.
You'll note that we try to avoid having a splintered electorate --
you know, decision by consensus and all that; and have a voting system
that's designed to find a compromise that's as acceptable as possible.
Cheers,
aj
--
Anthony Towns <aj@humbug.org.au> <http://azure.humbug.org.au/~aj/>
I don't speak for anyone save myself. GPG signed mail preferred.
``Dear Anthony Towns: [...] Congratulations --
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