[EM] IRV vs Plurality (back to the pile count controversy)

Fri Jan 22 05:42:01 PST 2010

OK James. As I said before, I agree with you that you were giving the
total number of profiles *if* voters were allowed to rank all
candidates, which they were not allowed to do in Minneapolis or
elsewhere in the US public elections if I am right.

Further, I think that Robert is correct, that one could collapse the
last N profiles into prior profiles if that is the system that is used
(allowing ranking all candidates), although I do not think that gives
any advantage, practically, to the counting process and may even
complicate it.

My formula provides the more practical number of how many profiles are
allowed to be cast by voters and how many profiles are needed if one
wants to count the number of votes cast for each profile and make IRV
precinct-summable for an actual election.

Obviously Condorcet counting methods are much simpler to make
precinct-summable than IRV, requiring far fewer number of sums per
precinct as the number of candidates increases.

I think one thing that some election methods experts sometimes fail to
consider are the election administration practicalities that are
crucial to whether or not a method is functionally practical to
provide public oversight over.

I am fully aware that it is voting system technology, costs, and the
increasing impracticality of manually auditing the election if the
full range of preference profiles is allowed, if one is making an
attempt to use paper ballots, that limits the number of choices a
voter may fill out.  I've studied this issue for 7 years now.

Cheers,

Kathy

On Fri, Jan 22, 2010 at 4:08 AM, James Gilmour <jgilmour at globalnet.co.uk> wrote:
> Kathy
> I think my post made clear that I was referring only to "preference profiles".  I was not dealing with the situation where some
> artificial, and highly undesirable, restriction had been placed on the numbers of rankings the voters could mark.
>
> I think my comments about the counting procedure adopted in Minneapolis should have indicated that I am well aware of the
> restrictions that can be imposed.  But note that in Minneapolis the restriction was an artificial one imposed by the certified
> counting machines available for use in the precincts.  There is nothing in the Minneapolis Election Ordinance that imposes such a
> restriction.  So when Minneapolis can obtain certified counting machines that can deal with fully ranked ballots, there will be no
> such restriction in practice.
>
> James
>
>> Behalf Of Kathy Dopp
>> Sent: Friday, January 22, 2010 12:43 AM
>> Subject: Re: [EM] IRV vs Plurality (back to the pile count controversy)
>>
>>
>> James,
>>
>> Your formulas below are only correct in the case that voters
>> are allowed to rank all the candidates who run for an
>> election contest. That may be true in Australia, but is not
>> true in the US where typically voters are allowed to rank up
>> to only three candidates.
>>
>> I put the general formula that applies to *all* cases with n
>> candidates and with r rankings allowed in my paper on IRV
>> that I wrote a year or two ago:
>>
>> Realities Mar Instant Runoff Voting
>> http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/InstantR
>> unoffVotingFlaws.pdf
>>
>>
>> Because it's hard to write a summation, fraction formula,
>> etc. here I'll let you look it up. It's on page 6 of the doc
>> linked above.
>>
>> Cheers,
>>
>> Kathy
>>
>>
>>
>> > From: "James Gilmour" <jgilmour at globalnet.co.uk>
>> > I do not intend to comment on your formula, but I calculate the
>> > numbers of possible unique preference profiles for
>> increasing numbers
>> > of candidates (N) as follows:
>> >
>> > N       Unique Preference Profiles
>> > 2       4
>> > 3       15
>> > 4       64
>> > 5       325
>> > 6       1,956
>> > 7       13,699
>> > 8       109,600
>> > 9       986,409
>> > 10      9,864,100
>> > 11      108,505,111
>> > 12      1,302,061,344
>> > 13      16,926,797,485
>> > 14      236,975,164,804
>> > 15      3,554,627,472,075
>> > 16      56,874,039,553,216
>> > 17      966,858,672,404,689
>> > 18      17,403,456,103,284,400
>> > 19      330,665,665,962,404,000
>> > 20      6,613,313,319,248,080,000
>> >
>> >
>> > Where there are large numbers of candidates, the maximum possible
>> > number of unique preference profiles will be limited by the
>> number of
>> > voters.  Thus if there are 10,000 valid votes and 12
>> candidates, the
>> > maximum possible number of preference profiles would be
>> 10,000 and not
>> > 1,302,061,344.
>> >
>> > In practice the actual number of preference profiles would be even
>> > lower, as significant numbers of voters would record identical
>> > patterns of preferences.  Thus in the Meath constituency
>> for the D?il
>> > ?ireann election in 2002 with 14 candidates (236,975,164,804
>> > possibilities), there were 64,081 valid votes, but only
>> 25,101 unique
>> > preference profiles.
>> >
>> >
>> > The Minneapolis STV (RCV) ballots were all hand sorted to unique
>> > preference profiles for each precinct and hand counted.  This was
>> > unnecessary but feasible as the voters could not record more than
>> > three preferences (rankings), no matter the numbers of
>> candidates. I
>> > understand the full preference profiles, probably at
>> precinct level,
>> > will be published on the City website, but they are not there yet.
>> >
>> > James Gilmour
>
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-- 

Kathy Dopp

Town of Colonie, NY 12304
phone 518-952-4030
cell 518-505-0220

http://utahcountvotes.org
http://electionmathematics.org
http://kathydopp.com/serendipity/

Realities Mar Instant Runoff Voting
http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/InstantRunoffVotingFlaws.pdf

Voters Have Reason to Worry
http://utahcountvotes.org/UT/UtahCountVotes-ThadHall-Response.pdf

Checking election outcome accuracy --- Post-election audit sampling
http://electionmathematics.org/em-audits/US/PEAuditSamplingMethods.pdf