[EM] Unranked ballot election challenge

[Tom Ruen]

Comparing Unranked-IRV with Approval, these methods have divergent winners
in less than 2% of random elections with 3 candidates and many voters. This
is a very small variation, but worthy to be considered.

Here's one (random) election I picked to demonstrate:

Approval ballots:
C=7886 (32.0%)
B=7411 (30.1%)
A=7298 (29.6%)
A+B=1103 (4.5%)
A+C=546 (2.2%)
B+C=405 (1.6%)

Looking at these ballots we can see a very close 3 way race among 3
candidates. We can see C has the largest united coalition and A and B have
the largest compromise coalition.

If we measure by approval:
A=7298+1103+526=8927  (36.2%) (First)
B=7411+1103+405=8919  (36.2%) (Second)
C=7886+405+526=8817    (35.8%) (Third)
A wins by a hair over B.

IRV gives a different result:
Round 1:
A=7886+(1103+546)/2=8112.5 (32.9%) (Third)
B=7411+(1103+405)/2=8165.0 (33.2%) (Second)
C=7886+(405+526)/2=8351.5 (33.9%) (First)
Eliminate A
Round 2:
B=7411+1103+405/2=8716.5 (35.4%) (First)
C=7886+405/2+526=8614.5 (35.0%) (Second)
NOTA=7886 (29.6%) (Third)
B wins

Well, so here we have a case to consider. B has more core supporters than A,
and A has more compromise supporters from C. Splitting votes compared to
full votes makes a difference.

Which result more accurately represents voter preference?

Tom Ruen