Economics cannot isolate itself from political theory: a mathematical demonstration
aa r X i v : . [ q -f i n . E C ] O c t ECONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: AMATHEMATICAL DEMONSTRATION
BRENDAN MARKEY-TOWLERA
BSTRACT . The purpose of this paper is to provide a confession of sorts from an economist topolitical science and philosophy. A confession of the weaknesses of the political position of theeconomist. It is intended as a guide for political scientists and philosophers to the ostensible policycriteria of economics, and an illustration of an argument that demonstrates logico-mathematically,therefore incontrovertibly, that any policy statement by an economist contains, or is, a politicalstatement. It develops an inescapable compulsion that the absolute primacy and priority of politicaltheory and philosophy in the development of policy criteria must be recognised. Economic policycannot be divorced from politics as a matter of mathematical fact, and rather, as Amartya Sen hasdone, it ought embrace political theory and philosophy.
1. T
HE PLACE AND IMPORTANCE OF P ARETO OPTIMALITY IN ECONOMICS
Economics, having pretensions to being a “science”, makes distinctions between “positive”statements about how the economy functions and “normative” statements about how it shouldfunction. It is a core attribute, inherited largely from its intellectual heritage in British empiricismand Viennese logical positivism (McCloskey, 1983) that normative statements are to be avoidedwhere possible, and ought contain little by way of political presupposition as possible where theycannot. Political ideology is the realm of the politician and the demagogue.To that end, the most basic policy decision criterion of Pareto optimality is offered. This cri-terion is weaker than the extremely strong Hicks-Kaldor criterion. The Hicks-Kaldor criterionpresupposes a consequentialist, specifically utilitarian philosophy and states any policy should beadopted which yields net positive utility for society, any compensation for lost utility on the partof one to be arranged by the polity, not the economist, out of the gains to the other. Against such acriterion which clearly washes its hands of the actions of powerful entities in the polity, alongsidethe standard problems of utilitarianism (Sen, 1973; Fumagalli, 2013), Pareto optimality augursonly that any policy be adopted which leads to an at least indifferent state for all, and an improvedstate for at least one.Aside from the presupposition (again) of a consequentialist philosophy, this appears quite a“weak” dictat, requiring not much by way of political presuppositions. It says nothing about whois to “lose” from policy, and only concerns “gain”. And yet such a weak dictat allows the economistto claim that by removing impediments to the perfect market (“market imperfections”), allowing
Key words and phrases.
Political theory, political philosophy, economic theory, economic policy, Pareto optimality. laissez-faire competition in markets free of extra-judicial governmental intervention, yields an“optimal” or “efficient” outcome for society. Because the first and second “welfare theorems”tell us (roughly) that within the strictures of the psychological model of the neoclassical rationalagent, market “equilibria” are Pareto optimal (Mas-Collel et al., 1995): no individual can be made“better off” without making some other individual “worse off”.If we restrict what constitutes a political statement to one which makes statements about whenpolicies should be implemented which will lead to the dis improvement of some individual’s situ-ation. Then economics appears to have made only a value judgement about who ought benefitfrom a policy (whosoever accrues such benefits). Not (by this restricted definition) a politicalstatement. And yet it has still demonstrated markets free from government intervention, and freefrom imperfections are “optimal” and “efficient”.But is the concept of Pareto optimality robust? Does it have any value as a criterion in the “real”,empirical world? Does it offer us a criterion for policy which does not make political statementsas defined here, and allow for economics to be divorced from political theory? Indeed assert itspriority and primacy therein?The purpose of this work is to demonstrate logico-mathematically, therefore incontroveritblythat the answer is No. The mathematics of Pareto optimality itself provide an inescapable argu-ment which compels us to recognise that even in the restricted form here, economics cannot butmake political statements. Economics must recognise the absolute primacy and priority of politicaltheory and philosophy in the development and implementation of policy.The author is not a political scientist or philosopher, and offers no pretensions to being esteemedas such or even to being versed in the literature to such an extent as one would be. The author isan economist, neoclassically trained, and is offering a confession of the weakness of the politicalposition held by the economics profession. What is offered is a guide for political scientists andphilosophers to the exactitudes of the ostensible policy criterion of the economist, and an illustra-tion, a mathematically rigorous and therefore incontrovertible illustration that this criterion offersno guide in empirical situations. That even political statements of a restricted nature must always be made by economists designing and implementing policy, and thus the concomitant compulsionto embrace political theory and philosophy as prior to any analysis of economic policy.This confession ought not be read as purely negative. It is as much an affirmation of Pro-fessor Sen’s long-time collaboration with Professor Nussbaum, embracing political theory andphilosophy as a means for developing a welfare economics with the intellectual richness of itsfoundation in the same, as it is a critique of economics. It ought be read as encouragement for both economists and political scientists and philosophers to continue the necessary development of Senand Nussbaum’s endeavour.The argument proceeds as follows. In the first succeeding section we consider some matters ofdefinition as regards the weakest possible conception of Pareto optimality. In the second section
CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 3 we relate this weakest form to that actually employed in neoclassical economics for policy ana-lysis (specifically, the defence of laissez-faire free markets corrected for “imperfections”). Andwe show how concerns begin to emerge as this criterion seems to deem as “efficient” or “optimal”extreme situations. Before we demonstrate, in the final substantive section, that in all non-extremeempirical situations, all states of the world are Pareto optimal, so that any policy analysis in empir-ical reality must necessarily make political statements, even in the restricted sense of those adoptedhere.Finally, before we begin proper, we might do well to ask (and we will return again to the answerbelow); so what? Why do we care? Why should we care?We should care that economics cannot usurp the primacy of political theory and philosophy inpolicy analysis because the delineation of economic science from political economy, the delin-eation of that fuzzy boundary between fact and value (Strauss, 1953), the seeking of “objectivity”is essential to a healthy political sphere (Sen, 1993). Something we may all agree is desperatelyneeded given the current political situation in the democracies of the world. Undergraduate eco-nomists are still taught the concept of Pareto optimality as the basis for economic policy, profes-sional economists still utilise it in research, it still forms the basis for the “proof” that laissez-fairemarkets (corrected for “imperfections”) are “efficient” or “optimal”. But there are no “ought”statements to be derived by the economist qua economist devoid of political content, politicalpresuppositions. To continue to pretend otherwise, by refusing to embrace political theory andphilosophy and acknowledge the primacy and priority of political concerns in policy implement-ation lends to the pronouncements of the economist a false scientistic authority detrimental, evendangerous, for the process of public reasoning.2. T
HE CONCEPT OF P ARETO EFFICIENCY IN ITS WEAKEST FORM
The following conceptualisation of Pareto efficiency is a weaker form of the concept used ineconomic theory (Mas-Collel et al., 1995; Sen, 1970), because individual preferences are definedwith respect to arbitrary sets of information contained within the state of society. We assumeonly that individuals care about Something. Not one particular Thing such as their acquisition ofcommodities.We first take the polity:
Definition 1. N is the set of all individuals in society.And that which their politics concerns - the state of society. Definition 2. S is the set of all possible information contained within society, so that a set s ∈ S (2 S being the set of all possible subsets of S ) contains all extant information about a particulariteration of society and will be called the state of society . S is an arbitrary topological space. CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 4
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.
