From: Arthur Keller <arthur_at_kellers_dot_org>

Date: Thu Apr 29 2004 - 13:10:56 CDT

Date: Thu Apr 29 2004 - 13:10:56 CDT

Having ranked preferences for only 2 of the 4 candidates, for

example. The choices are:

AB, BA, AC, CA, AD, DA, BC, CB, BD, DB, CD, DC.

Best regards,

Arthur

At 11:12 AM -0700 4/29/04, Daniel Lifschitz wrote:

*>Sorry I'm not sure I understand =). What do you mean by partial
*

*>permutations?
*

*>
*

*>Sincerely,
*

*>Daniel Lifschitz
*

*>
*

*>
*

*>
*

*>
*

*>-----Original Message-----
*

*>From: owner-voting-project@afterburner.sonic.net
*

*>[mailto:owner-voting-project@afterburner.sonic.net] On Behalf Of Arthur
*

*>Keller
*

*>Sent: Thursday, April 29, 2004 10:48 AM
*

*>To: voting-project@lists.sonic.net
*

*>Subject: RE: [voting-project] What is Data Model FOR?
*

*>
*

*>Dear Daniel, thanks for your message. n! is good enough closed form
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*>for me. But n! only gives you the full permutations of n!
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*>candidates, not the partial permutations of up to n candidates. Do
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*>you have a formula for that? Do you want to derive it?
*

*>
*

*>Best regards,
*

*>Arthur
*

*>
*

*>At 9:58 AM -0700 4/29/04, Daniel Lifschitz wrote:
*

*>>Sterling's Formula approximates n! I believe:
*

*>>
*

*>>n! = ( Root(2*pi*n) * (n/e)^n * (1 + theta(1/n))) Where theta 1/n is
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*>any
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*>>function in the set of functions theta(1/n).
*

*>>
*

*>>I just had a CS101 test on this =)
*

*>>
*

*>>Sincerely,
*

*>>Daniel Lifschitz
*

*>>
*

*>>
*

*>>
*

*>>
*

*>>-----Original Message-----
*

*>>From: owner-voting-project@afterburner.sonic.net
*

*>>[mailto:owner-voting-project@afterburner.sonic.net] On Behalf Of Arthur
*

*>>Keller
*

*>>Sent: Thursday, April 29, 2004 9:26 AM
*

*>>To: voting-project@lists.sonic.net
*

*>>Subject: RE: [voting-project] What is Data Model FOR?
*

*>>
*

*>>Mark, I'm confused by your answer.
*

*>>
*

*>>Since ranked preference voting says: A, B, C is different than B, A,
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*>>C, there are more than 6 possible vote combinations for 3 candidates.
*

*>>(ABC, ACB, BAC, BCA, CAB, CBA are the full ones; also A, B, C, AB,
*

*>>BA, AC, CA, BC, CB, and no choices selected. Wow, that's 16 choices.
*

*>>Does someone have a formula in closed form for the number of possible
*

*>>rankings for n candidates? For the full ones, its the number of
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*>>permutations of n candidates, or n! (n factorial).)
*

*>>
*

*>>You could list all the combinations and keep a count of how many
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*>>times each combination was a voter's selection. Or you could
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*>>incrementally build the list of combinations as they were encountered
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*>>in the canvassing, while maintaining the count of repetitions.
*

*>>
*

*>>Once the canvassing is completed, you can perform the appropriate
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*>>calculations. As long as you keep the raw counts of combinations,
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*>>you can do the calculation as often as you like. It's probably a
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*>>good idea to publish the raw counts of combinations so others can
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*>>check your final vote assignment algorithm or even do research to
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*>>develop new ones.
*

*>>
*

*>>Best regards,
*

*>>Arthur
*

*>>
*

*>>At 10:36 AM -0500 4/29/04, Mark Winegar wrote:
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*>>>Doug,
*

*>>>
*

*>>>You may be able to implement the canvassing of ranked preference votes
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*>>>as a simple array of contests. This should simplify the required logic
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*>>>of the canvassing process.
*

*>>>
*

*>>>Mark Winegar
*

*>>>
*

*>>>-----Original Message-----
*

*>>>From: Douglas W. Jones [mailto:jones@cs.uiowa.edu]
*

*>>>Sent: Thursday, April 29, 2004 10:27 AM
*

*>>>To: voting-project@lists.sonic.net
*

*>>>Subject: Re: [voting-project] What is Data Model FOR?
*

*>>>
*

*>>>
*

*>>>
*

*>>>On Apr 29, 2004, at 12:48 AM, David Mertz wrote:
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*>>>
*

*>>>> dr-jekyll@att.net wrote:
*

*>>>> |Does "vote aggregation" mean vote totals? The Data Model I
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*>>submitted
*

*>>>
*

*>>>> |does have a place for accumulating vote totals.
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*>>>>
*

*>>>> Aggregation is likely to involve move than a simple counter.
*

*>Maybe
*

*>>>> the counter suffices for a first pass, on some kinds of races.
*

*>But
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*>>>> consider, for example either N of M or ranked-preference contests.
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*>>>> The tallying of rank orders involves more than just counting the
*

*>>>> votes; for example, in IRV, it would go through stages with
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*>>>> reassignments of votes and recounts.
*

*>>>
*

*>>>I should note that the canvassing rules I proposed in my previous post
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*>>>don't apply directly to ranked preference votes, but there are
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*>>>generalizations that do apply. Designing canvassing procedures that
*

*> >>allow for self-audit throughout the process is most difficult for IRV
*

*>>or
*

*>>>STV systems. It is easier for weighted preference systems.
*

*>>>
*

*>>> Doug Jones
*

*>>> jones@cs.uiowa.edu
*

*>>
*

*>>
*

*>>--
*

*>>-----------------------------------------------------------------------
*

*>-
*

*>>-------
*

*>>Arthur M. Keller, Ph.D., 3881 Corina Way, Palo Alto, CA 94303-4507
*

*>>tel +1(650)424-0202, fax +1(650)424-0424
*

*>
*

*>
*

*>--
*

*>------------------------------------------------------------------------
*

*>-------
*

*>Arthur M. Keller, Ph.D., 3881 Corina Way, Palo Alto, CA 94303-4507
*

*>tel +1(650)424-0202, fax +1(650)424-0424
*

-- ------------------------------------------------------------------------------- Arthur M. Keller, Ph.D., 3881 Corina Way, Palo Alto, CA 94303-4507 tel +1(650)424-0202, fax +1(650)424-0424 ================================================================== = The content of this message, with the exception of any external = quotations under fair use, are released to the Public Domain ==================================================================Received on Fri Apr 30 23:17:23 2004

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