Hitotsubashi G-COE Conference Series of Choice, Games and Welfare: Equality and Welfare

1. Hitotsubashi G-COE Conference Series of Choice, Games and Welfare:Equality and Welfare Securing Basic Well-Being for All Reiko Gotoh and Naoki Yoshihara March 16-17, 2012

2. According to Sen, the concept of “capability” of an individual is defined as a set of “functionings” (vectors of various ‘doings’ and ‘beings’) which can be realized by transforming transferable goods and services (not only economic but also political or social, for example, a knowledge that “everyone has the right to recognition everywhere as a person before the law”, Article 6, the Universal Declaration of Human Rights), through the individual’s non-transferable ability to utilize them. • This concept provides a good introduction to understand the reason of inconveniences an individual faces. For example, if we know that an individual is too limited in the achievement of “moving”, we will ask ourselves: does she dislike moving or is she difficult in using transformations?

3. And if we wish to promote her achievement of “moving”, we will consider two kinds of way: making her attitude (preference, or evaluation of “moving”) change; or expanding her capability to choose more achievement of “moving”, for example, through the improvement of public transportations. • (Note)The following definition of disability is similar to capability approach: “disability results from the interaction between persons with impairments and attitudinal and environmental barriers that hinders their full and effective participation in society on an equal basis with others”(preamble, Convention on the Rights of Persons with Disabilities, 2006). • Let us illustrate the implication of “capability” concept contrasting these two ways.

4. accessing to IT y (x, y) achieved with evaluation v (x’ , y’) achieved with evaluation v’ i’s evaluation , v i’s capability C 45° moving x 0 i’s changed evaluation, v’ Figure: improvement of “moving” by the change of evaluation on functionings from v to v’

5. accessing to IT y (x’ , y’) achieved under capability C’ (x’, y) achieved under capability C’ 1’s capability C’ i’s evaluation 1’s capability C 45° moving x 0 Figure: improvement of the achievement of “moving” through the expansion of capability from C to C’

6. Here, we especially focus on the concept of “basic capability” (Sen, 1980, p.367) and investigate the social choice procedure to secure “basic capability for all”. • Ｗe define the concept of “basic capability” slightly modifying the original Sen’s idea in the following way. • When an individual's capability is below “basic capability”, she has a legitimate claim to society to provide the goods and services which are necessary to secure her “basic capability”, while the freedom to choose the appropriate functionings from her capability is preserved for her. • Conversely, we assume that society has an obligation to secure “basic capability” for all individuals.

7. But in what way? To say ‘for all’ sounds as much ambiguous as to say ‘for no one special’. • To secure basic capability for ‘all’ seriously, it is necessary to identify ‘the least advantaged’ in terms of capability in each social policy and choose social policies, under which the capabilities of the least advantaged are at least as good as (or not worse than) basic capability. • In this context, we can refer to “the difference principle” proposed by John Rawls(1971), which requires maximizing the benefits of the least advantaged, given economic circumstances including individuals’ work incentives.

8. Yet we must note that: Rawls’ difference principle assumes that the least advantaged can be endogenously or unanimously defined in a model, for example, as individuals with the least income in a society in each alternative policy. • In contrast, when we adopt the concept of capability as index, it is unrealistic to assume that the least advantaged can be identified endogenously or unanimously depending on alternative social policies.

9. This is first because unlike what is the case of income, the positions of individuals in terms of capabilities (which are historically, culturally and personally characterized) cannot be replaceable through social policies or transferable goods and services, • second, we find different types of “the least advantaged” who are common in lacking “basic capability” but cannot be compared one another, namely, we cannot say that their positions in terms of capabilities are ‘indifferent’, needless to say, one is ‘better’ or ‘worse’ than another.

10. [Example]: the quantitative achievement of ‘moving’ for a blind person, for example, ‘10 times a week’ must be discounted by the neglects he suffers (when he asks neighborhoods) during his “moving”, while the one for an injured person must be discounted by the pains she suffers (when she cannot find places for laying down) during her moving. How should we set up their discounting rates? • Based on this consideration, we adopt a model in which the concrete content of “basic capability”---the lists and the sizes of functionings which constitute “basic capability” as well as the unit of measurement of each functioning---can be different according to types of disadvantage. • In other words, we assume a situation that the conception (operational form) of ‘basic capability’ can take particular forms subject to the common acceptance of the universal concept of ‘basic capability’.

11. Besides, we introduce the concept of “(disadvantaged) group”, which consists of persons with the same type of difficulties in utilization ability (impairments) and shares a common conception (operational form) of “basic capability” as well as the unit of measurement. • It is assumed that a group can form a common appraisal on capabilities of its members and a common evaluation over alternative social policies to the extent that is needed to secure the basic capability for all the members, focusing on the least advantaged within the group.

