Welfare Economics, or Social Psychic Wellbeing. Note Quote.


The economic system is a social system in which commodities are exchanged. Sets of these commodities can be represented by vectors x within a metric space X contained within the non-negative orthant of an Euclidean space RNx+ of dimensionality N equal to the number of such commodities.

An allocation {xi}i∈N ⊂ X ⊂ RNx+ of commodities in society is a set of vectors xi representing the commodities allocated within the economic system to each individual i ∈ N.

In questions of welfare economics at least in all practical policy matters, the state of society is equated with this allocation, that is, s = {xi}i∈N, and the set of all possible information concerning the economic state of society is S = X. It is typically taken to be the case that the individual’s preference-information is simply their allocation xi, si = xi. The concept of Pareto efficiency is thus narrowed to “neoclassical Pareto efficiency” for the school of economic thought in which originates, and to distinguish it from the weaker criterion.

An allocation {xi}i∈N is said to be neoclassical Pareto efficient iff ∄{xi}i∈N ⊂ X & i ∈ N : x′i ≻ xi & x′j ≽ xj ∀ j ≠ i ∈ N.

A movement between two allocations, {xi}i∈N → {x′i}i∈N is called a neoclassical Pareto improvement iff ∃i∈N : x′i ≻ xi & x′j ≽ xj ∀ j ≠ i ∈ N.

For technical reasons it is almost always in practice assumed for simplicity that individual preference relations are monotonically increasing across the space of commodities.

If individual preferences are monotonically increasing then x′ii xi ⇐⇒ x′i ≥ xi, and x′ ≻ xi ⇐⇒ xi > x′i2.

This is problematic, because a normative economics guided by the principle of implementing a decision if it yields a neoclassical Pareto improvement where individuals have such preference relations above leads to the following situation.

Suppose that individual’s preference-information is their own allocation of commodities, and that their preferences are monotonically increasing. Take one individual j ∈ N and an initial allocation {xi}i∈N.

– A series of movements between allocations {{xi}ti∈N → {x′i}ti∈N}Tt=1 such that xi≠j = x′i≠j ∀ t and x′j > xj ∀ t and therefore that xj − xi → ∞∀i≠j ∈ N, are neoclassical Pareto improvements. Furthermore, if these movements are made possible only by the discovery of new commodities, each individual state in the movement is neoclassical Pareto efficient prior to the next discovery if the first allocation was neoclassical Pareto efficient.

Admittedly perhaps not to the economic theorist, but to most this seems a rather dubious out- come. It means that if we are guided by neoclassical Pareto efficiency it is acceptable, indeed de- sirable, that one individual within society be made increasingly “richer” without end and without increasing the wealth of others. Provided only the wealth of others does not decrease. The same result would hold if instead of an individual, we made a whole group, or indeed the whole of society “better off”, without making anyone else “worse off”.

Even the most devoted disciple of Ayn Rand would find this situation dubious, for there is no requirement that the individual in question be in some sense “deserving” of their riches. But it is perfectly logically consistent with Pareto optimality if individual preferences concern only to their allocation and are monotonically increasing. So what is it that is strange here? What generates this odd condonation? It is the narrowing of that which the polity care about to each individual allocation, alone, independent of others. The fact that neoclassical Pareto improvements are distribution-invariant because the polity is supposed to care only about their own individual allocation xi ∈ {xi}ti∈N alone rather than broader states of society si ⊂ s as they see it.

To avoid such awkward results, the economist may move from the preference-axiomatic concept of Pareto efficiency to embrace utilitarianism. The policy criterion (actually not immediately representative of Bentham’s surprisingly subtle statement) being the maximisation of some combination W(x) = W {ui(xi)}i∈N of individual utilities ui(xi) over allocations. The “social psychic wellbeing” metric known as the Social Welfare Function.

In theory, the maximisation of W(x) would, given the “right” assumptions on the combination method W (·) (sum, multiplication, maximin etc.) and utilities (concavity, montonocity, independence etc.) fail to condone a distribution of commodities x extreme as that discussed above. By dint of its failure to maximise social welfare W(x). But to obtain this egalitarian sensitivity to the distribution of income, three properties of Social Welfare Functions are introduced. Which prove fatal to the a-politicality of the economist’s policy advice, and introduce presuppositions which must lay naked upon the political passions of the economist, so much more indecently for their hazy concealment under the technicalistic canopy of functional mathematics.

Firstly, it is so famous a result as to be called the “third theorem of welfare economics” that any such function W(·) as has certain “uncontroversially” desirable technical properties will impose upon the polity N the preferences of a dictator i ∈ N within it. The preference of one individual i ∈ N will serve to determine the preference indicated between by society between different states by W(x). In practice, the preferences of the economist, who decides upon the form of W(·) and thus imposes their particular political passions (be they egalitarian or otherwise) upon policy, deeming what is “socially optimal” by the different weightings assigned to individual utilities ui(·) within the polity. But the political presuppositions imported by the economist go deeper in fact than this. Utilitari-anism which allows for inter-personal comparisons of utility in the construction of W(x) requires utility functions be “cardinal” – representing “how much” utility one derives from commodities over and above the bare preference between different sets thereof. Utility is an extremely vague concept, because it was constructed to represent a common hedonistic experiential metric where the very existence of such is uncertain in the first place. In practice, the economist decides upon, extrapolates, assigns to i ∈ N a particular utility function which imports yet further assumptions about how any one individual values their commodity allocation, and thus contributes to social psychic wellbeing.

