Liberal paradox
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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, that 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.
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
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