4. [3] A society made up of N individuals must make a collective decision over two alterna- tives, A and B. For example, suppose that A represents going to war and B represents maintaining the peace, or A represents levying high taxes to provide many public services and B represents keeping taxes low and financing few welfare state programs, etc. Each member of this society has her own preferred alternative between A and B, an no one is indifferent between these two alternatives. (a) [1] True or False, and explain: Installing a dictator and having her choose between alternatives A and B will yield a Parcto-efficient decision for this society. (b) [1] True or False, and explain: Holding a majority vote between alternatives A and B will yield a Parcto-efficient decision for this society. (c) [1] True or False, and explain: flipping a coin between alternatives A and B will yield a Parcto efficient decision for this society