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

[Abd ul-Rahman Lomax]

At 08:48 PM 2/4/2010, robert bristow-johnson wrote:

>... you're running away from the salient question.  are those 9 piles
>good enough to resolve the IRV election with 3 candidates or not?
>was salient information lost when the M>K pile was combined with the
>M>K>W pile, enough that could cause the IRV election (with the rules
>above) to be decided differently?

Yes, salient information was lost, or, more accurately, could have 
been lost if those were first round totals reported to central 
tabulation. Once we know that only three candidates are eligible to 
have votes counted, and if a "majority of votes" is irrelevant, i.e., 
IRV is being used as a plurality method, so that "majority" can mean 
something other than "majority of ballots containing a vote," then, 
yes, M>K and M>K>W are exactly equivalent.

But we cannot know this until all other candidates have been 
eliminated, we cannot know which candidates have been eliminated, not 
from a single precinct's point of view. The precinct must report, at 
least, the first round totals for all candidates, and write-ins 
lumped, at least, and those reports are completely missing from what 
RBJ proposes. Then, for the report to be useful for later tabulation 
with no further report to central tabulation, it must contain, for 
each candidate, subsequent rankings, so that the effect of 
eliminating that particular candidate can be known.

Lumping write-ins, there are thus six candidates, not five, and 
certainly not three. How could a precinct limit itself to reporting 
only votes for three candidates when there are five on the ballot 
plus write-in? What's the algorithm?