[EM] IRV proponents figure out how to make IRV precinct-summable

[Kristofer Munsterhjelm]

Kathy Dopp wrote:
> Wow,
> 
> I had to laugh out loud after finally figuring out these instructions
> that Chris Telesca of NC sent me in this PDF doc:
> 
> "Instant Runoff Voting, Single‐Seat Contests, ES&S Optical Scan
> Tabulation Procedures"
> 
> http://electionmathematics.org/em-IRV/NC/IRVcountingProced.pdf
> 
> Aren't IRV proponents (of the most fundamentally unfair voting method
> that has ever been used) CLEVER!
> 
> IRV proponents have figured out how to count a NC-style IRV election
> (where all but the top two candidates are dropped in the first round)
> in the polling locations on Election Night in a way that makes
> IRV-NC-style precinct-summable!

Sure - if you have an elimination method where you batch eliminate all 
candidates but k, where k is some constant, then do a count among those, 
that method will be summable. Since k is a constant, k! will also be. 
The constant would be extremely large for large numbers of k, though.

I wouldn't call this method IRV, either, but "contingent vote". About 
the only thing it has going over Plurality is that it never elects a 
Condorcet loser.

The summable version for k = 2 would work like this: you have an array 
of n, which is the Plurality count for the first election. Then you have 
an n*n matrix, call it c, where c[a, b] designates how many times A is 
ranked before B. The idea would be to first determine the two Plurality 
winners, then (call them x and y) check if c[x, y] > c[y, x]. If so, x 
wins; if c[x, y] < c[y, x], then y wins, otherwise there's a tie.

But hold on. Isn't c the Condorcet matrix?

> Wow. I'm really impressed for once by the skills of the IRV proponents
> in figuring out a way to make round #2 of IRV precinct-summable -
> which works in the NC version of IRV because all but two candidates
> are eliminated in round #1.
> 
> However, there are some issues with the IRV proponents' method for
> making IRV precinct-summable in this NC-style IRV contest that also
> restricts voters to ranking at most three candidates and therefore has
> at most two counting rounds altogether for a one-winner contest due to
> eliminating all but the two candidates who receive the most first
> choice votes (a method that could often eliminate the most popular
> majority candidate as happened recently in Burlington, VT
> http://rangevoting.org/Burlington.html)

That almost turns it into the Supplementary Vote (where people can only 
rank two candidates).

> 4. Are the election officials going to create the three PCMCIA cards
> accurately for EACH precinct or poll loc for each IRV contest, label
> them accurately and make sure that the right card is inserted at the
> exact right time in the process?

This sounds like simply bad programming. Having to use different PCMCIA 
cards is a limitation of the voting machine, not the system; and if they 
really want to use this method, they could presumably ask for a machine 
that counts c (and the Plurality counts) in one go. If c really is the 
Condorcet matrix, this may make it easier to move to Condorcet methods 
in the future, too.

> 6. Wow. I would LOVE to see what happens if the late-counted absentee,
> early, or provisional ballots changes who the top-two 1st choice vote
> winners are, and the entire polling location counts have to be thrown
> out and all the ballots have to be recounted!  Lovely thought for all
> those poll workers who are going to stay up all night counting but
> whose counts may be entirely scrapped later on whenever the number of
> first choice votes is very close for the candidate with the second
> most and third most first choice votes!

I don't see how that would be messy. Say the plurality count is 100 A, 
99 B, and c[A, B] is 125 and c[B, A] is 124. Then adding a few more B 
first, A second ballots will change the plurality count (to say, 101 A, 
105 B), and c (to say c[A, B] 131, c[B, A] 125). The actual winner 
calculation would proceed differently, but since the method is district 
summable, it's also individually summable ("districts" of one per voter).