For my demonstration that Plurality fails PSBC, I should say something abaout PSBC's premise stipulation that the X>Y MPP is not in a cycle of MPPs that are all at least as strong as it is.
With voted MPVs in Purality, it's simple: If a majorilty vote for X, then there can't be a path of MPVs from Y to X, because no majority vote Y over anyone, and no majority vote anyone over X.
But, for the MPPs mentioned in PSBC's premise, let's just say that there is no path, from Y to X, of MPPs that are all at least as strong as the X>Y MPP. That assumption in no way affects the conlusions that I reached in the demonstration.
That's because:
In my demonstration that I posted, I told why, in my example, a majority must vote for Y. Obviously that means that Y wins. The matter of whether or not there's a path, from Y to X, of MPPs that are all at least as great as the X>Y MPP has absolutely no effect on the fact that Y wins. Plurality looks at whom people vote for, and I told why a majority vote for Y. The matter of whether or not there's a path, from Y to X, of MPPs at least as great as the X>Y MPP doesn't decide how people vote. How those Y voters, X voters and Z voters vote is constrained by the stipulation that no one falsifies a preference. That stipulation requires them to vote for their favorite. And because that means that the X and Z voters split their vote in half, with 30% for X and 30% fopr Z, and 60% vote for Y, it means that Y wins. Regardless of whether or not there's a path, from Y to X, of MPPs that are all at least as strong as the X>Y MPP.
Mike Ossipoff
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