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Re: Another proposal.

Anthony Towns wrote:
On Tue, Nov 19, 2002 at 12:06:20AM +1100, Clinton Mead wrote:

Andrew Pimlott wrote:

So for example, the clause, in most drafts, that first eliminated
options that were defeated by the default option, was a direct
invitation to insincere strategic voting. It would encourage voters
to put the default option second, in an attempt to knock out the
other candidates early. Exactly what we're trying to avoid with the
Condorcet method.

But it's exactly what we're trying to achieve with the supermajority
requirement, isn't it? Allowing voters to vote strategically so as to
knock out candidates they don't like?

If I remember correctly, the biggest stumbling blocks in the voting proceedure committee were a) what is the supermajority requirement for, and b) how do we acomplish the same goal in a Condorcet-style voting system?

I still think that this is a fruitful route to pursue.

The main reason for supermajority requirements on some actions is to ensure that there is a large amount of support for those actions by the voting population. Extraordinary actions like modifying the Debian Constitution should not be done without the support of the developers -- more support than for a ordinary resolution.

When you are limited to two choices, the requirement of a supermajority voting in favor of the extraordinary action over doing nothing clearly indicates a large amount of support for the extraordinary action. This is why supermajority requirements are often written in that form.

But Condorcet voting (or ranked voting option in general) don't lend themselves to this same sort of overwhelming support idea, especially with a mixture of extraordinary actions, ordinary actions, and "do-nothing" actions. It becomes harder to define what "supported by a large number of voters" means.

I believe our conclusion was to use the "default" or "None of the Below" (NOTB) option on a ranked ballot as a proxy for approval on an Approval ballot.

In Approval balloting, it is easy to determine if a measure has supermajority support. Simply look at the "yes" votes for an option, compared to the "No" votes. If a supermajority voted "yes", then that option has supermajority support.

By defining an option as "approved" on a ballot if it is ranked higher than the NOTB, we can check the supermajority approval requirement for an option simply by comparing it to the NOTB option. When we say "an option defeated the default option by a supermajority", that's an operational way of saying "an option is approved by a supermajority of the voters".

That, I believe, is the rationale for judging supermajority requirements versus the NOTB option, as opposed to any other option.

But that doesn't solve the entire issue of extraordinary action. Examine the following results of an approval ballot between a non-free amendment A, non-free resolution b, and "further discussion" (Assumption: no majority vote would mean "stop talking and do nothing"):

Amendment A:  70%  (66% minimum needed for adoption)
Resolution b: 68%  (50% minimum needed for adoption)
Keep Talking: 25%  (50% minumum needed for adoption)

Here, A clearly got a higher rating that b, and beat the supermajority requirement as well. But b was nearly as well liked. My personally feeling is that the resolution, being the more "ordinary" action, should win over the extraordinary amendement in such a close ballot. But it's hard to tell. On an approval ballot, I'd probably scale the options based on their minimum vote needed to succeed, to get:

Amendment A:   1.06
Resolution b:  1.36
Keep Talking:  0.50

and note that that Resolution b: exceeded it's threshold by a larger proportion of the voters than the Amendment A, and thus, passes.

My feeling, for a Condorcet-style election procedure is that to deal with extraordinary options,

a) if there is an extraordinary option, there must be a NOTB on the ballot.
b) if an extraordinary option does not defeat NOTB by a supermajority, that extraordinary option cannot win. c) The winner of the normal Condorcet-style vote resolution method (in our case, CSSD) wins, if able.

I thought that the voting procedure committee had accepted esentially that conclusion.

The above method for dealing with supermajorities in Condorcet-style elections has one loose thread: when do extraordinary options lose?

If they lose (and are eliminated) before the CSSD procedure is applied, then the CSSD procedure is simplified by the elimination of extraneous choices.

If the supermajority option is checked

But look at the following set of ballots (A is extraordinary, N is NOTB, b and c are ordinary):

4 cAbN
1 cNAb
3 bcNa
3 AbcN

      A  b  c   N
A     0  8  3   7
b     3  0  6  10
c     8  5  0  11
N     4  1  0   0

A fails the supermajority requirement, so by my conclusion above, can't win the overall vote. If we eliminate it as an option before applying CSSD, then b is the Condorcet winner. If we leave it in while applying CSSD, then c is the CSSD winner (the b>c 6:5 defeat is the weakest defeat, and that breaks the c>A>b>c cycle, leaving c as the sole member of the Schwartz set).

My feeling is that A should not be eliminated until it needs to be, such as if A doesn't get supermajority support but is the CSSD winner. In that case, A should be eliminated and CSSD rerun on the remaining options.

The committee disagreed, and felt that early-elimination would be better. I think.

But speaking for myself, my belief the best overall procedure would be to:

a) get ranked ballots, with NOTB
b) determine CSSD winner(s)
c) in the case of a CSSD tie, compare the winners against NOTB, and pick the one with the greatest strength agaisnt NOTB, scaled by any supermajority requirement. d) if there is still a tie, and the tie is between a mixture of ordinary and extraordinary options, eliminate the extraordinary options. e) if there is still a tie, allow the ranking of the DPL for the tieing options to determine the winner.
f) if there is still a tie, choose randomly from the tied winners.
g) if the winner is an extraordinary option that does not have supermajority approval (compared to NOTB), then eliminate that option from all the ballots and return to step (b).

Just to throw something else into the mix.


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