Paradox of Liberalism

The paradox of liberalism ( English Impossibility of a Paretian liberal ) is a paradox in social choice theory proposed by Amartya Sen in 1970 . It is intended to show that there can be no social choice function that meets certain minimum requirements: thus there would be a contradiction between the Pareto criterion and a minimum of liberalism .

Axiomatic representation

The social choice function is always about the aggregation of individual preferences into a collective preference. So there are individuals with orders of preference . We are now looking for an aggregation function that creates a collective preference from the individual preferences . ${\ displaystyle i = 1, \ dots, n}$ ${\ displaystyle R_ {i}}$ ${\ displaystyle f}$ ${\ displaystyle R}$

To get the paradox the following assumptions are needed:

Collective and Individual Rational Preferences : We assume that all individual and collective preferences are transitive and complete.
Unlimited : The social choice function should provide a result for all logically possible preferences.
Pareto principle (also: unanimity): If all individuals prefer the alternative a to another alternative b, a should also be preferred collectively to b.
Minimum liberalism ( minimal liberalism ): There are at least two individuals who are locally important for two alternatives a and b. For example, if individual X is locally decisive for c and d, and X prefers alternative d to c, then d should also be preferred to c in the collective preference.

The paradox of liberalism now states that there cannot be a social choice function that fulfills all of the four requirements mentioned.

proof

Let us name the individuals who are locally decisive according to the assumption of minimal liberalism, A and B. All other individuals should be named C, D etc. Now we can distinguish three cases of proof:

First case. A and B are locally crucial for the same alternatives.

The evidence for this case is simple. It is assumed that A and B have opposite preferences for the alternatives over which they are locally decisive. (We can make this assumption on the basis of unlimitedness .)

Second case. In the alternatives, about which A and B are locally decisive, there is exactly one match.

Let A be decisive about the alternatives and B decisive about the alternatives . We can derive a contradiction with the following preferences: ${\ displaystyle \ {a, b \}}$ ${\ displaystyle \ {a, c \}}$

A.	a> b> c
B.	b> c> a
C, D, E, ...	b> c (position of a does not matter)

Due to the condition of minimal liberalism, we must assume a> b and c> a for the collective preference. Also, due to unanimity, we get b> c, since all individuals prefer b over c. However, these three statements are contradictory to one another, since they result in a non-transitive preference: a> b> c> a.

Third case. There is no agreement in the alternatives about which A and B are locally decisive.

Let A be decisive about the alternatives and B decisive about the alternatives . We can derive a contradiction with the following preferences: ${\ displaystyle \ {a, b \}}$ ${\ displaystyle \ {c, d \}}$

A.	d> a> b> c
B.	b> c> d> a
C, D, E, ...	b> c and d> a (other preferences don't matter)

By assuming minimal liberalism, we again get the collective preferences a> b and c> d. We can also conclude from unanimity that b> c and d> a. Then we get an intransitive preference again: a> b> c> d> a.

Examples

Lady Chatterley's lover

The most famous example of an application of the paradox was given by Sen himself. Lady Chatterley's Lover is a book by DH Lawrence that became famous for its sexual explicitness . Sen uses this background to build the following example:

Two people, P ( prude ) and L ( libertine ), have to decide whether Lady Chatterley's Lover is either read by the prude (x), read by the libertine (y), or not read by anyone (z). The preferences are as follows:

Prudish	z> x> y
libertine	x> y> z

The libertine believes that the book should definitely be read; even more from the prude than from him. The prude would like to forbid reading the book altogether; but if it is read, it is better by him than by the libertine, since he considers himself more morally stable to read the book. Now it seems to correspond to liberal values that each individual can decide for himself whether he or she reads the book or not; So P is locally decisive over x and z, and L is decisive over y and z. Unanimity also requires that x should always be preferred to y. So we get an intransitive collective preference: x> y> z> x.

background

The basic idea behind the assumption of minimal liberalism is the idea of privacy , which Sen took from the philosophy of John Stuart Mill : There are certain areas of human life over which the individual alone should decide.

Conclusions

The paradox postulates a contradiction between the Pareto criterion, which is dominant in neoclassical economics, and a minimum of liberal attitudes. Sen himself concluded from this that the Pareto criterion should not be understood as a universal rule:

"One of the main preoccupations of this paper has been the unacceptability of the Pareto principle as a universal rule."

"One of the main concerns of this paper was the unacceptability of the Pareto Principle as a universal rule."

literature

Amartya Sen: The Impossibility of a Paretian Liberal . In: Journal of Political Economy . tape 78 , no. 1 , 1970, doi : 10.1086 / 259614 , JSTOR : 1829633 (original article in which Sen first described the paradox).

Amartya Sen: Liberty, Unanimity and Rights . In: Economica . tape 43 , 1976, p. 217-245 , JSTOR : 2553122 .

Hartmut Kliemt: The Paradox of Liberalism. An introduction . In: Analysis and Criticism . tape 18 , 1996, p. 1–19 ( full text [PDF; 2.5 MB ]).

Lucian Kern: Is the Liberal Paradox a Prisoner's Dilemma? ( Full text [PDF; 3.3 MB ]).

Individual evidence

^ Sen: The Impossibility of a Paretian Liberal . 1970, III. An Example, S. 155 .
↑ Amartya Sen: Liberty, Unanimity and Rights . In: Choice, Welfare and Measurement . Harvard University Press, Cambridge (MA), London 1982, ISBN 0-674-12778-1 , pp. 313 .

[1] Sen: The Impossibility of a Paretian Liberal . 1970, III. An Example, S. 155 .

[2] Amartya Sen: Liberty, Unanimity and Rights . In: Choice, Welfare and Measurement . Harvard University Press, Cambridge (MA), London 1982, ISBN 0-674-12778-1 , pp. 313 .