[EM] Fwd: Ranked Pairs

[Richard, the VoteFair guy]

On 9/24/2023 1:31 PM, Colin Champion wrote:
 > Kevin – I'm not sure if you're right about IRV. If someone votes A=B>C,
 > I'd attribute half a first-place preference to each of A and B. I don't
 > know what other people would do.
 >     Colin

Under IRV another counting option is to pair this same-rank ballot 
(A=B>C) with another ballot that also reaches the counting round where 
the same two candidates (A and B) are top ranked (after ignoring any 
higher-ranked candidates who have been eliminated).  Then one of the two 
ballots goes to one of the two candidates and the other ballot goes to 
the other candidate.

Of course mathematically this is equivalent to splitting each ballot 
into 0.5 votes for candidate A and 0.5 votes for candidate B.  However 
this decimal interpretation violates what many non-math-savvy voters 
would regard as a violation of "one person one vote."  So academic 
testing software can use the easier-to-code decimal numbers.  But for 
real certifiable election software the non-ballot-splitting method would 
be easier to understand as fair.

Detail:  When a ballot can't be paired with a pattern-matching ballot, 
that ballot is ignored.  This is equivalent to the decimal option with 
rounding non-integer numbers down to the nearest integer.

Of course the pairing concept can be extended to any number of 
candidates -- 3, 4, etc. -- being ranked at the same choice level. 
However, beyond about 5 or 6 this approach consumes too much memory 
because every possible "pairing" must be tracked.  To avoid this issue I 
think it's reasonable to have a rule that says the ballot is set aside 
until the number of currently same-ranked candidates is 5 or less.

This "pairing" option is what I coded here:

https://github.com/cpsolver/VoteFair-ranking-cpp/blob/master/rcipe_stv.cpp

It calculates these methods:

* RCIPE
* RCIPE STV.
* IRV (for comparison purposes only)
* STV

Richard Fobes