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

Kathy Dopp kathy.dopp at gmail.com
Thu Jan 21 16:42:31 PST 2010

```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/InstantRunoffVotingFlaws.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
>
>
--

Kathy Dopp

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

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