Sen's Liberal Paradox

The theorem and an example

Whereas Arrow's impossibility theorem (Arrow, 1951) required several conditions such as transitivity and independence of irrelevant alternatives, Sen (1970) showed that impossibility arises from far weaker conditions. His example was Lady Chatterley's Lover. There is a single copy of the book, a prude P and a libertine L. P most prefers that no one read it, next that he read it himself, and least that L read it. L most prefers that P read it, next that he read it himself, and least that no one read it. Under liberalism, P decides whether he reads, so "no one reads" beats "P reads." L decides his own reading, so "L reads" beats "no one reads." But both prefer "P reads" to "L reads," so by the Pareto principle "P reads" beats "L reads." Social preference thus cycles, and no best option can be chosen.

Debate over resolutions

Gibbard (1974) proposed a rights-waiving version of the liberalism condition, under which a person gives up a right when exercising it would clash with others' rights, making it compatible with the Pareto principle. Blau (1975) identified "meddlesome" preferences, which are overly strong about others' private spheres, as the source of the problem and examined ways to filter them out. Responding, Sen (1976) stressed that the spirit of liberalism may lie in not honoring preferences about other people's private lives, and that the Pareto principle is not always justified in itself. This challenged a tradition that treated Pareto optimality as the minimal standard of welfare economics.

Interpreting rights and implications

Nozick (1974) objected that rights should be understood not as a matter of ranking social states but as constraints that limit the range within which people may choose. Building on this, Gärdenfors (1981), Sugden (1985) and Gaertner, Pattanaik and Suzumura (1992) modeled rights not as social preference orderings but as game forms, in which each person chooses freely from a permitted set of strategies. Sen (1992) replied that the game-form view is useful but does not by itself dissolve the paradox. Suzumura (1983) systematized the problem within the relationship between rational choice and social welfare. Along with the Gibbard–Satterthwaite theorem, the paradox is counted among the leading impossibility results of social choice theory, and it raises fundamental questions for institutional design that pursues both efficiency and individual liberty.

FAQ

What is Sen's liberal paradox in simple terms?

It's a theorem showing that the principle of following what everyone prefers and the liberal principle that each person decides their own affairs can't always both hold. When people have preferences about others' private lives, the two principles collide.

How can the paradox be resolved?

There's no single answer. Proposals include ignoring preferences about others' private spheres, interpreting rights as the range of choices each person can make in a game, or having people waive rights when conflicts arise, but each comes at a cost.

Sources reviewed: 2026-10-26

References

1. Arrow, K. J. (1951). Social Choice and Individual Values. New York: Wiley.
2. Sen, A. (1970). The impossibility of a Paretian liberal. Journal of Political Economy, 78(1), 152–157.
3. Sen, A. (1970). Collective Choice and Social Welfare. San Francisco: Holden-Day.
4. Gibbard, A. (1974). A Pareto-consistent libertarian claim. Journal of Economic Theory, 7(4), 388–410.
5. Nozick, R. (1974). Anarchy, State, and Utopia. New York: Basic Books.
6. Blau, J. H. (1975). Liberal values and independence. Review of Economic Studies, 42(3), 395–401.
7. Sen, A. (1976). Liberty, unanimity and rights. Economica, 43(171), 217–245.
8. Gärdenfors, P. (1981). Rights, games and social choice. Noûs, 15(3), 341–356.
9. Suzumura, K. (1983). Rational Choice, Collective Decisions, and Social Welfare. Cambridge: Cambridge University Press.
10. Sugden, R. (1985). Liberty, preference, and choice. Economics and Philosophy, 1(2), 213–229.
11. Sen, A. (1992). Minimal liberty. Economica, 59(234), 139–159.
12. Gaertner, W., Pattanaik, P. K., & Suzumura, K. (1992). Individual rights revisited. Economica, 59(234), 161–177.