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The liberal paradox is a logical paradox advanced by Amartya Sen, building on the work of Kenneth Arrow and his general possibility theorem, which showed that within a system of menu-independent social choice, it is impossible to have both a commitment to "Minimal Liberty", which was defined as the ability to order tuples of choices, and Pareto optimality. Look up paradox in Wiktionary, the free dictionary. ...
Amartya Sen Amartya Kumar Sen CH (Hon) (Bengali: Ômorto Kumar Shen) (born 3 November 1933 in Santiniketan, India), is an Indian philosopher, economist and a winner of the Bank of Sweden Prize in Economic Sciences (Nobel Prize for Economics) in 1998, for his work on famine, human development theory, welfare...
Kenneth Arrow Kenneth Joseph Arrow (born August 23, 1921) is an American economist, winner of the Bank of Sweden Prize in Economic Sciences in 1972. ...
In voting systems, Arrow’s impossibility theorem, or Arrow’s paradox demonstrates the impossibility of designing a set of rules for social decision making that would obey every ‘reasonable’ criterion required by society. ...
Social choice theory studies how individual preferences are aggregated to form a collective choice, such as, for example in voting systems. ...
In mathematics, a tuple is a finite sequence (also known as an ordered list) of objects, each of a specified type. ...
Pareto efficiency, or Pareto optimality, is a central concept in game theory with broad applications in economics, engineering and the social sciences. ...
Since this theorem was advanced in 1970, it has attracted a wide body of commentary from philosophers such as James M. Buchanan and Robert Nozick among many others. 1970 (MCMLXX) was a common year starting on Thursday (the link is to a full 1970 calendar). ...
For other people named James Buchanan, see James Buchanan (disambiguation). ...
Robert Nozick (November 16, 1938 – January 23, 2002) was an American philosopher and Pellegrino University Professor at Harvard University. ...
The most contentious aspect is that it seems, on one hand, to contradict the libertarian notion that the market mechanism is sufficient to produce a Pareto-optimal society - and on the other hand it argues that degrees of choice and freedom, rather than welfare economics should be the defining trait of that market mechanism. As a result it attracts commentary from both the left and the right of the political spectrum. See also Libertarianism and Libertarian Party Libertarian,is a term for person who has made a conscious and principled commitment, evidenced by a statement or Pledge, to forswear violating others rights and usually living in voluntary communities: thus in law no longer subject to government supervision. ...
Welfare economics is a branch of economics that uses microeconomic techniques to simultaneously determine the allocational efficiency of a macroeconomy and the income distribution associated with it. ...
Example
Suppose Alice and Bob have to decide whether to go to the cinema to see a chick flick, and that each has the liberty to decide whether to go themselves. If the personal preferences are based on Alice wanting to be with Bob and thinking it is a good film, and on Bob wanting Alice to see it but not wanting to go himself, then the personal preference orders might be: The names Alice and Bob are commonly used placeholders for archetypal characters in fields such as cryptography and physics. ...
The term chick flick means movies that are really teenage girls acting all unrealistcally. ...
- Alice wants: both to go > neither to go > Alice to go > Bob to go
- Bob wants: Alice to go > both to go > neither to go > Bob to go
There are two Pareto efficient solutions: either Alice goes alone or they both go. Clearly Bob will not go on his own: he would not set off alone, but if he did then Alice would follow, and Alice's personal liberty means the joint preference must have both to go > Bob to go. However, since Alice also has personal liberty if Bob does not go, the joint preference must have neither to go > Alice to go. But Bob has personal liberty too, so the joint preference must have Alice to go > both to go. Combining these gives Pareto efficiency, or Pareto optimality, is a central concept in game theory with broad applications in economics, engineering and the social sciences. ...
- Joint preference: neither to go > Alice to go > both to go > Bob to go
and in particular neither to go > both to go. So the result of these individual preferences and personal liberty is that neither go to see the film.
But this is Pareto inefficient given that Alice and Bob each think both to go > neither to go.
Liberalism and externalities
Ways out of the paradox There are at least some ways out of the paradox. First, the way Sen prefered, the individuals may decide simple to "respect" each other's choice by contraining their own choice. Assume that individual A orders three alternatives (x, y, z) according to x P y P z and individual B orders the same alternative according to z P x P y, there will be no pareto-efficent outcome. But, if A refuses to decide over z and B refuses to decide over x, then for A follows x P y (x is choosen), and for B z P y (z is choosen). Hence A chooses x and respects that B chooses z; B chooses z and respects that A chooses x. So, the pareto-efficient solution can be reached, if A and B constrain themselves and accept the freedom of the other player. A second way out of the paradox draws from game theory by assuming that individuals A and B pursue self-interested actions, when they decide over alternatives or pairs of alternatives. Hence, the collective outcome will be pareto-inferior as the prisonner's dilemma predicts it. The way out (except Tit-For-Tat) will be to sign a contract, so trading away one's right to act selfish and get the other's right to act selfish in return. A third possiblity starts with assuming that again A and B have different preferences towards four states of the world, w, x, y, and z. A's preferences are given by w P x P y P z; B's preferences are given by y P z P w P x. Now, liberalism implies that each individual is a dictator in a least one social area. Hence, A and B should be allowed to decide at least over one pair of alternatives. For A, the "best" pair will be (w,z), because w is most prefered and z is least preferend. Hence A can decide that w is choosen and at the same time make sure that z is not choosen. For B, the same applies and implies, that B would most preferably decide between y and x. Furthermore assume that A is not free to decide (w,z), but has to choose between y and x. Then A will choose x. Conversely, B is just allowed to choose between w and z and eventually will rest with z. The collective outcome will be (x,z), which is pareto-inferor. Hence again A and B can make each other better of by employ a contract and trade away their right to decide over (x,y) and (w,z). The contract makes sure that A decides between w and z and chooses w. B decides between (x,y) and chooses y. The collective outcome will be (w,y), the pareto-optimal result. Taken all together all three ways do not resolve the paradox as such. But, they answer the question: What can society do, if the paradox applies and no corresponding social decision function can handle the trade of between pareto-optimality and liberalism. One sees that mutual acceptance and self-constraints or even contracts to trade away actions or rights are needed.
References - ch. 6.4 "Critique of Liberal Values"
- ch. 6.5, "Critique of the Pareto Principle"
- ch. 6*, "The Liberal Paradox"
- _____, 1970b. “The Impossibility of a Paretian Liberal,” Journal of Political Economy, 78, pp. 152-157
Amartya Sen Amartya Kumar Sen CH (Hon) (Bengali: Ômorto Kumar Shen) (born 3 November 1933 in Santiniketan, India), is an Indian philosopher, economist and a winner of the Bank of Sweden Prize in Economic Sciences (Nobel Prize for Economics) in 1998, for his work on famine, human development theory, welfare...
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