Youtor
Nontransitive Dice and Paradoxes of Probability
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=HOgfR71NrHw
Nontransitive (or intransitive) dice demonstrate a paradoxical property of probability distributions. Just because A usually beats B and B usually beats C, does not mean that A usually beats C. In fact, the reverse can happen, where C beats A most of the time, and we have a cycle. • This video looks at intransitivity via Efron's dice, some of the ways it can occur, and the counterintuitive consequences, including Condorcet's paradox for voting systems. • 00:00 Introduction • 01:51 Let's roll! • 04:36 Intransitive games • 11:16 Intransitive dice • 15:29 Maximum intransitivity - a construction • 17:43 Time to vote/Condorcet's paradox and Arrow's theorem • 21:23 Outro
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