Notions of Fairness Versus the Pareto Principle: On the Role of Logical Consistency

Yale Law Journal

Volumn 110, Issue 2, 2000, Pages 237-248

  Kaplow, Louis ^a   Shavell, Steven ^a  

^a NONE

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EID: 0041386048     PISSN: 00440094     EISSN: None     Source Type: Journal    
DOI: 10.2307/797572     Document Type: Article

References (32)

1. Louis KAPLOW & STEVEN SHAVELL, PRINCIPLES OF FAIRNESS VERSUS HUMAN WELFARE: ON THE EVALUATION OF LEGAL POLICY (John M. Olin Ctr. for Law, Econ., & Bus., Harvard Law Sch., Discussion Paper No. 277, 2000), forthcoming in 114 HARV. L. REV. (2001).
2. Louis KAPLOW & STEVEN SHAVELL, PRINCIPLES OF FAIRNESS VERSUS HUMAN WELFARE: ON THE EVALUATION OF LEGAL POLICY (John M. Olin Ctr. for Law, Econ., & Bus., Harvard Law Sch., Discussion Paper No. 277, 2000), forthcoming in 114 HARV. L. REV. (2001).
3. We note, however, that many notions of fairness concerned solely with income distribution are not included in the notions of fairness that we examine and criticize. This is because many distributive concerns involve individuals' well-being and are thus, by definition, accommodated in the welfare economic framework that we defend. Id. secs. II.A-.B. Indeed, we do not formally limit the distributive principles that may be employed (the favored distribution could be utilitarian or egalitarian, or one could give more to Joe because he is tall and less to Jill because her preferences are objectionable), although, of course, the spirit of some of our arguments and others that could be adduced would narrow the range of plausible distributive principles substantially.
4. Louis Kaplow & Steven Shavell, The Conflict Between Notions of Fairness and the Pareto Principle, 1 AM. L. & ECON. REV. 63 (1999).
5. LOUIS KAPLOW & STEVEN SHAVELL, ANY NON-INDIVIDUALISTIC SOCIAL WELFARE FUNCTION VIOLATES THE PARETO PRINCIPLE (Nat'l Bureau of Econ. Research, Working Paper No. 7051, 1999), forthcoming as Louis Kaplow & Steven Shavell, Any Non-Welfarist Method of Policy Assessment Violates the Pareto Principle, 109 J. POL. ECON. (2001).
6. LOUIS KAPLOW & STEVEN SHAVELL, ANY NON-INDIVIDUALISTIC SOCIAL WELFARE FUNCTION VIOLATES THE PARETO PRINCIPLE (Nat'l Bureau of Econ. Research, Working Paper No. 7051, 1999), forthcoming as Louis Kaplow & Steven Shavell, Any Non-Welfarist Method of Policy Assessment Violates the Pareto Principle, 109 J. POL. ECON. (2001).
7. Howard Chang, A Liberal Theory of Social Welfare: Fairness, Utility, and the Pareto Principle, 110 YALE L.J. 173 (2000). Chang also considers other matters (notably, he criticizes an argument of Amartya Sen) that we do not take up here.
8. We should note at the outset that we have experienced general difficulty in interpreting Chang's article. Despite his technical economic training, Chang does not translate his argument and examples into unambiguous, formal statements or offer proofs of any of his claims, although our article to which he is responding consists almost entirely of formal statements and presents a proof of its main claim. The problem of Chang's imprecision includes the definition of fairness itself. We formally defined how we were using the term in each of our writings, KAPLOW & SHAVELL, supra note 4, at 2; Kaplow & Shavell, supra note 3, at 65-66 n.5; KAPLOW & SHAVELL, supra note 1, at 39 n.69, whereas we are not always sure whether Chang uses the term fairness in the same manner (for example, we cannot be sure he is excluding purely distributive notions, as we do, see supra note 2). Chang neither mentions our precise, formal definition at any point nor offers any definition of his own. (And, despite Chang's apparent displeasure with our definition, we note that it does encompass all of the many leading notions of fairness that we examine in KAPLOW & SHAVELL, supra note 1, pts. III-VI.)
