Liberal paradox
From Wikipedia, the free encyclopedia
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.
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.
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.
[edit] 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:
- 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
- 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.
