[EM] Real IRV Election, Disputable Result

[raphfrk at netscape.net]

Jonathan Lundell <jlundell at pobox.com> wrote:
>
>Jeff O'Neill (who I think is on this list) suggests a tree
>representation of an ranked election profile (Voting matters #21
><http://www.mcdougall.org.uk/VM/ISSUE21/INDEX.HTM>) as a means of
>speeding up the tabulation of the election. It seems to me that such
>a representation, suitable represented in a text file, could be used
>to collect and aggregate ballots from district subdivisions.

That doesn't seem to really reduce the size of the text file, according 
to the paper:

>>List-packed ballots are 65%of the size of raw ballots.
>>Tree-packed ballots are 45% of the size of list-packed
>>ballots and 29% of the size of raw ballots.

The size of the file is 29% the size of listing every vote.  This would 
be pretty massive.  I guess in this day and age, it could be done by 
computer.  However, hand counting has the advantage of being harder to 
rig on a massive scale.  This is more important than extreme accuracy.  
A complex computer program would be safe to use as long as each 
constituency can publish a reasonably short summary of the vote and 
then everyone can check the tally with their own computer.

I wonder if better compression could be achieved in a lossy way.

One option would be to set a max number of options at each level of the 
tree, for example, two nodes for each candidate.

There would be a root node for each candidate showing how many first 
choices.  This would then branch to the 2 most popular 2nd choices for 
that candidate.  The third line in the tree would be for the two most 
popular 3rd choices and so on.

Also, maybe a method for matching votes which are prematurely exhausted 
to one of the valid lines might be possible.  For example, if I voted 
A->B->D and only

A->B->C->D
and
A->B->F->G

are available, then my vote would be added to to the A->B->C->D choice 
as I prefer D to F.

The process would be that at each stage the next two choices that are 
the most popular are picked and each vote is then placed in the "pile" 
that it matches the best.
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