On VoxEU, Steven Durlauf offers an excellent overview over Kenneth Arrow’s work. Durlauf emphasizes five areas of research:
- The impossibility theorem, in the tradition of Condorcet.
- General equilibrium theory and the welfare theorems, in the tradition of Walras.
- Decision-making under uncertainty, the Arrow-Pratt measures of risk aversion and contingent commodities.
- Imperfect information, in the context of medical care and as a source of statistical discrimination.
- Economics of knowledge, anticipating the endogenous growth literature.
Like Faust, limitless curiosity and passion for knowledge meant that Arrow strove without relenting; but unlike Faust, Arrow needed no redemption. His intellectual integrity was pristine and unparalleled at every stage of his life. His character was as admirable and admired as his intellect. Arrow’s personal and scholarly example continues to inspire, nurture, and challenge.
On his blog A Fine Theorem, Kevin Bryan discusses the history of economic thought leading from the classical economists and Walras to Arrow and Debreu.
My read of the literature on GE following Arrow is as follows. First, the theory of general equilibrium is an incredible proof that markets can, in theory and in certain cases, work as efficiently as an all-powerful planner. That said, the three other hopes of general equilibrium theory since the days of Walras are, in fact, disproven by the work of Arrow and its followers. Market forces will not necessarily lead us toward these socially optimal equilibrium prices. Walrasian demand does not have empirical content derived from basic ordinal utility maximization. We cannot rigorously perform comparative statics on general equilibrium economic statistics without assumptions that go beyond simple utility maximization. From my read of Walras and the early general equilibrium theorists, all three of those results would be a real shock.
In the FT, Tim Harford (here) and Martin Sandbu (here) review Kenneth Arrow’s monumental contributions to economics.
In the New York Times, Eric Maskin and Amartya Sen explain Condorcet’s
system for electing candidates who truly command majority support. In this system, a voter has the opportunity to rank candidates.
Maskin and Sen’s fictitious example of the American primaries illustrates the difference between a plurality system (as used in the primaries) and a majority system a la Condorcet (where the winner is the one who defeats any other candidate in pairwise comparison). They also point out that
Kenneth Arrow’s famous “impossibility theorem” demonstrates that there is no perfect voting system, and majority rule is no exception. Specifically, as Condorcet himself noted, a majority winner might fail to exist … Such an outcome is quite unlikely in practice, but if it were to arise, a tiebreaking procedure would be needed.