And finally, utilitarianism not only makes political statements about who in the polity is to be assigned a disimproved situation. It makes statements so outlandish and outrageous to the common sensibility as to have provided the impetus for two of the great systems of philosophy of justice in modernity – those of John Rawls and Amartya Sen. Under almost any combination method W(·), the maximization of W(·) demands allocation to those most able to realize utility from their allocation. It would demand, for instance, redistribution of commodities from sick children to the hedonistic libertine, for the latter can obtain greater “utility” there from. A problem so severe in its political implications it provided the basic impetus for Rawls’ and Sen’s systems. A Theory of Justice is, of course, a direct response to the problematic political content of utilitarianism.

So Pareto optimality stands as the best hope for the economist to make a-political statements about policy, refraining from making statements therein concerning the assignation of dis-improvements in the situation of any individual. Yet if applied to preferences over individual allocations alone it condones some extreme situations of dubious political desirability across the spectrum of political theory and philosophy. But how robust a guide is it when we allow the polity to be concerned with states of society in general? Not only their own individual allocation of commodities. As they must be in the process of public reasoning in every political philosophy from Plato to Popper and beyond.

Consequentialism -X- (Pareto Efficiency) -X- Deontology


Let us check the Polity to begin with:

1. N is the set of all individuals in society.

And that which their politics concerns – the state of society.

2. S is the set of all possible information contained within society, so that a set s ∈ 2S (2S being the set of all possible subsets of S) contains all extant information about a particular iteration of society and will be called the state of society. S is an arbitrary topological space.

And the means by which individuals make judgements about that which their politics concerns. Their preferences over the information contained within the state of society.

3. Each individual i ∈ N has a complete and transitive preference relation ≽i defined over a set of preference-information Si ⊂ S such that si ≽ s′i can be read “individual i prefers preference information si at least as much as preference-information s′i”.

Any particular set of preference-information si ⊂ Si can be thought of as the state of society as viewed by individual i. The set of preference-information for individual i is a subset of the information contained within a particular iteration of society, so si ⊂ s ⊂ S.

A particular state of society s is a Pareto efficient if there is no other state of society s′ for which one individual strictly prefers their preference-information s′i ⊂ s′ to that particular state si ⊂ s, and the preference-information s′j ⊂ s′ in the other state s′ is at least as preferred by every other individual j ≠ i.

4. A state s ∈ S is said to be Pareto efficient iff ∄ s′ ∈ 2S & i ∈ N : s′i ≻ si & s′j ≽ sj ∀ j ≠ i ∈ N.

To put it crudely, a particular state of society is Pareto efficient if no individual can be made “better off” without making another individual “worse off”. A dynamic concept which mirrors this is the concept of a Pareto improvement – whereby a change in the state of society leaves everyone at least indifferent, and at least one individual in a preferable situation.

5. A movement between two states of society, s → s′ is called a Pareto improvement iff ∃ i ∈ N : s′i ≻ si & s′j ≽ sj ∀ j ≠ i ∈ N .

Note that this does not imply that s′ is a Pareto efficient state, because the same could potentially be said of a movement s′ → s′′. The state s′ is only a Pareto efficient state if we cannot find yet another state for which the movement to that state is a Pareto improvement. The following Theorem, demonstrates this distinction and gives an alternative definition of Pareto efficiency.

Theorem: A state s ∈ 2S is Pareto efficient iff there is no other state s′ for which the movement s → s′ is a Pareto improvement.

If one adheres to a consequentialist political doctrine (such as classical utilitarianism) rather than a deontological doctrine (such as liberalism) in which action is guided by some categorical imperative other than consequentialism, the guide offered by Pareto improvement is the least controversial, and least politically committal criterion to decision-making one can find. Indeed if we restrict political statements to those which concern the assignation of losses, it is a-political. It makes a value judgement only about who ought gain (whosoever stands to).

Unless one holds a strict deontological doctrine in the style, say, of Robert Nozick’s Anarchy state and Utopia (in which the maintenance of individual freedom is the categorical imperative), or John Rawls’ A Theory of Justice (in which again individual freedom is the primary categorical imperative and the betterment of the “poorest” the second categorical imperative), it is more difficult to argue against implementing some decision which will cause a change of society which all individuals in society will be at worst indifferent to. Than arguing for some decision rule which will induce a change of society which some individual will find less preferable. To the rationalisitic economist it seems almost petty, certainly irrational to argue against this criterion, like those individuals who demand “fairness” in the famous “dictator” experiment rather than accept someone else becoming “better off”, and themselves no “worse off”.

Researching NITI Aayog: Drunken Risibility

I am raising the issue of trying to bring NITI Aayog under the purview of fiscal governance. Unlike the Soviet-era Planning Commission of India, this so-called think tank is supposedly to look at a synergistic relation with the Finance Commission. Under the former, Finance Commission was relegated to determining revenue gaps of states and filled up these by means of devolution of taxes and grants in aids. Such constraints elevated Planning Commission’s job to planning capital expenditure. Interestingly, NITI is stripped off what never really was Planning Commission’s mandate, and vested with monitoring progress of programmes. This is where the screw turns, and the role of Finance Commission gets back to the Finance Ministry’s acquiescing to its recommendations. This means that not only NITI acts as a pulley to lift up Finance Commission to its constitutional agenda, but also stays away from influencing Finance Ministry in that the Ministry could work in tandem with Commission in determining capital, grant requirements the states would either fall short of, or enjoy a surplus with. NITI’s creation is politico-financial with the polity deciding on quantum of finance to be disbursed through a blue print that wouldn’t have any autonomy left. So, while targeting mechanisms and instruments to bring constitutional financial institutions under scanner, one should, as a researcher not lose sight of why NITI is an ingenious lubricant to bring forth growth-led development model to fruition…….