Let N=\left\{1,2,3...n \right\} be a set of elements called voters. Given that S \amalg N means S is a subset of the set N.
Let \C=\left\{S:S\amalg N \right\} be the set of all subsets of N.
Members of C are called coalitions.
Let f be a function defined from C to \left\{0,1 \right\}. A coalition S\amalg N is said to be winning if f(S)=1 ; it is said to be losing if f(S)=0.
A pair (N,f) as above is defined as a voting game if the following conditions hold :-
a) N is a winning coalition.
b) The null set is a losing coalition.
c) If S is winning, with S'\amalg S, then S' is also winning.
d) If both S and S' are winning coalitions, then S\cap S'\ne \phi, i.e S and S' have a common voter.
Find a voting game in which the number of winning coalitions is 2^{n-1}.
I took almost ten minutes to undertsand what this sum actually wants - let alone solving it..
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