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 ---- Election-Methods mailing list - see http://electorama.com/em for list info