9. Kaplow & Shavell, supra note 3, at 68-70.
10. To an extent, Chang can be seen as challenging this demonstration, because, as we explain in Part II, he does not seem to accept the view that normative principles have to be applied consistently. We do note, however, that the continuity assumption that he challenges regarding our second demonstration is not employed in our first demonstration. The reader may wonder about notions of fairness concerned with the distribution of income or well-being, which would be moot in symmetric cases. As we indicate above in note 2, however, such principles are not among the notions of fairness that we criticize, and we are explicit about this in our prior writing. E.g., Kaplow & Shavell, supra note 3, at 67; KAPLOW & SHAVELL, supra note 1, sec. II.A.
11. Kaplow & Shavell, supra note 3, at 73-74.
12. Chang, supra note 5, at 222 n.193, questions our observation to this effect and refers to our making strong and demanding assumptions, but we see his comments as red herrings. We simply ask the reader to contemplate the converse: Suppose that no matter how much the degree of fairness differed between two regimes, a notion of fairness never implied that one regime was superior to another when all else was equal, namely, when everyone had the same level of well-being. Clearly, there is no sense in which the notion of fairness is receiving any independent weight. (Put technically, our formal definition asks whether an evaluative principle can be implemented if the analyst knows how regimes affect individuals' well-being but has no information about any other characteristics of the regimes, including how fair they are. If the supposition in the text is false, then the analyst can make the evaluation knowing only well-being (for whenever the information on well-being is the same, so is the assessment); hence, as we define it, there is no independent notion of fairness involved.) We are also puzzled by Chang's statements in the same note that our language usage (concerning the meaning of an "individualistic" social welfare function) is ambiguous and inconsistent. First, we offer a formal definition for the term in question. KAPLOW & SHAVELL, supra note 4, at 2. Second, our other use of the term to which Chang refers is also formally stated. Id. Third, although we do not offer a formal proof of stated equivalence between our two usages, this is only because the equivalence in our framework is (we thought) obvious. (When Chang questioned the equivalence, we supplied him with the proof, tracking the above-described intuition, which he has not questioned.)
13. Consider another way to see the intuition behind the general argument (which, to prove rigorously, requires stronger assumptions). (1) Suppose that there exist two regimes. F and W, such that F is more fair, welfare is higher in W, and F is viewed as superior overall to W. (This must be true of at least some such choices of F and W if fairness ever determines social choice.) (2) Construct W' from regime W as follows: Maintain the same degree of (un)fairness and total welfare, but redistribute income such that the resulting distribution of well-being in W' is the same as in F. (If, for example, the redistribution reduces inequality and one's welfare assessment favors a more egalitarian outcome, the overall adjustment in generating W' from W would reduce total income sufficiently to keep total welfare constant.) (3) Since F is more fair than W' by the same amount that it was more fair than W, and since welfare is no higher in W' than it was in W, it must be that F is deemed overall superior to W'. (4) However, W' has higher total welfare than F and also the same distribution of welfare as F (that is how we constructed W'). Hence, everyone must be worse off in F than in W', even though F is judged to be superior overall under the notion of fairness.
