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Government by the people. Until recently, democracies counted very few persons among ‘the people’. Now they include all adult citizens, including, in many nations, recent immigrants, and democracy is virtually universally revered as the best or the right form of government. In the democratic upsurges in Eastern Europe in 1989, a rallying-cry from crowds in the street was ‘
We are the people’. Every chanter, every listener, knew what that meant, and most of them presumably thought it a claim of morality, of right.

In its simplest form, democracy entails having all citizens participate in voting on policies. In large states this is not sensible or even possible and participation takes place in sequential forms. First, representatives are chosen and then they decide on policies. It is widely believed that different structures for representation could produce substantially different outcomes. Hence, there is no simple formula for democracy that relates popular preferences to political outcomes in large polities.

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Because the general character of democracy is widely understood, we may focus discussion most acutely by beginning with its difficulties. Contemporary public choice theory began in the analysis of two critical problems for democratic decision. (1) The economist Kenneth Arrow showed that orderly individual preferences do not generally aggregate into orderly collective preferences, which may be ill-defined. This result is essentially a generalization of a long-ignored result of C. L. Dodgson (Lewis Carroll). (2) The economists Anthony Downs and Mancur Olson argued that individual motivations for action are incompatible with collective preferences even when the latter are well defined. The logic of democracy is doubly flawed. One might respond to thefirst result by saying that democracy need not be determinate even though individual preferences might be. Of course democracy will be a mess when the society is a mess. The second r…

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