12. Accessing to IT capability of IndividualI capability of Individual j Social policy No support IT support moving support moving & IT support moving of i moving of j accessing to IT of i Accessing to IT of j BC: basic capability Moving x figure: Group of blind individuals the least advantaged i and j have different utilization ability to achieve “moving” and “accessing to IT” and their capabilities change differently according to the kinds of supports (moving support &IT support).

13. The agenda of this paper is to examine the possibility of constructing a social choice rule (called social relation function: SRF) that associates a social evaluation of alternative social policies to each individual or/and group information, in order to choose the class of social policies securing ``basic capability for all'', given each circumstance. • The social relation function we investigate here shares an essential feature with the traditional Arrovian social welfare function (Arrow, 1951) or the Sennian social welfare functional (Sen, 1970, p.126, d'Aspremont and Gevers, 2002) in that the ultimate informational basis to determine “social values” is nothing more than “individual values” within a society. Yet, we diverge from both of them in several aspects.

14. In Arrovian framework, each individual's characteristic within a profile is her preference which may represent her ``subjective evaluation''; further full intra-personal comparability (completeness of ordering) as well as full inter-personal non-comparability are assumed. • The Sennian social welfare functional permits each individual's utility function to be interpreted as her ``observable situation'' which is inter-personally comparable, yet it also assumes full intra-personal comparability (completeness of ordering) and is usually represented by a numerical function (individual utility function).

15. In contrast to the Arrovian and the Sennian frameworks, in this paper, a capability appraisal with respect to individual i, which can be interpreted as a ranking of her capabilities, does not necessarily means her ``subjective appraisal''. Rather, we interpret that it is an appraisal which is publicly scrutinized and recognized as reasonable in terms of her observable capabilities. • Moreover, an individual appraisal on capabilities is allowed to be incomplete and ordinal binary relations, as well as inter-personally comparable to the extent that the least advantaged can be identified within a group but does not guarantee full comparability among the least advantaged even in a group. For, example,

16. BC C(x) of the least advantaged i C’(x) of the least advantaged j Figure. Example: capability C (x)and C’ (x)cross each other and C is included in basic capability while C’ (x) is cross with BC.

17. These characteristics of our framework derive from the characteristics of the concept of capability or basic capability itself: observability (see “positional objectivity”, Sen 2002) and plurality: the plurality of lists, units and weights of functionings. Note: • Within a group, which shares the same list of functionings and unit of measurement, comparison of capabilities whether intra-personally or inter-personally may be possible, for example, by adopting a specific weight of functionings and a certain “Atkinson Welfare Index”.

18. Figure: Atkinson Welfare Index: To what point in the line of full equality the actual distribution is regarded to be equivalent? y achieved point with a certain weight of x and y utilitarian index CES function’s index Rawlsian index 45° x 0 δ:weight coefficient of x and y, ρ:substitution coefficient of x and y Thus, distribution depends on δ, ρ and x/y

19. Yet, the basic concern of this paper is to avoid some pre-experiential decision on specific methods of comparison, rather to hand in the decision to the disadvantaged groups. Here is the true value of social choice theory, more precisely, the value of replacing the problem of measurement of capability with the problem of social choice. • In this paper, the group evaluations are preferentially reflected in a “social evaluation” of alternative social policies, while the domain of profiles of group evaluations and the procedure of aggregating diverse group evaluations are publicly regulated by certain conditions. • Now is the time to introduce our basic model in a formal way and explain the conditions imposed on the social relation function and on the group evaluations, which are supposed to embody the goal of “securing basic capability for all”.

31. Given that persons with a particular disadvantage can be considered as `specialists` of that disadvantage, the NR condition seems reasonable on the one hand. • On the other hand, in terms of respecting the plurality of the conceptions of the good that individuals have, the CWP condition seems reasonable. • It is not, however, self-evident that these two conditions are compatible with each other. The agenda of the rest of the paper is to verify the compatibility of these two conditions. This is done in the four steps. • First, we examine whether or not SRF which satisfies NR can without fail bring about social evaluations which satisfy transitivity. • Theorem 1 provides a negative answer to this question. • Therefore, second, we look for a way to avoid this negative result and introduce an additional condition, Full-comparability of Destitution (FCD).

