Henry Baker wrote:
Although the Democrats have the most votes in the Committee, they held a 'voice vote' in which the appointee was approved. They then recorded the votes individually, showing that more individuals voted against than for.
(I guess this is a form of 'dark matter' votes, wherein the sum total is large enough, but a census of individuals can't turn up enough to account for the total.)
Perhaps the Democrats have agreed not to make waves and allow the appointee to progress w/o difficulty; but the individual committee members want to be on record as opposing the approval. They get it both ways--a blue ribbon day for a politician on either side of the aisle!
I'm curious if there are any real mathematical situations wherein a class loses, but when considered as individuals, they win. I presume we'd have to be talking about infinite sets, though, in order to even entertain such a notion.
My favorite form of Simpson's paradox, using baseball batting averages, comes to mind. In the first half of the baseball season, A has a better batting average than B (.275 vs. .250); and the same for the second half of the season (.325 vs. .300). But overall, B can have a better average, due to hidden bias: (25+100)/(100+300) > (55+65)/(200+200). Nick