If the crowd is allowed to participate, here's what I would do. Each person in the crowd who wants to participate is given a black card and a white card. There is a countdown, and at the end of it, each member of the audience is to raise one card or the other in the air. Official pictures are taken, and the audience is also encouraged to take their own photographs. The generated bit is 1 if there are an odd number of white cards, 0 if there are an even number of white cards. The black cards aren't strictly necessary, but should help resolve ambiguity over whether a given white card is raised. If the crowd is large, it would be better to select a dozen members of the audience to to up on stage, and only those dozen get to choose black or white. They can be positioned with barriers so they cannot see each other, but the audience can see all of them, Of course, this requires those audience members to be randomly selected, in a way that convinces the crowd that the selection process is random. But all the audience needs to be convinced of is that if there is dishonesty, at least one of the selected members is not part of the conspiracy. I've seen methods like throwing an object into the audience, where the person who catches it is supposed to throw it backwards over their head, and the person who catches that throw (or the one after that, but specified in advance) is the selection. To be convinced that the final result is random, I don't need to believe that the audience members are selected with exactly equal probability; I just have to be convinced that a large number of people (larger than the size of the conspiracy) had a reasonable chance of being selected. If you have to convince an audience member who thinks that there is a massive conspiracy, and everyone in the entire crowd except him is in cahoots trying to make him think the selection is random, this doesn't work. Andy On Wed, May 31, 2017 at 5:31 PM, Dan Asimov <asimov@msri.org> wrote:
You have to perform a random binary experiment in front of a crowd of people —
so no fooling is allowed — in such a way that everyone is convinced that
the experiment was fair. The people include some technical experts but many
who are not.
What is the simplest / easiest / cheapest way to ensure that the crowd will
be convinced that the experiment was fair (the two outcomes had an equal
chance of occurring) ???
—Dan
P.S. I do not have an answer to this, but maybe there is a "best" answer. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com