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Rule-utilitarianismJordan Howard Sobel aa University of California , Los AngelesPublished online: 15 Sep 2006.
To cite this article: Jordan Howard Sobel (1968) Rule-utilitarianism, AustralasianJournal of Philosophy, 46:2, 146-165, DOI: 10.1080/00048406812341121
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Australasian lournal of Philosophy Vol. 46, No. 2; August, 1968
JORDAN HOWARD SOBEL
RULE-UTILITARIANISM
According to Richard Brandt, a certain simple and initially attractive version of rule-utilitarianism cannot be preferable to act-utilitarianism since it has identieal, ly the same consequences for action as does act- utilitarianism. 1 Allan Gibbard ~ argues against Brandt's reduction thesis: he presents cases designed to show that this thesis is in error. In the present essay, first, Brandt's thesis is spelled out and Gibbard's counter- thesis is stated in full. Then, in Section Two, Gibbard's cases are examined and other cases are introduced. Here it is shown that one of Gibbard's cases reveals that the two utilitarianisms diverge far more than he supposes; indeed, this case points to a flaw in the rule-utilitarianism under discussion that Gibbard failed to notice, a flaw that is, furthermore, very different from the one that Brandt thinks vitiates the doctrine. Next, in an appendix to Section Two, a technical extension of the discussion is presented. Gibbard assumes in his cases a certain natural restriction: he requires his agents to choose amongst a limited number of 'pure' strategies. In my discussion of his cases I follow him and assume this restriction most of the time. But in several footnotes, and especially in the appendix to Section Two, certain consequences of making available all 'mixed' strategies are considered. Finally, in Section Three, Brandt's argument for his reduction thesis is analyzed and a diagnosis of his error is presented.
Section One
Brandt holds that the following two doctrines have identically the same consequences for action: ~
RU: An act is right if and only if it conforms with that set of general prescriptions for action such that, if everyone always did, from among all the things which he could do on a given
x Richard B. Brandt, 'Toward a Credible Form of Utilitarianism', Morality and the Language of Conduct, edited by Hector-Ned Casta~eda and George Nakhnikian (Wayne State University Press: Detroit, 1963), pp. 107-143. Allan F. Gibbard, 'Rule-Utilitarianism: Merely an Illusory Alternative?' Australasian lournal of Philosophy (August, 1965), pp. 211-220.
s Brandt, op. cit., p. 120.
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occasion, what conformed with these prescriptions, then at least as much intrinsic good would be produced as by con- fortuity with any other set of general prescriptions.
AU: An act is right if and only if were it performed at least as much intrinsic good would be produced as would be produced were any other act open to the agent performed.
The above formulation of RU is ambiguous and indeterminate in several ways, but Brandt's intentions are I think clear and if I am right it is possible to express them unambiguously as follows:
RU: An act is right if and only if it conforms with the ideal set of general prescriptions. A set, G, of general prescriptions is ideal if and ordy if, for each logically possible social world, W, if every member of W were to conform to G on each occasion of action, then the outcome would be at least as good as it would be were every member to conform on each occasion of action to any other set of general prescriptions.
A social world is here conceived of as having at least two possible histories each of which would be punctuated by a finite number of moments of action. At each moment of action in each possible history there would be one or more agents in the world and at least one agent would have more than one action open to him. I shall say that at each moment of action the world would confront a situation. The n m situation con- fronted in a given possible history would present the world with at least two possible patterns of action; each of these patterns of action would either lead to an n + 1 th situation or would constitute a termination of the world's social history. The following tree diagram presents, for illustration, the possible histories of a simple social world:
11 ----~T
T stands for the initial situation. (I assume that I involves two agents each with two possible actions, and that it presents the world with four possible patterns of action.) The arrows represent possible patterns of
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action, each 'S' represents subsequent possible situations and each 'T' marks a possible termination of this world's history. I assume that only one agent is involved in situations S~, S~, and $82- Others may be in the world, but in these situations only one agent has a choice, only one agent is 'involved' in these situations. Distinct situations must differ but may differ only in their histories: for example, we could assume that S~ and S~ differ only in their histories; S ~ and S 22 would have to differ in their pos- sible futures as well. Each distinct path of arrows from the T to a 'T' repre- sents a distinct possible history for the world. For example, (1 ,5) , (2) , and (1,6,11) are distinct possible histories of this world. This simple social world has ten possible histories.
I assume that each of a social world's possible histories would have a determinate total outcome or set of consequences and that total outcomes can in principle be compared with respect to their intrinsic values. Since conformity by all agents at all moments of action to various sets of rules would generate various histories for a given world, we can describe an ideal set of general prescriptions as a set, G, of general prescriptions such that, for each possible social world, W, any history o f W generated by general conformity by all agents at all times to G would have at least as good a total outcome as would any other possible history of W.
