Adam Tarr wrote:
So the question is, which of these majority wins matter, and which ones don't? "Adam Tarr" is not in the Schwartz set, so does not even make it to our tiebreaker. But notice, under both methods, that C's "non-majority" defeat of B has mattered, to this point, just as much as A's majority win over C and B's majority win over A, insofar as all three candidates are still in the running. We should not be able to say at this point, without applying further criteria, whether C should or should not be among the winners. Yet it seems that you have already decided C cannot be among the winners (therefore the A over C defeat is not erased). Can there be no tiebreaker under which C wins? My own intuition, looking at the numbers, says this is pretty close to a three-way tie. Perhaps the A over C majority has not been respected after all?Tom McIntyre Wrote:MIKE OSSIPOFF wrote:
101: A
50: BAC
100: CBA
About 60% of the voters have indicated that they'd rather elect
B than A. And so margins elects A.
WV counts, keeps, & honors the B>A majority. A has a majority defeat that wv doesn't lose or erase. With margins, what happens to that majority against A? Margins erases it.
And about 60% prefer A to C. What about honoring *that* majority? One of these majorities has to be lost. Both WV and margins count, keep, & honor one of them, and erase the other.
The A over C defeat is not erased. The only way you could consider that defeat erased, would be if C had won the election. Take the extreme example: say there was a fourth candidate, "Adam Tarr", who received zero votes. Does electing A, B, or C constitute "erasing a majority", because the other two candidates' defeats of mr. Tarr are not counted? Of course not. Such a standard would force us to declare every nontrivial multicandidate election as a tie.
Let's take another example:
101: A
1: BAC
101: CBA
In this case, B defeats A 102>101, A defeats C 102>101, and C defeats B 101>1 (with 101 abstaining). B>A and A>C are victories by majority, but very weak victories. C>B is a non-majority win, but a resounding victory. Just to get to a three-way tie, we must assume that all 101 abstaining votes really meant to choose B over C (and that's one possibility out of 2^101 or over 2,000,000,000,000,000,000,000,000,000,000, if we force each one take a preference). The only possible choice that will reflect the will of the electorate is that C wins. C is the winner picked by margins, but WV stubbornly insists on the sanctity of a majority of all voters and picks B.
I really think this insistence on victory by a majority only makes sense in a two-option election, in which case there's really no other way to go. Even then, what about the large number of eligible voters who usually stay home? We must consider that at least some of them do so because they have no preference. If a third candidate were to enter the race, some of these voters may choose to come and vote, selecting only the third candidate and not specifying a preference between the initial two. By the counting method that says C>B is not a majority victory, we now may be able to say that there is not a majority win between the first two. So even in a two-candidate election, what we really mean when we say "majority" is "majority of the voters who bothered to specify a preference". That's the only way to define majority that gives the same result under both these two and three candidate scenarios. And under this definition, C>B is a majority win.
I think the concept of "majority", in the sense that you mean it, is a concept that sounds intuitive, but is ultimately not workable in the same way that cyclic ties sound counterintuitive, but actually make sense (which, BTW, I have a good geometrical argument as to why cyclic ties make sense, if anyone cares to see it). In fact, we can alter the above examples to make C the Condorcet winner despite not having this sort of majority in either pairing, and despite B>A being this sort of majority. That's because margins -- not WV -- is used when determining the Condorcet winner. Everyone seems to be happy with margins and with non-majority wins when picking a Condorcet winner, so it doesn't make sense to me that they should suddenly become inadequate halfway through the counting process. I'd rather toss the idea that a win involving a majority of all those coming to the polls must never be defeated by a win involving a majority of those specifying a preference at the polls.
Tom McIntyre
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