14. Chang's most direct statement about continuity is, we believe, misleading. He states that "[t]here is no apparent reason why a slight increase in consumption of some good might not have a discontinuous impact on social welfare, especially if it is so widespread as to be shared by all individuals in society." Chang, supra note 5, at 224. First, he does not explain, as we do in the text to follow, that discontinuity means that the ratio of the impact on social welfare to small changes in consumption becomes infinite (as one considers smaller and smaller changes in consumption). Thus, any slight increase in consumption (say, a peanut per capita) is posited by Chang, in finding discontinuity plausible, to be vastly more important than any degree of unfairness, no matter how large. (This explains why Chang's other statements, see id. at 210-11 & n.165, are also incorrect with regard to the concept of continuity.) Second, the idea that the number of individuals might be relevant is fallacious, for the amount of increase in the consumption good per person can be arbitrarily small-indeed, whatever unit one imagines (say, one peanut) can be divided by the number of people in determining how much of a per capita increase to consider (so, if the population is a million, we can imagine each individual gaining by only a millionth of a peanut). In addition, Chang states that the literature on social choice theory generally does not assume continuity. Id. at 224 n.197. Chang does not mention, however, that continuity is often moot in much of that literature, because it is concerned only with discrete possibilities (that is, it does not allow anything, such as the amount of a good an individual has, to vary gradually) and because it uses only rankings (which, for example, allows no statements about degrees of preference or well-being, which renders consideration of most notions of distributive justice impossible). In our more encompassing and realistic framework, the assumption of continuity is relevant and, as we explain in the text, compelling.
15. Chang repeatedly refers to our "particular" continuity property, e.g., id. at 223, although our usage is entirely standard, straight from any textbook or dictionary that includes mathematical terms.
16. See id. at 222-26.
17. For example, we would not take seriously a notion of fairness that was used to break literal ties (where even a fraction of a cent would swing the decision one way or the other) but that otherwise never mattered.
18. Chang, supra note 5, at 226-32.
19. Chang suggests that our independence assumption is analogous to that used in Arrow's Theorem and thus may be subject to criticism. Id. at 226-29. But our independence assumption is, in important respects, weaker than Arrow's. Arrow assumed that the social ranking of X and Z can depend only on different individuals' rankings of X and Z - and thus not on the intensity of their preferences or on any difference between one individual's gain and another's loss (interpersonal comparisons). This limitation implies, among other things, that ordinary distributive judgments are ruled out in social decisionmaking. This aspect of Arrow's assumption is specifically identified by those Chang quotes, id. at 228-29 & n.206. in support of the contention that independence is a controversial assumption. See ALFRED F. MACKAY, ARROW'S THEOREM: THE PARADOX OF SOCIAL CHOICE 48 (1980); DENNIS C. MUELLER, PUBLIC CHOICE II 393-95 (1989). Our independence assumption, by contrast, does not rule out preference intensities or interpersonal comparisons (and thus allows distributive judgments). Rather, it only requires logical consistency in the sense discussed in the text. Chang does not mention this crucial difference.
20. Chang suggests that our independence assumption is analogous to that used in Arrow's Theorem and thus may be subject to criticism. Id. at 226-29. But our independence assumption is, in important respects, weaker than Arrow's. Arrow assumed that the social ranking of X and Z can depend only on different individuals' rankings of X and Z - and thus not on the intensity of their preferences or on any difference between one individual's gain and another's loss (interpersonal comparisons). This limitation implies, among other things, that ordinary distributive judgments are ruled out in social decisionmaking. This aspect of Arrow's assumption is specifically identified by those Chang quotes, id. at 228-29 & n.206. in support of the contention that independence is a controversial assumption. See ALFRED F. MACKAY, ARROW'S THEOREM: THE PARADOX OF SOCIAL CHOICE 48 (1980); DENNIS C. MUELLER, PUBLIC CHOICE II 393-95 (1989). Our independence assumption, by contrast, does not rule out preference intensities or interpersonal comparisons (and thus allows distributive judgments). Rather, it only requires logical consistency in the sense discussed in the text. Chang does not mention this crucial difference.
21. It may not be apparent how our proof, sketched above, uses this assumption. One way to express the point is that, when we hypothetically contemplated regime Unfair-II, we implicitly assumed that the statement that regime Fair was superior to regime Unfair was not thereby rendered invalid. To be sure, as we note in the text to follow, it is common and appropriate in moral argument to change one's view in some cases through the contemplation of other cases. Our point is that, once one believes one has arrived at a complete and correct moral view, after considering all imaginable cases, one is not free to proclaim both that X is morally superior to Z and that Z is morally superior to X, solely depending on what else is stated to be "on the table" at the moment of an actual decision. (We acknowledge that there may be some instances in which a choice might be said to depend upon other options, such as when a person might be upset at the very fact that an available, preferred option has been rejected, but such possibilities are irrelevant in our framework because the regimes that are to be assessed by a normative criterion are explicitly defined as complete descriptions, see KAPLOW & SHAVELL, supra note 4, at 1, which would already include any such feelings. The moral question is: Given all such information, which is morally superior, X or Z?)