32.   Theorem 2 proves that FCD is sufficient to guarantee the existence of SRF which satisfies NR, while ensuring the transitivity of social evaluations. • Based on these results, in the third step, we directly examine the compatibility of NR and CWP. • Theorem 3 shows that it is impossible to guarantee the existence of SRF which satisfies both NR and CWP, even if we strengthen the comparability of capability appraisals by introducing FCD. • Finally Theorem 4 clarifies what a kind of condition further strengthening comparability of capability appraisals is sufficient to avoid this negative result . Let us introduce these theorems formally. Theorems Lemma 1: Let the reflective satisfy BCC, RM, and RC. Then, it is transitive.

34. Theorem 3: Suppose FCD. Then, there exists a capability appraisal ≿, under which there is no SRF which satisfiesNR andCWP. • Given this impossibility theorem, we introduce an additional condition, Dominance (D), which requires that if one capability is clearly worse in comparison to BC, while another is not (i.e. at least as good as BC), we should make a comparative judgment between the two, even if we cannot directly compare them.

35. BC C(x) C’(x) Dominance Condition (D): C’(x) C i (x) Figure: capability C (x)and C’ (x)cross each other and C is included in basic capability while C’ (x) is cross with BC.

36. With a condition D in addition to FCD, we can guarantee the existence of SRF which satisfies NR and CWP as follows: • Theorem 4: LetFCDandDhold. Then, there existsa SRF which satisfies NRand CWP.  [implications of theorems] • Let us summary the implications of these theorems and confirm the contributions of this paper. • First, note that if we assume completeness for group evaluations, PR coincides with the Strong Pareto condition.

38. Given that the Strong Pareto condition satisfies transitivity, if we can assume completeness for a group evaluation, it must satisfy transitivity under PR. While, theorem 2 shows that FDC which guarantees full-comparability only in the domain below BC (any pair of y and y’) is sufficient to avoid cyclicity under NR (stronger version of PR). Why is this condition sufficient? Isn’t the fully full-comparability necessary? The answer is no. • C(x) (example) C(x’) • C(y) • C(y’) • The key to avoid cyclicity in other domains is nothing other than the works of the Refrain condition (RC) and the Basic Capability condition (BCC). Let us confirm it. • First, conceivable cases other than any pair of y and y’ are: any pair of x and x'; any pair of z and z'; any pair of x and y; any pair of x and z; and any pair of y and z. C(z)?, C(z’)? *red line means BC

39. RC prohibits each group to make a comparison between any pair of x and x' or any pair of z and z', thus NR keeps silent. • BCC requires full comparison between any pair of x and y; between any pair of x and z; and between any pair of y and z for every group evaluation. • In conclusion, cyclicity is avoided in all conceivable cases. • This result indicates that the conditions devised in this paper are not only plausible in terms of normative considerations in securing ``basic capability for all'', but also effective in guaranteeing the transitivity of the social relation function. • Second contribution is more philosophical. Recently Sen proposed a ``comparative approach'' to justice in place of a ``transcendental approach'' to justice (Sen 2009a, pp.15-18, Sen, 2009b, pp.46f).  

40. According to Sen, the latter is a traditional approach in ethics which focuses on the description of an ideal social state, while the former is in ethics a new approach, but familiar to economics, which ranks alternative social states. This paper is an attempt to formulate a ``comparative approach'' to justice in the following sense. • First, we can use ``basic capability'' as a criterion to identify whether a policy is ``just'' or ``unjust''. BCC works by rejecting ``unjust'' policies when there exists a ``non-unjust'' alternative (non-unjust policies include not only just policies but also those which are neither just nor unjust policies). • However, a ``comparative approach'' to justice requires even more. It requires comparing pairs of ``unjust'' policies to one another and to make it possible to choose ``less unjust'' policies from the set of feasible alternatives. In this paper, it is the RM condition with the support of FCD which does this work.

41. Instead of summarizing let us clarify the basic conceptions underlying this paper. • In this paper, ``(disadvantaged) group'' is defined as the maximum unit within which inter-personal comparison of capabilities is possible to the extent that the least advantaged ---individuals whose capabilities never dominate the capabilities of others--- can be identified in each social policy. • Yet, since the relative weights of various functionings cannot be uniquely determined, there remains a form of incomparability between the least advantaged within a group, i.e. some of which may be at least as good as ``basic capability'', while some are worse than ``basic capability''. • In this sense, the process to form a group appraisal is itself a collective choice which needs to be regulated by certain conditions.