Definition 3.
Each individual i ∈ N has a complete and transitive preference relation (cid:23) i definedover a set of preference-information S i ⊂ S such that s i (cid:23) s ′ i can be read “individual i preferspreference information s i at least as much as preference-information s ′ i ”.Any particular set of preference-information s i ⊂ S i can be thought of as the state of societyas viewed by individual i . The set of preference-information for individual i is a subset of theinformation contained within a particular iteration of society, so s i ⊂ s ⊂ S .A particular state of society s is a Pareto efficient if there is no other state of society s ′ for whichone individual strictly prefers their preference-information s ′ i ⊂ s ′ to that particular state s i ⊂ s ,and the preference-information s ′ j ⊂ s ′ in the other state s ′ is at least as preferred by every otherindividual j = i . Definition 4.
A state s ∈ S is said to be Pareto efficient if and only if ∄ s ′ ∈ S & i ∈ N : s ′ i ≻ s i & s ′ j (cid:23) s j ∀ 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 mirrorsthis (and we will see provides an alternative definition of Pareto optimality) is the concept of aPareto improvement - whereby a change in the state of society leaves everyone at least indifferent,and at least one individual in a preferable situation. Definition 5.
A movement between two states of society, s → s ′ is called a Pareto improvement ifand only if ∃ i ∈ N : s ′ i ≻ s i & s ′ j (cid:23) s j ∀ j = i ∈ N .Note that this does not imply that s ′ is a Pareto efficient state, because the same could potentiallybe said of a movement s ′ → s ′′ . The state s ′ is only a Pareto efficient state if we cannot findyet another state for which the movement to that state is a Pareto improvement. The followingTheorem, quite well known, demonstrates this distinction and gives an alternative definition ofPareto efficiency. Theorem 1.
A state s ∈ S is Pareto efficient if and only if there is no other state s ′ for which themovement s → s ′ is a Pareto improvement . If one adheres to a consequentialist political doctrine (such as classical utilitarianism) ratherthan a deontological doctrine (such as liberalism) in which action is guided by some categoricalimperative other than consequentialism, the guide offered by Pareto improvement is the least con-troversial, and least politically committal criterion to decision-making one can find. Indeed if werestrict political statements to those which concern the assignation of losses , it is a-political. Itmakes a value judgement only about who ought gain (whosoever stands to).
CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 5
Unless one holds a strict deontological doctrine in the style, say, of Nozick (1974) (in which themaintenance of individual freedom is the categorical imperative), or Rawls (1971) (in which againindividual freedom is the primary categorical imperative and the betterment of the “poorest” thesecond categorical imperative), it is more difficult to argue against implementing some decisionwhich 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 individualwill find less preferable. To the rationalisitic economist it seems almost petty, certainly irrational toargue 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”.3. T
HE CONCEPT OF P ARETO E FFICIENCY IN WELFARE ECONOMICS
Now we will turn to the concept of Pareto efficiency employed in its far stronger form in welfareeconomics. The economic system is a social system in which commodities are exchanged. Sets ofthese commodities can be represented by vectors x within a metric space X contained within thenon-negative orthant of an Euclidean space R N x + of dimensionality N x equal to the number of suchcommodities . Definition 6.
An allocation { x i } i ∈ N ⊂ X ⊂ R N x + of commodities in society is a set of vectors x i 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 isequated with this allocation, that is, s = { x i } i ∈ N , and the set of all possible information concerningthe economic state of society is S = X . It is typically taken to be the case that the individual’spreference-information is simply their allocation x i , s i = x i . The concept of Pareto efficiency isthus narrowed from that above to what we may call “neoclassical Pareto efficiency” for the schoolof economic thought in which originates, and to distinguish it from the weaker criterion. Definition 7.
An allocation { x i } i ∈ N is said to be neoclassical Pareto efficient if and only if ∄ { x i } i ∈ N ⊂ X & i ∈ N : x ′ i ≻ x i & x ′ j (cid:23) x j ∀ j = i ∈ N .This is consistent with the definition given by standard economics texts, being a preference-axiomatic form statement of Pareto optimality in Definition 10.B.2 by Mas-Collel et al. (1995,p.313). The concept of Pareto improvement can be narrowed to “neoclassical Pareto improvement”in the same manner. Definition 8.
A movement between two allocations, { x i } i ∈ N → { x ′ i } i ∈ N is called a neoclassicalPareto improvement if and only if ∃ i ∈ N : x ′ i ≻ x i & x ′ j (cid:23) x j ∀ j = i ∈ N . For the unindoctrinated, imagine N x -many rulers laid out next to each other, R N x + are these rulers, x a set of pointsmarked off on each of them. CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 6
For technical reasons it is almost always in practice assumed for simplicity that individual pref-erence relations are monotonically increasing across the space of commodities.