22. In some of our private correspondence, Chang seemed to accept our view that rejecting independence was morally indefensible, indicating that he merely wished to establish as a logical matter that our position depended on this assumption. Now it is surely correct that logic itself does not require that one accept logical consistency in normative analysis, but if this is the extent of his challenge then there is no dispute about whether the assumption is ultimately an appropriate -indeed a compelling - one. In fact, elsewhere in his article, he takes Sen to task for deeming a hypothetical regime irrelevant to moral analysis on grounds of infeasibility: Sen's "objections go to the 'pragmatic' question of whether the solution is feasible, not to the 'ethical' question of whether the trade would be socially desirable if it were available to us as a social choice, and it is the ethical question that is relevant for our purposes here." Chang, supra note 5, at 202; see also id. at 202 n.135 (citing Hammond's statement that arguments such as Sen's involve "misconceptions" due to "confusion").
23. Id. at 214.
24. To illustrate some of the problems with both of his arguments about our assumptions, we offer an example that is in the spirit of much of Chang's discussion of the idea that individuals should be allowed to waive (alienate) their rights if it is to their advantage. In regime A, Bill, the richest, most well-off (and most unpleasant) person in the society does very well, and every other person is in misery, on the brink of starvation; no one's "rights" are violated. In regime B, Bill is a cent worse off than he is in A, because a trivial violation of one of his rights occurs, and everyone else is markedly better off. Chang's approach would require adopting regime A, because Bill does not have to waive his right, which can be given infinite weight even though Bill hardly cares about it and the rest of society suffers greatly. Now, if we imagine a regime C, in which no rights are violated. Bill is much worse off than in A, and everyone else is better off than in A but not as well off as in B, Chang's preference for higher overall welfare would lead him to choose C. This time Bill has no veto because his right is not violated (even though Bill loses far more moving to C than to B, where we gave him a veto). Of course, if one compares B and C, one can see that everyone is better off in B - yet B was rejected (versus A) and C was adopted (versus A). This, then, raises the question of which regime should really be chosen. (A is chosen over B, because Bill has a right; B over C. because of adherence to the Pareto principle; and C over A, because of the welfarism half of Chang's liberal welfarism.) If the choice is purely between A and B, Chang says A is morally superior. If among all three, he says B is morally superior.
25. Relatedly, since the modified notion of fairness that emerges from Chang's procedure may differ markedly from the original notion with which one began, it is also important to inquire whether the original rationale for the notion will continue to be applicable (an inquiry that obviously will be difficult if one cannot readily determine what the modified notion will look like).
26. Chang, supra note 5, at 215-19.
27. In prior exchanges with Chang, we have shown that his example, id. at 220-21, like others he has suggested to us previously, fails. In the manner he has verbally interpreted the present example to us we have shown that his modified fairness function is not a notion of fairness as we define it. (In essence, the only "fairness" left concerns distribution, which, as we have said explicitly in all of our writings, is not included in our definition and thus not subject to our claim. Supra note 2. Indeed, Chang identifies two aspects of social decision in his example. Chang, supra note 5, at 220. The first ends up being governed by welfare, and not fairness, to avoid a Pareto conflict, id. at 221, and the second involves the need to determine the distribution of wealth, id. We further showed that other interpretations of his example (which may be what many readers would infer Chang means from the first half of his article) would involve a violation of the Pareto principle. Chang's statement that he has given an example of a notion of fairness (as we have consistently defined it, see supra notes 2, 6) that does not conflict with the Pareto principle is no more than a pure assertion that we have previously demonstrated to be false.
