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

[James Gilmour]

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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