A 2⁄3 majority prefer Kasich to any other candidate. The point is that Independence of Irrelevant Alternatives dictates that if a group prefers X to Y, and prefers X to Z, that they logically must prefer X if all three are options. It’s like if I ask you to choose between chocolate and vanilla and you pick chocolate; if I tell you strawberry is also an option, that shouldn’t make you switch to vanilla.
There’s no group that prefers Kasich to Trump and also prefers Kasich to Clinton. It’s 2⁄3 in each case, but those two groups of 2⁄3 only have an overlap of 1⁄3.
I’m not familiar with voting theory, so I might be missing the point, but the sentence “there exists a 2⁄3 majority of the voting population all of whom prefer Kasich to any other candidate” is false. (The problem might be the ambiguity of the English language: it is true that “for any candidate besides Kasich, there exists a 2⁄3 majority who prefers Kasich to that candidate”.)
A 2⁄3 majority prefer Kasich to any other candidate. The point is that Independence of Irrelevant Alternatives dictates that if a group prefers X to Y, and prefers X to Z, that they logically must prefer X if all three are options. It’s like if I ask you to choose between chocolate and vanilla and you pick chocolate; if I tell you strawberry is also an option, that shouldn’t make you switch to vanilla.
There’s no group that prefers Kasich to Trump and also prefers Kasich to Clinton. It’s 2⁄3 in each case, but those two groups of 2⁄3 only have an overlap of 1⁄3.
I’m not familiar with voting theory, so I might be missing the point, but the sentence “there exists a 2⁄3 majority of the voting population all of whom prefer Kasich to any other candidate” is false. (The problem might be the ambiguity of the English language: it is true that “for any candidate besides Kasich, there exists a 2⁄3 majority who prefers Kasich to that candidate”.)
That is irrelevant.