28. Chang's procedures make various comparisons, choose "best" points, and change "ranks" in particular ways. However, on the domain that we considered, which realistically allows for continuous variation (for example, in how much funds may be spent on courts or in how much of a good people may have), there are what is formally referred to as an uncountably infinite number of comparisons to make. And, the concept of "best point" (used in his first procedure) is not defined, except at boundaries, as Chang acknowledges. Id. at 218 n.183. (By analogy, if one is asked to state the second highest real number in the interval from 0 to 10.0, inclusive, after the highest number (10.0) is removed, there is, as some readers will recall, no such thing as the next highest real number. Yet Chang's procedure cannot move forward until the second highest number is identified.) Moreover, the changes in "ranks" required in his second procedure - which Chang explicitly offers to remedy the preceding problem - are undefined for essentially the same reason. (Chang states that one should give an alternative a rank that is "higher than the rank in question but lower than any higher rank." Chang, supra note 5, at 219. Suppose that the "rank" in question is 10.0 and all the real numbers between 10.0 and 11.0 have been assigned to other alternatives. Obviously, there does not exist a real number higher than 10.0 but no higher than any other real number between 10.0 and 11.0.) Chang's failure to write his procedures in a more formal manner, actually to show their operation on the sort of domain in question (which allows continuous variation of parameters), and to prove that any particular output of the procedures has the alleged properties - despite our suggestions for over a year that he do so - is suggestive of their underlying deficiencies.
29. Thus, his statements that we could use "a reasonable rule of thumb" and eschew "investing much of our scarce resources in the search for . . . Pareto improvements," id. at 230-31, are wrong in his own framework. (Relatedly, he suggests that one may focus primarily on the fairness optimum, id. at 231, but because he rejects our assumptions, this works only if that optimum is identified in a literally perfect, precise manner, which of course is impossible.) It should also be clear, contrary to Chang's suggestion, id. at 219 n. 186, that these defects are unique to his particular approach. For example, under welfare economics (and most notions of fairness that people actually believe in), only the policies under consideration would have to be evaluated in order to choose among them, and the use of approximations would usually yield approximately good results. (Indeed, in the latter part of his footnote, he acknowledges differences between welfare economics and his approach but does not reveal how they render his, and only his, procedure inoperable.)
30. E.g., KAPLOW & SHAVELL, supra note 1, secs. II.D, VIII.B.
31. Chang himself is difficult to interpret. He does not offer a definition of external preferences and criticizes the one definition in the literature that he mentions explicitly. Chang, supra note 5, at 183 n.40. In response to one of the definitional problems he mentions briefly, he asserts that we "can distinguish" the problematic preferences from others, by reference to which preferences "are not 'intrinsically immoral,'" id. at 189 n.67, a patently question-begging response since the whole point of the distinction was to identify which preferences should be deemed immoral. Finally, Chang concludes his discussion of censoring preferences by stating that to avoid what he regards as decisive objections to the preference-censoring position as formulated by others, he would admit (that is, not censor) "personal preferences based on external preferences." Id. at 191-94. This seems to imply, however, that although he would exclude the preferences of, say, sadists that were expressed in terms of the supposed political inferiority of their victims, he would admit sadistic preferences reflecting the pure pleasure of seeing the victims suffer-hardly a distinction that succeeds in capturing the intuitions that Chang claims motivate the preference-censoring view in the first place.
32. There exist additional difficulties as well. It is not clear, for example, how to define what it means to censor a preference since, in general, the intensity of an individual's other preferences may well depend on the extent to which the preference to be censored is in fact satisfied. Also, paradoxically, censoring a preference could lead to results under which more of the undesirable activity occurs. (Ignoring a sadist's preferences may lead us to deem him worse off-because a source of his satisfaction is not counted-which under some distributive theories would entitle him to a greater share of resources, part of which he may devote to satisfying his sadistic preferences.)