Definition 9.
If individual preferences are monotonically increasing then x ′ i (cid:23) i x i ⇐⇒ x ′ i ≥ x i , and x ′ i ≻ x i ⇐⇒ x i > x ′ i .This is problematic, because a normative economics guided by the principle of implementinga decision if it yields a neoclassical Pareto improvement where individuals have such preferencerelations above leads to the following situation. Theorem 2.
Suppose that individual’s preference-information is their own allocation of commod-ities, and that their preferences are monotonically increasing. Take one individual j ∈ N and aninitial allocation { x i } i ∈ N .- A series of movements between allocations (cid:8) { x i } ti ∈ N → { x ′ i } ti ∈ N (cid:9) Tt = such that x i = j = x ′ i = j ∀ tand x ′ j > x j ∀ t and therefore that x j − x i → ¥ ∀ 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 ifthe 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 withoutincreasing the wealth of others. Provided only the wealth of others does not decrease. The sameresult would hold if instead of an individual, we made a whole group, or indeed the whole ofsociety “better off”, without making anyone else “worse off”.Even the most devoted disciple of Ayn Rand would find this situation dubious, for there is norequirement that the individual in question be in some sense “deserving” of their riches. Butit is perfectly logically consistent with Pareto optimality if individual preferences concern onlyto their allocation and are monotonically increasing. So what is it that is strange here? Whatgenerates this odd condonation? It is the narrowing of that which the polity care about to eachindividual allocation, alone, independent of others. The fact that neoclassical Pareto improvementsare distribution-invariant because the polity is supposed to care only about their own individualallocation x i ∈ { x i } ti ∈ N alone rather than broader states of society s i ⊂ s as they see it.To avoid such awkward results, the economist may move from the preference-axiomatic conceptof Pareto efficiency to embrace utilitarianism. The policy criterion (actually not immediately rep-resentative of Bentham’s surprisingly subtle statement) being the maximisation of some combin-ation W ( x ) = W (cid:0) { u i ( x i ) } i ∈ N (cid:1) of individual utilities u i ( x i ) over allocations. The “social psychicwellbeing” metric known as the Social Welfare Function. Since x i is a vector, x i > x ′ i acquires the special meaning that each element of x i is at least as large as x ′ i and at leastone element is strictly greater. CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 7
In theory, the maximisation of W ( x ) would, given the “right” assumptions on the combinationmethod W ( · ) (sum, multiplication, maximin etc.) and utilities (concavity, montonocity, independ-ence etc.) fail to condone a distribution of commodities x extreme as that discussed above. Bydint of its failure to maximise social welfare W ( x ) . But to obtain this egalitarian sensitivity to thedistribution of income, three properties of Social Welfare Functions are introduced. Which provefatal to the a-politicality of the economist’s policy advice, and introduce presuppositions whichmust lay naked upon the political passions of the economist, so much more indecently for theirhazy 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 anysuch function W ( · ) as has certain “uncontroversially” desirable technical properties will imposeupon the polity N the preferences of a dictator i ∈ N within it. Arrow’s famed “impossibility” the-orem (Arrow, 1951; Sen, 1970; Geanakoplos, 2005; Reny, 2001; Man and Takayama, 2013). Thepreference of one individual i ∈ N will serve to determine the preference indicated between by so-ciety between different states by W ( x ) . In practice, the preferences of the economist, who decidesupon the form of W ( · ) and thus imposes their particular political passions (be they egalitarian orotherwise) upon policy, deeming what is “socially optimal” by the different weightings assignedto individual utilities u i ( · ) within the polity. An excellent example of this is Diamond and Saez(2011), who demonstrate the “social optimality” of a 90% top taxation rate by assuming outrightthat the wellbeing of the wealthiest contributes nothing at the margin to social welfare .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 ) requiresutility functions be “cardinal” - representing “how much” utility one derives from commoditiesover and above the bare preference between different sets thereof. Utility is an extremely vagueconcept, because it was constructed to represent a common hedonistic experiential metric wherethe very existence of such is uncertain in the first place (Fumagalli, 2013). In practice, the eco-nomist decides upon, extrapolates, assigns to i ∈ N a particular utility function which imports yetfurther assumptions about how any one individual values their commodity allocation, and thuscontributes to social psychic wellbeing.And finally, utilitarianism not only makes political statements about who in the polity is to beassigned a disimproved situation. It makes statements so outlandish and outrageous to the commonsensibility as to have provided the impetus for two of the great systems of philosophy of justice in As Sen (1970) lists them: unrestricted domain in S , the “Pareto property” (condoning Pareto improvements), andindependence of irrelevant alternatives in preference between any two alternatives in S . It is interesting to note that total confiscation is only not condoned there as “socially optimal” for it does not tradelosses from avoidance behaviour against revenues raised as tax rates are increased so as to maximise revenue from thissource.
CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 8 modernity - those of Rawls (1971) and Sen (1999, 2009) . Under almost any combination method W ( · ) , the maximisation of W ( · ) demands allocation to those most able to realise utility from theirallocation. It would demand, for instance, redistribution of commodities from sick children to thehedonistic libertine, for the latter can obtain greater “utility” there from. A problem so severe inits political implications it provided the basic impetus for Rawls’ and Sen’s systems. A Theory ofJustice 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 statementsabout policy, refraining from making statements therein concerning the assignation of disimprove-ments in the situation of any individual. Yet if applied to preferences over individual allocationsalone it condones some extreme situations of dubious political desirability across the spectrum ofpolitical theory and philosophy. But how robust a guide is it when we allow the polity to be con-cerned 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 toPopper and beyond. We will see now, not at all. In all empirical situations Pareto optimality offersno guide to policy-making, for policymaking must inevitably make value judgements about who isto be assigned dis improvement in their situation.4. U
NDER WHAT CONDITIONS ARE P ARETO IMPROVEMENTS POSSIBLE IN ECONOMICDECISION MAKING ABOUT ALLOCATION ?Let us now broaden our view to a weaker conception of Pareto one in which we no longer restrictourselves to assume that individuals care only about their own allocation of goods and resources.Any economic decision making is ultimately a decision to implement a movement between twoallocations { x n } n ∈ N → { x ′ n } n ∈ N , the question whether the associated movement between two statesof society s → s ′ associated with this movement between two allocations is a Pareto improvement.Because we are focussed on problems of economic decision making at the societal level, letus suppose that the set of commodities X ⊂ R N x + is contained within the set of information aboutsociety X (so that X ⊂ S ), and that the allocation { x n } n ∈ N is contained within the set of informationfor any particular state of s (so that { x n } n ∈ N ⊂ s ). It seems reasonable to suppose that s willcontain also any number of transformations of this allocation { x n } n ∈ N . For instance, the statisticaltransformations which produce the summary statistics of the allocation.Let us now hold society outside of the economy constant so that we may restrict ourselves toscenarios in which the preference-information of individuals contains only some single-valued,individual-specific transformation f i : (cid:8) { x n } n ∈ N (cid:9) → R of the possible allocations (cid:8) { x n } n ∈ N (cid:9) ⊂ X of society. We might think of f i as representing something like the process of reasoning appliedby i to the allocation { x n } n ∈ N of commodities in the economic system in order to arrive at that The system of Dworkin (1981a,b), like that of Sen (1999, 2009) being developed as a constructive response toRawls (1971) too could be construed as a reaction to the (to the common sensibility) outlandish policies condoned byutilitarianism.
CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 9 information f i (cid:0) { x n } n ∈ N (cid:1) on whose basis they will form their preferences about the state of society.Let us also suppose without great loss of generality that individual preferences over that preference-information is monotonically increasing.Hence for what follows we may effectively restrict our attention to scenarios in which (cid:23) i isdefined for s i = f i (cid:0) { x n } n ∈ N (cid:1) and monotonically increasing over the same. Definition 10.
If preferences are increasing over individual-specific transformations of alloca-tions of commodities f i , and the non-economic state of society is held constant (and thus ef-fectively irrelevant), then f i (cid:0) { x n } n ∈ N (cid:1) (cid:23) f i (cid:0) { x ′ n } n ∈ N (cid:1) ⇐⇒ f i (cid:0) { x n } n ∈ N (cid:1) ≥ f i (cid:0) { x ′ n } n ∈ N (cid:1) , and f i (cid:0) { x n } n ∈ N (cid:1) (cid:23) f i (cid:0) { x ′ n } n ∈ N (cid:1) ⇐⇒ f i (cid:0) { x n } n ∈ N (cid:1) > f i (cid:0) { x ′ n } n ∈ N (cid:1) .We can restate the definition of Pareto improvement for this class of situations accordingly. Definition 11.
A movement between two states of society, s → s ′ is called a Pareto improvement if and only if ∃ i ∈ N : f i (cid:0) { x ′ n } n ∈ N (cid:1) ≻ f i (cid:0) { x n } n ∈ N (cid:1) & f j (cid:0) { x ′ n } n ∈ N (cid:1) (cid:23) f j (cid:0) { x n } n ∈ N (cid:1) ∀ j = i ∈ N .Neoclassical Pareto improvements are a special case of this definition, specifically that specialcase where x i = f i (cid:0) { x n } n ∈ N (cid:1) ∀ (cid:8) { x n } n ∈ N (cid:9) ⊂ X . While we are restricting our analysis here tochanges in the economic state of society, this restriction still models a relatively general set ofsituations with respect to the individual preferences upon which Pareto efficiency is predicated.For instance, it is widely accepted in behavioural economics, and has been for known for over acentury (Veblen, 1899; Duesenberry, 1949; Hirsch, 1977; Kahneman and Tversky, 1979; Easterlin,2001; Ariely, 2008; Clark et al., 2008; Frank, 2011; Layard, 2011; Barberis, 2013), that individualpreferences are not defined for absolute allocation of commodities, but rather allocation relativeto some reference point or “anchor”. Often, this reference point or anchor is other’s consumptionpatterns, in which case we have, for instance f i (cid:0) { x n } n ∈ N (cid:1) = x i x ∗ The reference point x ∗ may be the arithmetic mean of population consumption, | N | (cid:229) n ∈ N x n , oralternatively the arithmetic mean over that portion of the population which is in the “neighbour-hood” of the individual in question .We may now establish when a movement between two states of society constitutes a Paretoimprovement in this context. Theorem 3.
Suppose that we have a movement between two states of society { x n } n ∈ N → { x ′ n } n ∈ N such that ∃ { i } ⊂ N : x ′ i > x i and x ′ j ≤ x j ∀ j ∈ N \ { i } , and that individuals have monotonic prefer-ences {(cid:23) · } ·∈ N over the individual-specific preference-information f · (cid:0) { x ′ n } n ∈ N (cid:1) . The movement isa Pareto improvement if and only if Technically speaking of course, if x ∈ R N x + : N x > f i (cid:0) { x n } n ∈ N (cid:1) = x i [ x ∗ ] − . The reference point expression would remain unchanged if it is the arithmetic mean. CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 10 f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) x ′ i − x i ≥ ∀ k ∈ N , i ∈ { i } ⊂ Nand f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) x ′ j − x j ≤ ∀ k ∈ N , j ∈ N \ { i } with strict inequality in either case for at least one k ′ ∈ N. The conditions as sufficient are somewhat less interesting than they are as necessary. If theconditions are not met, the movement between two states of society is not a Pareto improvement.If they are not met for every possible movement between two states of society, then every state ofthe world is a Pareto optimal state.
Corollary 1.
