suppose 3 players, w, a, c, choose among three activities: riding bikes, watching a movie, or playing fortnite (a wildly popular computer game). denote these activities as r, m, f respectively. each player must participate in the activity chosen by the group. the play- ers, being somewhat eccentric, are going to make a group choice by an amendment agenda. but they have to decide the order.
(a) suppose the preferences are m > r > f for w, m > f > r for a, and f > m > r for c. players w and c are willing to let player a purchase the right to choose the order of votes in the amendment agenda. before they decide a price, a needs to know whether he should pay anything for this right, or turn down the offer. if so, what order of moves should he choose? explain your reasoning.
(b) suppose instead the preferences are r > m > f for w, m > f > r for a, and f > r > m for c. isitpossibleinthiscase that a could gain from purchasing the right to choose the order of votes in an amendment agenda? if so, what order of votes should he choose? explain your reasoning.