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Note that this is a definition of majority/minority, not a theorem proved about them. It's indeed true that by definition, there are no majorities for finite se
by taejo 9y ago
Note that this is a definition of majority/minority, not a theorem proved about them. It's indeed true that by definition, there are no majorities for finite sets.
- schoen 9y agoI didn't quite understand your reply. Did you mean to say that there are no majorities for infinite sets? Edit: It sounds elsewhere like the whole point of this may be the distinctive, counterintuitive properties of infinite sets (in this case especially under AC), but I'm continuing to be a bit confused by the presentation and context.
- soVeryTired 9y agoThe article has taken the word "majority" and redefined it to be something counterintuitive, and only partly related to the standard use of the word majority. A under "normal" usage, the words majority / minority have this property: > The intersection of two minorities is a minority, and the union of two majorities is a majority As the GP points out in his reply to my original comment, you can get this property from >If a vote is held and the Ayes have it, and then any number of voters switch from Nay to Aye, the Ayes still have it Now the author is redefining the terms minority and majority so they have this property: > The union of two minorities is a minority, and the intersection of two majorities is a majority But that's not possible unless you have infinite votes. As GP points out, it's clearest when you take "minority" to mean finite, and "majority" to mean "infinite, with finite opposition".
- schoen 9y agoThanks!