If within the confines of the conditions to which Theorem 3 applies, the necessary andsufficient conditions for Pareto improvement fail to hold for every movement { x n } n ∈ N → { x ′ n } n ∈ N between two states of society, then every state of society { x n } n ∈ N is Pareto optimal. Now let us consider what the necessary and sufficient conditions of theorem 3 demand ofeach individual’s process of reasoning f k ( · ) about the economic state of society { x n } n ∈ N . When k ∈ { i } ⊂ N and the individual is within the set of those who face an increased allocation of com-modities, they are fairly obvious, fairly reasonable conditions. The first inequation states simplythat the individual k form an assessment f k (cid:0) { x ′ n } n ∈ N (cid:1) of the economic state of society { x ′ n } n ∈ N which is increasingly preferable or indifferent “in” (with respect to, as a result of) the increase oftheir own increased allocation of commodities, and those of their peers within the set { i } ⊂ N ofthose who face an increased allocation of commodities . And the second inequation requires thatthe individual k form an assessment f k (cid:0) { x ′ n } n ∈ N (cid:1) of the economic state of society { x ′ n } n ∈ N whichis indifferent or decreasingly preferable “in” (with respect to, as a result of) the increase of theincreased allocation of commodities to those within the set k ∈ N \ { i } of those who face decreasedallocation of commodities. Which is essentially (and rather crudely) to say that they must findthe increase of their own commodities desirable, and find indifferent or preferable the increase ordecrease of commodities to others as necessity for Pareto improvement has it.On the other hand, when we consider k ∈ N \ { i } and the individual is within the set of thosewho face an decreased allocation of commodities, these conditions become both far more interest-ing, and also rather far-fetched. The first inequation requires that the individual k form assessment f k (cid:0) { x ′ n } n ∈ N (cid:1) of the economic state of society { x ′ n } n ∈ N which is increasingly preferable or indiffer-ent “in” (with respect to, as a result of) the increase of allocation to those of the individuals withinthe set { i } ⊂ N of those who face an increased allocation of commodities. The second ineqautionrequires that the individual k form an assessment f k (cid:0) { x ′ n } n ∈ N (cid:1) of the economic state of society Though, as we will discuss below, this latter requirement even is somewhat dubious
CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 11 { x ′ n } n ∈ N which is increasingly preferable or indifferent “in” (with respect to, as a result of) theincrease of their own decreased allocation of commodities, and those of their peers within the set N \ { i } of those who face an weakly decreased allocation of commodities.Now we see that these conditions are quite strong, to the extent that we might humorouslyrefer to them as the “Kumbaya”, the “hakuna matata” or “blissful ignorance” conditions. A politycharacterised by these conditions would be a utopian society. Literally. In the sense that uto-pia stems from the ancient Greek for “no-place”. Or, more seriously, we might call them the“universal, unconditional altruism/ignorance”, or in a more sinister nomenclature the “Brave NewWorld/concealment” condition. They require, essentially, that every individual in society find itpreferable, at least indifferent to see some other individual acquire a increased commodity alloca-tion - become “better off” - if that is what is happening to that other individual. Hence the necessityof “universal, unconditional altruism”, or “ignorance”. But they also require at the same time that every individual in society find it preferable, or at least indifferent that they themselves or someother individual acquire a decreased commodity allocation - become “worse off” - if that is whatis happening to themselves or that other individual. Hence “Brave New World” , or “concealment”,if the decreased allocation is to be concealed from the necessary individuals to enforce by defaulttheir indifference. Such a polity is at once the most “Christian” and the least “Christian” of nations(in the naive old fashioned sense of that word), for as the necessity for Pareto optimality requires it,the movement of society either inspires charitable feelings, pleasure at the dispossession of others,or ignorance.These conditions would outlaw the holding to by any in the polity of the whole of Leftist politics(Judt, 2010), which most definitely calls for not for a universal altruism, rather either an altruismof the “rich” toward the “poor”, or the coercion of the “rich” by the “poor” on the basis that the“poor” do not find increased commodity allocation to one group preferable. One is reminded ofthe final few lines of Marx and Engels (1848):“Let the ruling classes tremble at a Communistic revolution. The proleterians havenothing to lose but their chains. They have a world to win. WORKING MEN OFALL COUNTRIES, UNITE!”They would also outlaw the holding to by any in the polity of the whole of Rightist as well as thestronger liberal politics (Mill, 1859; Strauss, 1953; Lucas, 1965; Nozick, 1974), which would resist Recall the exquisitely disturbing conditioning spoken to genetically engineered children grown in a test-tube as theysleep in
Brave New World :“Alpha children wear grey. They work much harder than we do, because they’re so frightfully clever.I’m really awfully glad I’m Beta, because I don’t work so hard. And then we are much better thanthe Gammas and the Deltas. Gammas are stupid. They all wear green, and Delta children wearkhaki. Oh no, I don’t want to play with Delta children. And Epsilons are too stupid to be able toread or write. Besides, they wear black, which is such a beastly colour. I’m so glad I’m a Beta”.Aldous Huxley, Brave New World , pp.24-25 (Flamingo Huxley Centenary edition)
CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 12 the wholesale coercion of the “rich” (or otherwise “deserving”) in a redistribution of commoditiesaway from them toward the “poor”. And most certainly anarchism, which would reject as at alldesirable any coercion in the allocation of resources (Marshall, 1992).It is an empirical fact, already discussed, that assessments of the economic state of society takea form similar to f k (cid:0) { x n } n ∈ N (cid:1) = x k x ∗ indicating relativity of individual assessments of society to some reference point. The referencepoint x ∗ being, for instance, the arithmetic mean of population consumption, | N | (cid:229) n ∈ N x n . Suchthat if there is some movement in which ∃ i ∈ N : x ′ i − x i > f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) x ′ i − x i < dis improvement.It is quite easy to rationalise this empirical fact. It is well known, and has been well knownsince Hirsch (1977) that economic outcomes depend on relative standing in the distribution ofacquired commodities. The obtention of a job, the ability to obtain certain commodities such aseducation at an elite school, indeed the obtention of any commodity which is finite, all depend onthe ability of the individual to “outbid” others, and this in turn depends on their relative standingin the distribution of commodities acquired. The