[EM] Election-Methods Digest, Vol 96, Issue 22

[Nicholas Buckner]

Actually, on a weird second thought, wouldn't a method that refused to
identify a winner in a three-way tie (Condorcet paradox) be compatible
with both? It would be I guess case 5 (A, B, C, D, no winner). It
wouldn't be a very practical method, as we need our voting methods to
decide ties, but isn't deciding the tie what breaks the Participation
criterion? My voting method only made the mistake of picking a winner
in the first place (a mistake I'd happily do again).

Also, I am sorry Markus Schulze that it seemed I was ignoring you. I
was actually engrossed in programming two things. The first program
found the exact limits a quota in my system would break down if
defined as votes/(slots+1)+1(2*votes). If slots = 1, it is 89,478,486.
If slots = 2, it is 100,663,296. 3: 134,217,728. 4: 167,772,160. 5:
178,956,971. I'll post the source code soon. I was going to use it to
justify changing how the program functions to create a mimic function
that allows for trillions of votes. Two, the second program was to try
to find the simplest example my voting system breaks down (like if you
changed the Moulin example case 1 to 3,3,5,5 instead of 3,3,4,5, an
example I found 12 hours ago, but was trying to see if my program was
limited to only under-half way examples)... I was hoping to quantify
the percentage of cases where a guess in order for Condorcet ties
leads to violating the Participation Criterion. I was also hoping to
apply this quantifier to other examples in an effort to show certain
methods try to stick to it as best they can while other methods are
more random or worse backwards in their Condorcet tie picking.

I was still trying to generate a list of statistics this program would
collect: how many candidates are needed (because I believe some
methods will break down at three candidates even though all will break
down at four); how many votes are needed (both in the pre-add and
post-add); how many un-forced errors are there (how many times is it
not a Condorcet tie that still breaks the Participation Criterion); in
the case where these criterions conflict, how many rank reshufflings
are positive (move closer to the new voter's preferences) and how many
are negative (move away from the new voter's preference, possibly by
overshooting), and what is the net result (-8 (A>B>C>D + A>B>C>D
causes D>C>B>A, highly unlikely but a possibility) to +8); what rank
in the new vote causes a conflict (previous winner in first, second or
third).

I don't think the test is too complex. There are 24 possible voting
groups (4! or 4*3*2) given anywhere from 0 to x votes (5 was the limit
in the Moulin sample) initially and then given y new votes in one of
the 24 possible voting groups. Without a max vote counter, this could
turn into a 2.73E+21 combination problem, a initial vote limit (my
problem would have been found in vote limit = 16) could significantly
reduce that (given the max would be 120 without). (Timing wise, I
found that 89,478,486 number in seconds on my computer, so it is
possible to find given enough time)

I don't suppose anyone has any suggestions about additional statistics
to be collected, as I would love to target other methods later?

Humbly,
Nicholas Buckner