[EM] IRV ballot pile count (proof of closed form)

[James Gilmour]

Abd ul-Rahman Lomax  > Sent: Friday, February 05, 2010 4:50 PM
<CUT>
> Practically speaking, I'd assume, the precincts would be provided 
> with a spreadsheet showing the possible combinations, and they would 
> report the combinations using the spreadsheet, transmitting it. So 
> some cells would be blank or zero. With 5 candidates on the ballot, 
> the spreadsheet has gotten large, but it's still doable. What happens 
> if preferential voting encourages more candidates to file, as it 
> tends to do? 23 candidates in San Francisco? Even with three-rank 
> RCV, it gets hairy.

Respectfully, I would suggest this would NOT be a wise way to collect the data.  As I pointed out in my e-mail that correctly listed
the maximum possible number of preference profiles for various numbers of candidates, the actual number of preference profiles in
any election (or any one precinct) with a significant number of candidates, will be limited by the number of voters.  Further,
because some (many) voters will choose the same profiles of preferences, the actual number of preference profiles will likely be
even lower  -  as in the Dáil Éireann election I quoted.

Thus a spreadsheet containing all possible preference profiles would be unnecessarily large and the probability of making mistakes
in data entry would likely be greater than if each precinct recorded only the numbers for each profile actually found in that
precinct.

<CUT>

> There is a way to avoid such massive reporting, which is to report 
> interactively, which is what is done in Australia. Only one set of 
> totals is reported from a precinct at a time, the totals for the 
> current round. (which can be just uncovered votes due to eliminations 
> that have been reported to the precinct from central tabulation.)
> 
> However, the problem with this is that a single error in a precinct 
> can require, then, all precincts to have to retabulate. 

Yes, this "distributed counting" would work.  But there is an even simpler solution  -  take all the ballots to one counting centre
and then sort and count only the ballots that are necessary to determine the winner (or winners in an STV-PR election).  That what
has been done for public elections in Ireland and the UK for many decades and it works well without problems.  But I do appreciate
that is far too simple and practical a solution and it suffers from NMH.

James Gilmour

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