more others gain in their allocation, the more theindividual’s position in the distribution deteriorates, and with it, their ability to obtain commodities.It is also a well known characteristic that the acquisition of commodities reflects the selectionwithin the evolutionary process in economies of an increasingly (in the absence of any interven-tion or response by competitors) dominant entity (Nelson and Winter, 1982; ? ), whose economicdominance of other entities under certain conditions only increases the more they are selected( ? ). And it is not mere conspiracy theory, but fact that concentration of commodities to cer-tain entities in the polity endows them with political power as well as economic predominance(Cardinale and Coffman, 2014; Cardinale, 2015). As the evolutionary process increasingly alloc-ates commodities to an increasingly dominant entity, the ability of this entity to dominate the politythrough politics and economics increases at the expense of the individual.We can fairly safely conclude therefore that in empirical reality, there is no movement betweeneconomic states of society which constitutes a Pareto improvement. Unless all members of thepolity are indifferent to the movement (highly unlikely), there will always be at least one individualwho arrives, through their process of reasoning, at an assessment of the movement as yielding a Because if f k (cid:0) { x n } n ∈ N (cid:1) = x k x ∗ , then f k ( { x ′ n } n ∈ N ) − f k ( { x n } n ∈ N ) x ∗ − x ∗′ ≤
0, and if x ∗ = | N | (cid:229) n ∈ N x n then x ∗ − x ∗′ x ′ i − x i ≥ f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) x ∗ − x ∗ ′ × x ∗ − x ∗ ′ x ′ i − x i CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 13 less preferable state of society. And thus, by corollary 1, all states of the world in empirical realityare Pareto optimal.If every state of society is Pareto optimal, no policy can be implemented which does not eitherleave all in the polity indifferent, or at least one facing a dis improvement in their assessment ofthe state of society. Policies which cause a movement between economic states of society, if theyare to change anything at all with respect to preferability, will necessarily dispossess some indi-vidual of a preferable assessment of the state of society. Economic policy must therefore alwaysstatements about the assignation of dis improvements to this individual or that. Even if we restrictwhat constitutes a political statement to statements which augur the deprivation of some individual,assign to them dis improvements, the formulation and implementation of economic policy cannottherefore avoid making political statements.5. T
HE PROPER PLACE OF ECONOMICS , AND WHY IT MATTERS
Is the concept of Pareto optimality robust? Does it have any value as a criterion in the “real”empirical world? Does it offer us a criterion for policy which does not make political statements,and allow for economics to be divorced from political theory, and even assert its priority andprimacy therein?The present work has demonstrated logico-mathematically, incontrovertibly, that the answer isNo. We are compelled inescapably by the mathematics of Pareto optimality itself to recognisethat in all empirical situations economics cannot not even make political statements of a restrictednature - about the assignation of “losses” - let alone of an unrestricted nature - making valuejudgements about the assignation of “gains”. This conclusion we arrived at by recognising thatwhen we allow the polity to form their assessments of the desirability of social states, the empiricalreality of those assessments means that all states of the world are Pareto optimal. There is nopolicy to be implemented which affects a non-neutral change in the economic states of societywhich does not assign dis improvement to some individual’s assessment of the economic state ofsociety. Economics cannot be divorced from politics, and it the absolute primacy of politicaltheory and philosophy in the development and implementation of policy must be recognised. Wecannot escape the compulsion to embrace political theory and philosophy as prior to any analysisof economic policy.So what? Why should we care? We should care because separating what is economic sciencefrom what is political economy, firming as far as possible the fuzzy boundary between fact andvalue (Strauss, 1953), seeking thereby “objectivity” is essential to a healthy political sphere (Sen,1993). The process of public reasoning is predicated on there being some degree of objectivity inthe views put forth therein Sen (2009).The democracies of the world sorely need a basic restoration of health to their processes thereof,being in (and having been for some time - see Habermas (1962)) a crisis of superficial and corrosive
CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 14 public discourse constituted by competing demagoguery on the part of human mouthpieces forpowerful and moneyed elements of the polity. Demagoguery which will use whatever tools itcan in desperation to occupy a privileged place in the prejudices of the public, including a falsescientistic, faux objective authority such as offered by economic policy analysis proceeding on thebasis of “a-political”, scientific economics guided by the search for Pareto optimality.The fact that such authority is assumed by statements which are yet political of necessity whileappearing ostensibly not so is corrosive to the public debate by obscuring what is fact and what isvalue, and thereby usurping the authority which is due to political theory and philosophy in the pub-lic debate. We have shown there are no “ought” statements to be derived by the economist devoidof political presuppositions. Yet undergraduate economists are still taught the concept of Paretooptimality as the basis for economic policy, professional economists still utilise it in research, itstill forms the basis for the “proof” that laissez-faire markets (corrected for “imperfections”) are“efficient” or “optimal”.Still yet the argument we have made ought not be seen as purely negative. It is as much anaffirmation of the collaboration of Professors Sen and Nussbaum, placing political theory andphilosophy at the foundation of welfare economics and thus obtaining the intellectual richnesscontained within for economics, as it is a critique of economics. It ought be read as encouragementfor both economists and political scientists and philosophers.Far better for the sake of the process of public reasoning that economists recognise the absoluteprimacy and priority of political theory and philosophy in the formulation and implementation ofpolicy. As was stated at the outset of this work, to continue to pretend otherwise lends to thepronouncements of the economist a false scientistic authority detrimental, even dangerous, for theprocess of public reasoning. Far better for economists to engage fully with political theory andphilosophy in the manner of Sen (1999, 2009) in developing a new welfare economics. Expandingon the efforts of Professors Sen and Nussbaum in particular to integrate into a system a set of anintellectually rich, reasoned positions regarding the political theory, and political philosophy ofeconomics. 6. A
PPENDIX : P
ROOFS OF T HEOREMS
Proof of Theorem 1.
