# RE: What is Data Model FOR?

From: Arthur Keller <arthur_at_kellers_dot_org>
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
>for me. But n! only gives you the full permutations of n!
>candidates, not the partial permutations of up to n candidates. Do
>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
>any
>>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?
>>
>>
>>Since ranked preference voting says: A, B, C is different than B, A,
>>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
>>permutations of n candidates, or n! (n factorial).)
>>
>>You could list all the combinations and keep a count of how many
>>times each combination was a voter's selection. Or you could
>>incrementally build the list of combinations as they were encountered
>>in the canvassing, while maintaining the count of repetitions.
>>
>>Once the canvassing is completed, you can perform the appropriate
>>calculations. As long as you keep the raw counts of combinations,
>>you can do the calculation as often as you like. It's probably a
>>good idea to publish the raw counts of combinations so others can
>>check your final vote assignment algorithm or even do research to
>>develop new ones.
>>
>>Best regards,
>>Arthur
>>
>>At 10:36 AM -0500 4/29/04, Mark Winegar wrote:
>>>Doug,
>>>
>>>You may be able to implement the canvassing of ranked preference votes
>>>as a simple array of contests. This should simplify the required logic
>>>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:
>>>
>>>> dr-jekyll@att.net wrote:
>>>> |Does "vote aggregation" mean vote totals? The Data Model I
>>submitted
>>>
>>>> |does have a place for accumulating vote totals.
>>>>
>>>> Aggregation is likely to involve move than a simple counter.
>Maybe
>>>> the counter suffices for a first pass, on some kinds of races.
>But
>>>> consider, for example either N of M or ranked-preference contests.
>>>> The tallying of rank orders involves more than just counting the
>>>> votes; for example, in IRV, it would go through stages with
>>>> reassignments of votes and recounts.
>>>
>>>I should note that the canvassing rules I proposed in my previous post
>>>don't apply directly to ranked preference votes, but there are
>>>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

```--
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Arthur M. Keller, Ph.D., 3881 Corina Way, Palo Alto, CA  94303-4507
tel +1(650)424-0202, fax +1(650)424-0424
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Received on Fri Apr 30 23:17:23 2004

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