A Seat Worth a Twelfth
A company has four shareholders with 40, 30, 20 and 10 votes (100 in total). A motion passes if it gets at least 51 votes. In the Shapley-Shubik index, voters join a coalition in a uniformly random order, and the *pivot* is the voter whose arrival first lifts the running total to at least 51. A voter's power is the probability of being the pivot. What is the Shapley-Shubik power of the 10-vote shareholder? Give a reduced fraction.
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Source: Shapley-Shubik power index (Shapley and Shubik, 1954); the weighted voting system is invented for AxiomIQ. Statement written for AxiomIQ.