Proof. (Necessity): Suppose, by way of contradiction, that there exists another state s ′ for whichthe movement s → s ′ is a Pareto improvement. Then, by definition ∃ i ∈ N : s ′ i ≻ s i & s ′ j (cid:23) s j ∀ j = i ∈ N , and so ∃ s ′ ∈ S & i ∈ N : s ′ i ≻ s i & s ′ j (cid:23) s j ∀ j = i ∈ N . But then s could not be Pareto efficient.Hence a state s ∈ S is Pareto efficient only if there is no other state s ′ for which the movement s → s ′ is a Pareto improvement.(Sufficiency): If we can find no state s ′ for which the movement s → s ′ is a Pareto improvement,there exists no state s ′ for which ∃ i ∈ N : s ′ i ≻ s i & s ′ j (cid:23) s j ∀ j = i ∈ N . Therefore ∄ s ′ ∈ S & i ∈ N : CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 15 s ′ i ≻ s i & s ′ j (cid:23) s j ∀ j = i ∈ N , and so s is a Pareto efficient state. Hence a state s is Pareto efficient ifthere is no state s ′ for which the movement s → s ′ would be a Pareto improvement. (cid:3) Proof of Theorem 2.
Proof.
The movement between two allocations, { x i } i ∈ N → { x ′ i } i ∈ N is a neoclassical Pareto im-provement if and only if ∃ i ∈ N : x ′ i ≻ x i & x ′ j (cid:23) x j ∀ j = i ∈ N . Let us allocate more commoditiesto j in a movement { x i } i ∈ N → { x ′ i } i ∈ N such that x ′ j > x j while holding all other allocations con-stant, so that x i = x ′ i ∀ i = j ∈ N . Since individuals have monotonically increasing preferences overonly their own allocation, x ′ j ≻ j x j , while x i (cid:23) i x i ∀ i = j ∈ N . Hence the movement in questionis a neoclassical Pareto improvement. We can repeat the argument again to verify that anothersuch movement between allocations is a neoclassical Pareto improvement. This can continue adinfinitum , and the first argument is established.Now suppose that the first allocation was neoclassical Pareto efficient. If we now discover newcommodities and allocate them entirely to individual j , by the argument above we implement aneoclassical Pareto improvement. But if we have now allocated the new commodities entirelyto individual j , the only movement between allocations in the absence of any discovery of newcommodities can be to redistribute the existing allocation. Any such redistribution will entail amovement { x i } i ∈ N → { x ′ i } i ∈ N between allocations whereby x ′ j > x j for at least one j and x ′ i < x i for at least one i . Since preferences are monotonically increasing this means that x ′ j ≻ j x j and x ′ i ≺ x i , hence x ′ i (cid:14) x i , in which case this movement is not a neoclassical Pareto improvement.Since this applies to any redistribution of the existing allocation, no movement is a neoclassicalPareto improvement, and by Theorem 1 the allocation arrived at by allocating all newly discoveredcommodities to j is neoclassical Pareto efficient prior to any further discovery. This establishes thesecond argument. (cid:3) Proof of Theorem 3.
Proof.
The movement { x n } n ∈ N → { x ′ n } n ∈ N such that ∃ { i } ⊂ N : x ′ i > x i and x ′ j ≤ x j ∀ j ∈ N \ { i } isa Pareto improvement if and only if f k (cid:16)(cid:8) x ′ n (cid:9) n ∈ N (cid:17) (cid:23) f k (cid:0) { x n } n ∈ N (cid:1) ∀ k ∈ N & ∃ k ′ ∈ N : f k ′ (cid:16)(cid:8) x ′ n (cid:9) n ∈ N (cid:17) ≻ f k ′ (cid:0) { x n } n ∈ N (cid:1) Now if preferences are monotonically increasing over individual-specific preference-informationthen we can say in fact that the movement will be Pareto optimal if and only if f k (cid:16)(cid:8) x ′ n (cid:9) n ∈ N (cid:17) − f k (cid:0) { x n } n ∈ N (cid:1) ≥ ∀ k ∈ N & ∃ k ′ ∈ N : f k ′ (cid:16)(cid:8) x ′ n (cid:9) n ∈ N (cid:17) − f k ′ (cid:0) { x n } n ∈ N (cid:1) > CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 16 (Necessity) : Suppose, by way of contradiction that ∃ k ∈ n , i ∈ { i } ⊂ N : f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) x ′ i − x i < ∃ k ∈ n , j ∈ N \ { i } : f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) x ′ j − x j > k ′ ∈ N . Take each case in turn. First,if ∃ k ∈ n , i ∈ { i } ⊂ N : f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) x ′ i − x i < { i } ⊂ N : x ′ i > x i = ⇒ x ′ i − x i > f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) < { x n } n ∈ N → { x ′ n } n ∈ N being a Pareto improvement. Second, if ∃ k ∈ n , j ∈ N \ { i } : f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) x ′ j − x j > x ′ j ≤ x j ∀ j ∈ N \ { i } = ⇒ x ′ j − x j ≤ f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) <
0, which contradicts the movement { x n } n ∈ N → { x ′ n } n ∈ N being a Pareto improvement. Finally,suppose there is no strict inequality in either case for at least one k ′ ∈ N , so that f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) x ′ i − x i = ∀ k ∈ N , i ∈ { i } ⊂ N and f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) x ′ j − x j = ∀ k ∈ N , j ∈ N \ { i } Or, collapsing these to one expression: f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) x ′ n − x n = ∀ k , n ∈ N But then f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) = ∀ k , n ∈ N , which contradicts the necessity of therebeing at least one k ′ ∈ N : f k ′ (cid:0) { x ′ n } n ∈ N (cid:1) − f k ′ (cid:0) { x n } n ∈ N (cid:1) > { x n } n ∈ N → { x ′ n } n ∈ N to be a Pareto improvement . (Sufficiency) : Suppose we have f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) x ′ i − x i ≥ ∀ k ∈ N , i ∈ { i } ⊂ N and CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 17 f k (cid:0) { x ′ n } n ∈ N (cid:1) − f k (cid:0) { x n } n ∈ N (cid:1) x ′ j − x j ≤ ∀ k ∈ N , j ∈ N \ { i } with strict inequality in either case for at least one k ′ ∈ N . Then as { i } ⊂ N : x ′ i > x i = ⇒ x ′ i − x i > f k (cid:16)(cid:8) x ′ n (cid:9) n ∈ N (cid:17) − f k (cid:0) { x n } n ∈ N (cid:1) ≥ ∀ k ∈ N , i ∈ { i } ⊂ N And as we have x ′ j ≤ x j ∀ j ∈ N \ { i } = ⇒ x ′ j − x j ≤ f k (cid:16)(cid:8) x ′ n (cid:9) n ∈ N (cid:17) − f k (cid:0) { x n } n ∈ N (cid:1) ≥ ∀ k ∈ N , j ∈ N \ { i } and with strict inequality in either case for at least one k ′ ∈ N . Which confirms the sufficientconditions for the movement { x n } n ∈ N → { x ′ n } n ∈ N to be a Pareto improvement. (cid:3) Proof of corollary 1.
