Rational Expectation Theory and Ideological Factor of National Security

707 Words3 Pages
Deriving the Utilitarian Principle Rational expectations theory begins with individual preferences, which are defined over a set of possible states that society might assume. Each state provides utility to individual , who prefers state to state when . Individuals may rank the states differently, which raises the question of how to rank states in a way that takes into account everyone’s preferences. This is the problem of designing a social welfare function, which ranks states socially by assigning them social utilities. More precisely, if is a tuple of utility functions, one for each individual, then a social welfare function for assigns an social utility to each state . Then is socially preferable to if the social utility of is higher; that is, if . For Instance, a utilitarian national security function sets . That is, state is preferable to when generates more utility across the population. This kind of calculation obviously assumes that the utilities are comparable across persons, at least to the extent necessary to add them up in a meaningful way. The issue of interpersonal comparability is in fact a central theme of rational expectations theory (20), and it is analyzed as follows. The key is to ask how the individual utility functions could be altered without changing the social ranking. Suppose, for example, that each individual’s utility is multiplied by the same factor . One would not expect this to change the social ranking of states, because it simply rescales the units in which utility is measured. Suppose, however, that the units are rescaled and a different constant is added to each state’s utility. That is, each individual’s utility is changed to . Should this change the rankin... ... middle of paper ... ...the same total utility. It therefore suffices to show that all such states are ranked equally, because the strict Pareto condition then implies that is ranked higher than if and only if appears on a higher line, which is precisely the utilitarian ranking. To show this, consider any utility vector on a given line as shown in the figure. Let , and let m be the midpoint of the line segment from a to . Due to anonymity, and must receive the same ranking. Now suppose, contrary to the claim, that is preferred to . The transformation maps into and into . Due to unit comparability, this transformation does not change rankings, and is preferred to . By transitivity, this implies is preferred to , a contradiction. Because a is an arbitrary point on the line, all points on the line must be ranked equally with and therefore with each other.
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