Chance, Strategy, and Choice by Smith Samuel Bruce

Author:Smith, Samuel Bruce
Language: eng
Format: epub
Publisher: Cambridge University Press
Published: 2015-06-30T04:00:00+00:00

The academic committee is a weighted voting system as in Definition 7.3. Here the quota is q = 30. Recall that we write such a system as

We compute the power index for this voting system.

As in the case of the U.N. Security Council, it suffices to compute

and

We make this calculations using the following tables counting winning coalitions. The distinguished player (D1 and P1) is included in the first column. In the second column, we decrease the number of deans included. The third column adds in professors as needed to make the coalition winning and the distinguished player a critical player. The counts are then made by multiplying the “choose” values or sum thereof from each column. Recall that we have defined = 1.

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