Quasi- Concave Social Welfare Functions

Boston College, Chestnut Hill MA

Investigators

Abstract

Utilitarianism suggests that societies should be interested in maximizing the sum of individual utilities. Modern objections to utilitarianism are that it implies indifference to randomization. When society is indifferent between giving an indivisible good to one of several individuals, nothing is gained by choosing the recipient by a lottery. Nonlinear alternatives to utilitarianism can solve this problem. Such alternatives use what is technically labeled as 'quasi concave social welfare functions.' Here we suggest another difference between utilitarianism and these alternatives. Rather than starting with situations of social indifference, we concentrate on situations of extreme inequality, and investigate the implications utilitarian and non-utilitarian have in these situations. Suppose society is facing trade-off between reducing the number of those who are worse off and improving their overall position. Both objects are desired, but often one comes at the cost of the other. Our theoretical conjecture is that the more society prefers randomization in symmetric situations, the more it will prefer improving the position of those who are at the bottom at the cost of increasing their numbers. In the less theoretical part of this research, we would like to establish the following claim: free, liberal societies move in the same direction as the one suggested by quasi concave preferences. Charity Suppose society is composed of two groups, `haves' and `have nots.' We have a given budget to help the second group, and the choice is between two policies: "Individual help" that takes individuals from the second group and transfer them into the first, and "community help," where the money is spent on improving facilities for the second group. We can also choose any feasible combination of the two. Increasing the amount spent on community help means less money for individual help, therefore higher probability of being at the lower group, but the welfare of all individuals of this group is increasing with the money spent on such programs. We predict that a quasi-concave society will prefer the community to the individual help. Cruel and Unusual Punishment Harsh punishment is more deterring than mild one. By using such punishments we can reduce the number of people who will be punished, and improve the position of those who do not commit crimes, at the cost of reducing the welfare of those who are at the bottom. Our conjecture is that the utilitarian society will use harsher penalties than the quasi-concave society. Safety and Prevention Sometimes, quasi-concave societies choose outcomes whose optimality is questionable. Suppose society can choose between improving public safety, or spending money on saving people who had an accident. Suppose further that more people could be saved the first way. It follows from our conjectures that for a given budget, the quasi concave society will spend less on prevention and more on saving people after an accident happens than the utilitarian society.