4 Three individuals Ann, Bob and Colin would like to determine a group preference ordering over two possible joint projects X and Y, that is, they would like to nd a. function that maps every possible prole of individual preference orderings over X and Y into a group preference ordering. (a) (i) What properties is an Arrow social choice rule supposed to have? {ii} Will A' B and C be able to dene such a. choioe rule? Carefully explain your answer with reference to Arrow's Impossibility The- orem. {b} Denote the possible (strict) preference proles over X and Y as in the following table; for example, in prole I everybody prefers X over Y. Assume that the social choice function F(-) selects the group prefer ence ordering given by the bottom line: Is it possible to dene F(VIII)' such that all desirable properties are fullled? (1:) Assume now that there is an additional' third alternative Z, and consider the following two possible preference proles: Assume that FU) = X >- Z > Y. What does this imply for F(II) if the Independence of Irrelevant Alternatives property is fullled