UBC Theses and Dissertations
Essays in group decision-making Nandeibam, Shasikanta S.
The thesis comprises of two essays. Although the two essays deal with somewhat different situations and use different approaches, both of them essentially examine the problem of making decisions that affect some group of individuals. The first essay is on moral hazard and looks at the principal's problem in a principal-agent(s) free-rider problem in which, unlike most existing work, the principal is not precluded from participating in the production process. Furthermore, there are no uncertainties, but moral hazard is caused by joint production which renders the action of each individual in the production process unobservable. A multi-stage extensive game in which only the principal can propose the output sharing rule determines both the set of individuals who actually participate in the joint production process and the output sharing rule. The main conclusion we draw in the first essay is that, when designing the optimal output sharing rule, the principal need not look for any output sharing rule more sophisticated than the linear or piecewise linear rules we frequently observe. We also characterize the condition under which the principal chooses to take part in production, and conclude that the issue of mitigation of moral hazard and sustainability of efficiency crucially hinges on whether the principal actually participates in production or not. More concretely, we show that moral hazard dissipates completely whenever the principal does not participate in production, however, even then she does not achieve as much welfare as in the First Best situation if her best option in the First Best situation is to take part in production. The second essay is in stochastic social choice theory. In a paper published in 1986 in Econometrica, Pattanaik and Peleg formulated stochastic analogues for each of Arrow's axioms and concluded that the stochastic social choice functions that satisfy their axioms are essentially randon dictatorships when individuals have strict preferences. More precisely, there is a unique weight associated with each individual such that the vector of these individual weights has the properties of a probability distribution over the set of individuals, and, given any preference profile and any feasible set, the probability that a feasible alternative is chosen is equal to the sum of the weights of those individuals who have this alternative as their best feasible alternative. We extend the analysis of Pattanaik and Peleg by allowing individuals to have weak preferences. As in their paper, it turns out that the probabilistic versions of Arrow's condition simply that there are individual weights. However, now, given a preference profile and a feasible set, we partition the society so that any two individuals from different elements of the partition have no common best feasible alternatives, but the set of best feasible alternatives of each individual in an element of the partition overlaps with that of some other individual in the same element. Using this partition, it is shown that the only restriction on the stochastic social choice function is that the sum of the weights of all individuals belonging to the same element in the partition is equal to the probability that some alternative which is best in the feasible set for one of these individuals is chosen. When everyone has unique best feasible alternatives, the rules characterized here reduce to those of Pattanaik and Peleg.