(Peleg 1991) In the 17th century, some communities in Eastern Europe employed a voting method that recognized the fact that popular interests and the interests of the wealthy or propertied often diverge. To address both of these "constituencies", it was decided that collective decisions should be subject to both voting by "count" and "account", that is, a decision should receive a majority of the popular vote and a majority of the vote in which propertied interests vote in proportion to their wealth. Formally, consider two voting games v and w. In v a coalition S is winning (v(S) = 1) if it constitutes a majority of N, and in w, S is winning if it possesses over half the aggregate wealth. Then overall, S is winning if the product v(S)w(S) = 1. Consider a 3 player example in which wealth is distributed as follows: Player 1 50 Player 2 200 Player 3 350 a. Identify the winning coalitions in the product game vw. b. Compute the Shapley value of the component games and the product game, and discuss the distribution of power in each. c. Alternatively, consider the "sum" (v+w). Compute the Shapley value of (v+w) and contrast that with the product game vw.