I do not understand Warren's example. Specifically, I do not know what he has in mind as the independent events whose conjunction is being considered. Note that the event "there exists an ordering such that x_j<j/N for each j=1,2,3,...,N" is not the conjunction of the N events "there exists an ordering such that x_1<1/N", "there exists an ordering such that x_2<2/N", ..., "there exists an ordering such that x_N<N/N". I figured someone else would point this out, but nobody else has, so maybe other people see what Warren had in mind and I'm missing something? Jim Propp On Tue, Nov 11, 2014 at 12:09 PM, Warren D Smith <warren.wds@gmail.com> wrote:
Perhaps this nicely typeset page will help you understand the problem:
http://rangevoting.org/CombinedTestFail.html
The answer is NOT a*b*c*...* despite the tests being independent. This is a trap too many fall into. Indeed, if there were N uniform(0,1) independent randoms, and somebody told you "there exists an ordering such that x_j<j/N for each j=1,2,3,...,N" you do NOT want to be an idiot and conclude "my god, that is an amazingly exponentially improbable miracle." Actually, it is quite likely even for N=100. Eh? So hopefully I've piqued your interest now.
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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