Re: Proposal -- Change constitution to adopt Smith/Condorcet vote tallying
A walkthrough of the proposed change, to see if I understand it (and to
highlight a potential problem I see):
Scenario: A general resolution is proposed, describing a proposed
numbering and naming of the next Debian Distribution after woody. Two amendments
are made, asking for a different number/name combination. The final
ballot looks like so:
A [ ] The next Debian Distribution shall be 2.4, and called "sarge"
B [ ] The next Debian Distribution shall be 3.0, and called "sarge"
C [ ] The next Debian Distribution shall be 3.0, and called "jessie"
F [ ] Further Discussion
(Rationale: sarge is the last named toy in Toy Story who's name hasn't
been used. jessie is the heroine in Toy Story 2.)
The votes, as cast, are
25 AC
40 CBF
20 BACF
> ! A.6. Smith/Condorcet Vote Counting
>
> 1. This is used to determine the winner amongst a list of options.
> Each ballot paper gives a ranking of the voter's preferred
> options. (The ranking need not be complete.)
Ballots given above...
> ! 2. A square "initial totals table" is constructed, recording the
> ! ballot totals: the number in the table at row j, column k indicates
> ! the number of ballots which prefer ballot option j to ballot
> ! option k.
The initial totals table looks as follows:
(note: I'm assuming that non-ranked items are equally undesirable for
that particular ballot)
A B C F
A 0 25 45 45
B 60 0 20 60
C 40 65 0 85
F 40 0 0 0
> ! 3. A square "adjusted totals table" is constructed such that all
> ! entries in row j from the initial totals table have been multiplied
> ! by m and divided by n where option j has an n:m majority
> ! requirement. For options with no such majority requirement,
> ! the row in the adjusted totals table is the same as the row from
> ! the initial totals table.
The adjusted totals table is the same as the initial totals table.
> ! 4. A four column "winning criteria table" is constructed with one row
> ! for each cell in the adjusted totals table: the "for" column
> ! holds option j; the "against" column holds option k; the "votes
> ! in favor" column holds the value from the adjusted totals table
> ! for row j, column k; the "votes against" column holds the value
> ! from the adjusted totals table for row k, column j.
This table, constructed as described, will have 16 entries:
For Against Votes In Favor Votes Against
--- ------- -------------- -------------
A A 0 0
A B 25 60
A C 45 40
A F 45 40
B A 60 25
B B 0 0
B C 20 65
B F 60 0
C A 40 45
C B 65 20
C C 0 0
C F 85 0
F A 40 45
F B 0 60
F C 0 85
F F 0 0
> ! 5. The winning criteria table is sorted in descending order based on
> ! the "votes in favor" column (and, where values in the "votes in
> ! favor" column are equal, in ascending order based on the "votes
> ! against" column).
For/Against Votes In Favor Votes Against
----------- -------------- -------------
C/F 85 0
C/B 65 20
B/F 60 0
B/A 60 25
A/C 45 40
A/F 45 40
C/A 40 45
F/A 40 45
A/B 25 60
B/C 20 65
A/A 0 0
B/B 0 0
C/C 0 0
F/F 0 0
F/B 0 60
F/C 0 85
> ! 6. If there is a single option in "for" column of the winning criteria
> ! table which does not appear in "against" column, that option is
> ! the chosen option.
All options are in both columns
> ! 7. If there are multiple options in the "for" column of the chosen
> ! criteria table which do not appear in "against" column, the person
> ! with a casting vote picks the chosen option.
All options are in both columns
> ! 8. Until there is a chosen option, the last row of the winning
> ! criteria table is examined and (permanently) removed from the
> ! winning criteria table. At the same time, any adjacent row(s) are
> ! removed, if they are identical to what the removed row has in the
> ! "votes in favor" and "votes against" columns.
F/C removed, no winner
F/B removed, no winner
A/A, B/B, C/C, D/D removed, no winner.
B/C removed, no winner
A/B removed, no winner
C/A, F/A removed, no winner
A/F A/C removed, C no longer in "Against" Column
C is declared the winner.
> ! 9. Once the chosen option is picked, the ballots are re-checked:
> ! if the number of ballots which mention the chosen option is less
> ! than a quorum for the vote, the default option wins. Otherwise,
> ! the chosen option wins.
C was cast on all 85 ballots cast. C wins.
Suggested changes:
Minor: When creating the winning criteria table, include only rows
where the "votes in favor" column equals or exceeds the "votes
against", and do not include the i/i rows.
That would have shortened the above sorted table to just the C/F, C/B,
B/F, B/A, A/C, and A/F rows. The last two rows would have been
eliminated first, and C would have won.
I don't think that change would have an effect on the outcome, but
would make book-keeping easier. For one thing, if there is a Condorcet
winner (meeting the criteria of proposed step 6).
BTW, can you state an instance where proposed step 7 would have a role?
I guess it could happen when you have a (reduced) table like:
A/B 50>30
C/B 45>35
A/C 40=40
C/A 40=40
The last two rows would be eliminated, leaving:
A/B 50>30
C/B 45>35
Major: Measure quorum being met by the total number of ballots cast,
before vote-counting is done. I.e., if quorum is (say) 40 votes, then
the vote is valid if 40 or more ballots were cast, even if the winner
wasn't mentioned on at least 40 of them. If 39 ballots are cast, the
vote did not achieve quorum, and is not counted.
> !
> When the Standard Resolution Procedure is to be used, the text which
> refers to it must specify what is sufficient to have a draft
> resolution proposed and/or sponsored, what the minimum discussion
>
>
>
> Rationale: We've had a number of problems from ambiguities in our
> constitutional vote tallying procedure. Changing the voting procedure
> to Smith/Condorcet (as several people have suggested) would give us the
> same results on historical votes as the existing procedure, and would
> not suffer the ambiguities of the current procedure.
>
> I've chosen to describe this procedure in a fairly simplistic mechanical
> fashion, to try to avoid later ambiguities in interpretation, from the
> new procedure.
>
> This proposal would fix ambiguity #2 and #4, which were summarized in my
> 12/13 debian-vote message. This proposal does not attempt to address
> the other two ambiguities mentioned in that message.
>
> While we're amending the constitution, I'd also like to fix a minor
> spelling problem (minimum was misspelled).
>
> Thanks,
>
> --
> Raul
>
>
> --
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--
Buddha Buck bmbuck@14850.com
"Just as the strength of the Internet is chaos, so the strength of our
liberty depends upon the chaos and cacophony of the unfettered speech
the First Amendment protects." -- A.L.A. v. U.S. Dept. of Justice
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