A sort of Paretian liberalism

Abstract

This paper reviews Amartya Sen's well-known result on ‘the impossibility of a Paretian liberal’. In so doing, it takes stock of certain difficulties associated with conventional social choice theoretic formulations of the notion of individual liberty. An alternative formulation, in the spirit of an ‘outcome-oriented’ version of Nozick's approach to individual liberty as the freedom to fix certain personal features of the world, is advanced. An ‘extended’ version of a conventional social choice function, called a ‘social selection function’ (SSF), is introduced: the domain of the SSF is enlarged to include, apart from preference profiles, what are called ‘personal choice profiles’ and ‘rights-waiving profiles’. Within this framework, it is noted that a version of Sen's original impossibility result can be recovered. It is also pointed out that there is an alternative, ethically plausible construction that can be placed on the notion of ‘Paretian liberalism’, and it is demonstrated that this is a coherent construction.

Key words:

• Minimal liberalism
• Gibbard liberalism
• preference profiles
• personal choice profiles
• rights-waiving profiles
• social choice function
• social selection function
• Paretian liberalism

Acknowledgement

The author, while acknowledging the comments and suggestions made by an anonymous referee, retains full responsibility for any surviving errors and inadequacies.

Notes

¹ An anonymous referee points out that the personal feature choice function has been designed in such a way that every individual is allowed to choose just one feature from his personal issue, which s/he finds ‘too strict’, and also compatible with being ‘forced’ into a unique choice when the individual is indifferent among features. The referee, of course, is correct in pointing out that under the restriction of a singular choice of personal feature by each individual, there will be one, and only one, social state that is rights-respecting: the set of rights-respecting states will cease being a singleton set if individuals are permitted to declare more than one personally favoured feature, as might happen in the presence of indifference among features. While agreeing with this, I would suggest that nothing of substance is lost, and something of simplicity is gained, by restricting each individual's choice from her personal issue to a single feature: after all, there is nothing particularly coercive in the invitation to an individual to make up her mind. (Perhaps indifference can be resolved by the simple expedient of tossing a coin or some variant thereof.)

²The referee points out that a social selection function constrained by Conditions U* and P*L* can yield an ‘… outcome [that] seems unrealistic and we are yet to provide an explanation for such a choice.’ The problem, s/he suggests, arises from treating the three arguments of the SSF – the personal feature choice profile, the preference profile, and the rights-waiving profile – as independent. The referee illustrates with the help of the following example: ‘[Suppose]N = {1,2}, and (∀i ∈ N)(X_i  = {b,s}). We have four possible social states: x = (s,s), y = (s,b), z = (b,s) and w = (b,b). Here we have X = {x,y,z,w}. Let both individuals hold the following preference ordering, xPyPzPw. Let both individuals assign value 1 to the feature b and 0 to s. Also, let m≠m*. Our assumptions are consistent with U*. We have x* = w and the SSF satisfying U* and P*L* gives us, B(f,σ,m) = {w}. Here w will be the selected social state which is the least preferred alternative in the preference orderings of both individuals. The outcome seems unrealistic and we are yet to provide an explanation for such a choice.’ The explanation – if one is required – is that the persons in the example seem to be a bit unreal! Interpreting ‘s’ to mean ‘sleeping on stomach’, and ‘b’ to mean ‘sleeping on back’, the preference profile suggests that, left to himself, each person prefers sleeping on his stomach to sleeping on his back, and yet, each also declares his uniquely favoured personal feature to be that of sleeping on his back! This is at least a little eccentric, and it is this eccentricity that ‘explains’ a social choice in which both individuals wind up with their least preferred alternative w. If we wish to prevent such ‘unrealistic’ outcomes, we may have to impose some sort of domain restriction; but the whole point of Condition U* is, precisely, to avoid proscribing ‘eccentricity’, or even lunacy!

³‘Such a [possibility of strategic] manipulation’, as the referee points out, ‘is also possible when an individual chooses her feature alternative in order to construct her personal feature choice function.’ Indeed, the possibility extends also to strategic misrepresentation of preferences. But this paper confines itself to a very brief discussion of the possibility of strategic behaviour only in the context of the rights-waiving decision. Sufficient unto the day …