Proof.
If the conditions to which Theorem 3 are the case, and the necessary and sufficient condi-tions identified by that theorem for Pareto improvement fail to hold then by that theorem, becausethey are necessary, there is no Pareto improvement in that movement. If those conditions fail tohold for every movement between two states of the world { x n } n ∈ N → { x ′ n } n ∈ N , then there is noPareto improvement to be made by movement from any and every state of the world { x n } n ∈ N . Thusby theorem 1, this is sufficient (and necessary) for every state of the world { x n } n ∈ N to be Paretooptimal. (cid:3) R EFERENCES
Ariely, D., 2008. Predictably Irrational. Harper Perennial, New York.Arrow, K., 1951. Social choice and individual values. Wiley, New York.Barberis, N., 2013. Thirty years of prospect theory in economics. Journal of Economic Perspectives27 (1), 173–196.Cardinale, I., 2015. Resources, Production and Structural Dynamics. Cambridge University Press,Cambridged, Ch. Towards a political economy of resources, pp. 198–210.Cardinale, I., Coffman, D., 2014. Economic interdependencies and political conflict: The politicaleconomy of taxation in eighteenth century Britain. Economia Politica XXXI (3), 277–300.Clark, A., Frijters, P., Shields, M., 2008. Relative income, happiness and utility: An explanationfor the Easterlin paradox and other puzzles. Journal of Economic Literature 46 (1), 95–144.Diamond, P., Saez, E., 2011. The case for a progressive tax: From basic research to policy recom-mendations. Journal of Economic Perspectives 25 (4), 165–190.Duesenberry, J., 1949. Income, Saving, and the Theory of Consumer Behavior. Harvard UniversityPress, Cambridge, Massachusetts.Dworkin, R., 1981a. What is equality? part 1: Equality of welfare. Philosophy and Public Affairs10 (3), 185–246.
CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 18
Dworkin, R., 1981b. What is equality? part 2: Equality of resources. Philosophy and Public Affairs10 (4), 283–345.Easterlin, R., 2001. Income and happiness: Toward a unified theory. Economic Journal 111, 465–484.Frank, R., 2011. The Darwin Economy. Princeton University Press, Princeton.Fumagalli, R., 2013. The futile search for true utility. Economics and Philosophy 29 (3), 325–347.Geanakoplos, J., 2005. Three brief proofs of Arrow’s impossibility theorem. Economic Theory26 (1), 211–215.Habermas, J., 1962. The Structural Transformation of the Public Sphere. Polity, Cambridge.Hirsch, F., 1977. The Social Limits to Growth. Routledge, London.Judt, T., 2010. Ill Fares the Land. Penguin, London.Kahneman, D., Tversky, A., 1979. Prospect theory: An analysis of decision under risk. Economet-rica 47 (2), 263–292.Layard, R., 2011. Happiness, revised Edition. Penguin, New York.Lucas, J., 1965. Against equality. Philosophy 40 (154), 296–307.Man, P., Takayama, S., 2013. A unifying impossibility theorem. Economic Theory 54 (2), 249–271.Marshall, P., 1992. Demanding the Impossible, A History of Anarchism. Harper Perennial, Lon-don.Marx, K., Engels, F., 1848. The Communist Manifesto. Penguin, London.Mas-Collel, A., Winston, M., Green, J., 1995. Microeconomic Theory. Oxford University Press,Oxford.McCloskey, D., 1983. The rhetoric of economics. Journal of Economic Literature 21 (2), 481–517.Mill, J., 1859. On Liberty. Penguin, London.Nelson, R., Winter, S., 1982. An Evolutionary Theory of Economic Change. Belknap HarvardUniversity Press, Cambridge, Massachussetts.Nozick, R., 1974. Anarchy, State and Utopia. Basic Books, New York.Rawls, J., 1971. A Theory of Justice. Belknap Harvard University Press, Cambridge, Massachus-setts.Reny, P., 2001. Arrow’s theorem and the Gibbard-Satterthwaite theorem: a unified approach. Eco-nomics Letters 70, 99–105.Sen, A., 1970. Collective Choice and Social Welfare. North-Holland, Amsterdam.Sen, A., 1973. On Economic Inequality. Oxford University Press, Oxford.Sen, A., 1993. Positional objectivity. Philosophy and Public Affairs 22 (2), 126–145.Sen, A., 1999. Commodities and Capabilities. Oxford University Press, Oxford.Sen, A., 2009. The Idea of Justice. Harvard University Press, Cambridge, Massachusetts.Strauss, L., 1953. Natural Right and History. University of Chicago Press, Chicago.
CONOMICS CANNOT ISOLATE ITSELF FROM POLITICAL THEORY: A MATHEMATICAL DEMONSTRATION 19
Veblen, T., 1899. The Theory of the Leisure Class. Oxford University Press, Oxford World’s Clas-sics. S CHOOL OF E CONOMICS , U
NIVERSITY OF Q UEENSLAND , A
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