ECONOMY

david austen-smith 903
by studying how the set of maximal elements varies with changes in the feasible set.
Now it is certainly true that individuals make political decisions but those decisions of
interest to political science are not primarily individual consumption or investment
decisions; rather, they are decisions to vote, to participate in collective action, to adopt
a platform on which to run for elected office, and so forth. In contrast to canonical
decision-making in economics, therefore, what an individual chooses in politics is not
always what an individual obtains (e.g. voting for some electoral candidate does not
ensure that the candidate is elected). Thus, the link between an individual’s decisions
in politics and the consequent payoffs to the individual is attenuated relative to
that for economic decisions: the basic political model of individual choice is game
theoretic.
The preceding observations suggest two approaches to understanding how individual
preferences connect to political, or collective, choices and both are pursued: a
direct approach through extending the individual decision-theoretic model to the collectivity
as a whole, an approach essentially begun with Arrow (1951, 1963) andBlack
(1958); and an indirect approach through exploring the consequences of mutually
consistent sets of strategic decisions by instrumentally rational agents, an approach
with roots in von Neumann and Morgenstern (1944) and Nash (1951).
Under the direct (collective preference) approach to social choice, individuals’
preferences are directly aggregated into a “social preference” which, as in individual
decision theory, is then maximized to yield a set of best (relative to the maximand)
alternatives, the collective choices. But although individual preferences surely influence
individual decisions such as voting, there is no guarantee that individuals’
preferences are revealed by their decisions (for example, an individual may have strict
preferences over candidates for electoral office, yet choose to vote strategically or to
abstain). Under the indirect (game-theoretic) approach to social choice, therefore, it
is individuals’ actions that are aggregated to arrive at collective choices. Faced with
a particular decision problem, individuals rarely have to declare their preferences
directly but instead have to take some action. For example, in a multicandidate
election under plurality rule, individuals must choose the candidate for whom to vote
and may abstain; the collective choice from the election is then decided by counting
the recorded votes and not by direct observation of all individuals’ preferences over
the entire list of candidates. It is useful to be a little more precise.
A preference profile is a list of preferences, one for each individual in the society,
over a set of alternatives for that society. An abstract collective choice rule is a rule that
assigns collective choices to each and every profile; that is, for any list of preferences,
a collective choice rule identifies the set of outcomes chosen by society. Similarly,
a preference aggregation rule is a rule that aggregates individuals’ preferences into
a single, complete, “social preference” relation over the set of alternatives; that is, for
any profile, the preference aggregation rule collects individual preferences into a social
preference relation over alternatives. It is important to note that while the theory
(following economics) presumes individual preferences are complete and transitive,
the only requirement at this point of a social preference relation is that it is complete.
For any profile and preference aggregation rule, we can identify those alternatives (if