42. However, the meaning of this form of incomparability should be kept distinct from that of the incomparability (also called “incommensurability”) between groups. • We can treat the former as a technical or political problem and certain conditions of compromise can be introduced to deal with it as we do in this paper (the Dominance condition), while the latter is one about which there should be no compromise as long as we take seriously the plurality of disadvantages. • This distinction between two forms of incomparability corresponds to the distinction introduced by Sen (Sen, 2002, 182) between: ``tentative incompleteness'' derived from some pairs of alternatives which are not yet ranked but may all get ranked with more deliberation or information; and ``assertive incompleteness'' derived from some pairs of alternatives which are asserted to be ``non-rankable''.

43. The second concerns two different kinds of conflicts which may occur between different groups. • One kind of conflicts are ones that arise from each group's need to achieve ``basic capability''; the other kind of conflicts are ones that derive from each group's desire to enjoy better capabilities beyond ``basic capability''. • The former kind of conflicts is avoidable, if there are resources enough to secure basic capability for each group, while the latter is not if the desire towards better capability is without limit. The former deserves considerations in terms of justice, while the latter does not. • This is the reason why in this paper the work of Monotonicity condition is restricted to the domain below ``basic capability'', in the domain above ``basic capability'' conflicts are avoided through the work of the Refrain condition, which prohibits each group to make any kind of ranking.

44. The third point concerns to two kinds of comparative adjectives, ``better or worse'' and ``less or more unjust''. • In this paper, ``better or worse'' is used in the comparison of individual capabilities while ``less or more unjust'' is used in the comparison of social policies. • This usage is derived from the distinction of conceptions of ``good'' and of ``justice'' according to Rawls (Rawls, 1971). • In the political liberalism of Rawls conceptions of ``justice'' are expected to realize an overlapping consensus of plural conceptions of the good. • We suppose that the conceptions of “capability” and of ``basic capability'' as well as of well-being correspond to conceptions of the good, the plurality of which should be respected, while the goal of securing ``basic capability for all'' corresponds to the conception of justice, which aims at an overlapping consensus.

45. Final point is the distinction between income and capability. It is logically possible to reduce the capability index to the income index and the goal of ``basic capability for all'' can be reduced to ``basic income for all''. • If all necessities are satisfied through the market and depend on individual income, and if we can take the extra demand of income which particular groups need in order to achieve the same capability as standard consumers as their legitimate claim this reduction seem reasonable. • Yet it is usually difficult to do this, since what kinds of functionings are basic and how much extra income is needed to secure a person’s basic capability might be different depending on individual difficulties. • Moreover, necessities such as right to freedom, dignity as human beings and the social basis of self-respect cannot simply be satisfied through the market with more income. • What then is needed to secure basic capability for all? Such is the central question which capability approach pursues.

46. References • Arrow, K. J. (1951/1963): Social Choice and Individual Values, 2nd ed., New York: Wiley. • d’Aspremont, C. & L.Gevers (2002) “Social Welfare Functionals and Interpersonal Comparability,” Arrow. K., A. K. Sen and K. Suzumura (eds.) Handbook of Social Choice and Welfare, vol.1, Amsterdam: North-Holland, 459-541. • Foster, J (1984): “On Economic Poverty: A Survey of Aggregate Measures,” Advances in Econometrics, 3, pp. 215-251. • Pattanaik, P. K., and Youngsheng Xu (2007): “Minimal relativism, dominance, and the standard of living comparison based on functionings,” Oxford Economic Papers, 59, 354-374. • Rawls, J. (1971): A Theory of Justice, Cambridge, Mass.: Harvard University Press. • Sen, K. A.(1970): Collective Choice and Social Welfare, San Francisco: Holden-Day. • Sen, A. K. (1981): Poverty and Famines: An Essay on Entitlement and Deprivation, Oxford. • Sen, A. K. (1985): Commodities and Capabilities, Amsterdam: North-Holland. • Sen, A. K. (1987): The Standard of Living, Cambridge University Press: Cambridge. • Sen, A. K.(1997): On Economic Inequality, expanded edition with a substantial annex by James E. Foster and Amartya K Sen, Oxford: Clarendon Press.

47. Sen, A. K. (1999a): Reason before Identity, The Romanes Lecture for 1998, Oxford, Oxford University Press. • Sen, A. K. (1999b): Development as Freedom, New York: Alfred A. Knopf. • Sen, A. K.(2002): Rationality and Freedom, Cambridge: Harvard University Press. • Sen, A. K. (2006): Identity and Violence-The Illusion of Destiny, New York: W.W. Norton & Company. • Sen, A. K. (2009a) The Idea of Justice, Allein Lane, Penguin Books. • Sen, A. K. (2009b): “Economics, Ethics and Law,” Gotoh R. and P. Dumouchel (eds.) Against Injustice: The New Economics of Amartya Sen, Cambridge University Press, 39-54.