My conception of a social world is as a game of strategy. Since in what follows I assume that there is a single correct determination of the relative values of the outcomes, and since I also assume (though this assumption does not play a role in my arguments) that the agents involved are in full and correct agreement on the relative values of the outcomes, the worlds or games discussed are all of a type that might be termed 'strictly non-competitive' or 'double-sum'. One might also describe them as 'pure co-ordination' worlds or games. There is no room in them for competition and if they, under any circumstances, present problems, these will be problems of organization and co-ordination. Such games have sometimes been characterized as trivial. 4 Game theorists for the most part have no t found t hem interesting and they have not been much dis- cussed. However, that strictly non-competitive games are of theoretical interest in ethics, especially in connection with utilitarianisms, is I think shown by the part they play in the arguments of Section Two of the present essay.
Brandt's claim is that RU would have the very same consequences for action as would AU. Since these theories would, he thinks, coincide in their practical implications, he concludes that 'it is a, mistake to advocate
4 Lute and Raiffa state that 'in the extreme case where there is perfect agreement [on the values of the outcome or pay-offs] the analysis is trivial'. R. Duncan Lute and Howard Raiffa, Games and Decisions (John Wiley and Sons: New York, 1957), p. 88; see also p. 59. Anatol Rapaport expresses a similar view on p. 95 of his Two-Person Game Theory (The University of Michigan Press: Ann Arbor, 1966).
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[RU] as a theory preferable to [AU]'? Gibbard is concerned to reject Brandt's conclusion, as well as certain related theses. Gibbard presents, as claims to be refuted, the following four statements of ways in which AU and RU might be thought to coincide: G
(1) For each logically possible social world for any action, if it would be AU-right then it would be RU-right.
(2) For each logically possible social world if every action done is AU-right then every action done is RU-right.
(3) For each logically possible social world--for any action, if it would be RU-right then it would AU-right.
(4) For each logically possible social world if every action done is RU-right then every action done is AU-right.
(1) and (3) taken together make Brandt's reduction thesis. (2) and (4) are theses which it is convenient and appropriate to examine along with Brandt's.
Sect ion T w o Gibbard presents three cases. In each he describes a social world
of the logically simplest form that would serve his purposes. His worlds have only two agents, one moment of action, and two actions open to each agent at the moment of action. Each of Gibbard's worlds has only four possible histories. The first social world Gibbard presents refutes (1) and (2). The second is supposed to refute (3). The third is sup- posed to refute (4). The first of Gibbard's cases is stated in full below, and its structure is revealed in a tabular presentation. Structures alone are given for his other cases. This concentration on abstract structures facilitates the discussion and makes easier the construction of new cases for specific purposes.
Gibbard places Smith and Jones in isolation booths: their actions are fully independent. Each can either press a button or refrain from pressing it. In his first case, ff both buttons are pressed, both men receive cake and ice cream. If only one button is pressed, both men receive electric shocks. If neither button is pressed, the men receive neither refreshment nor shocks. To complete the first case, neither man is going to press his button.
Note that it is no part of Gibbard's case either that Smith and Jones are AU-men or that they are RU-men, nor does the case include any assumptions concerning what the agents know either of their situations or of each other. In short, though it is assumed that each man will refrain from pushing his button and, what is more important, that each man wouM refrain even if the other agent were not to refrain, no assumptions are made concerning how or why these agents arrive at their determinations
5 Brandt, op. cit., pp. 122-123. 8Gibbard, op. cir., p. 214.
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to refrain f rom pressing their buttons. In fact, for all Gibbard says, these determinations can be viewed as entirely irrational in their origins:
Gibbard 's first case is of the following structure:
I
Agents Relative value of outcomes.
T J
P P 3
P* R 1
R P* 1 > R* R* 2
Agents T and J are confronted with alternatives P and R. The numbers give, for each of the world's four possible histories, the relative value of the outcome that would result were this history actualized; the larger the number, the better the outcome. The arrow indicates what will happen: T and J will both do R. The asterisks indicate what w o u M happen under certain hypotheses: the asterisks indicate what would be done, and the relative value of the total outcomes that would result, were a given agent to do P or R. For example, that 'P ' is asterisked on line two means that were T to do P, J would do R, and the outcome that would result would have a relative value of 1. That 'R ' is asterisked on line four in the first column means that were T to do R, since J would do R, the relative value of the outcome would be 2. I t should be noted that the subjunctives represented by the asterisks do not imply causal connections between the actions of T and J. The tabular structure is neutral with respect to this point. Of course Gibbard assumes in his first case, and in fact in all of his cases, absolute causal independence: his agents are in 'isolation booths'. Thus in his structure I world he assumes that each agent will do R no matter what the other agent does and that ' the actions of one . . . have no influence at all on the actions of the o the r ' : The table leaves room for Gibbard's causal independence assumption by being, in itself, neutral on the issue of causal connections and influence.
What, in structure I social worlds, do AU and R U dictate? We take A U first and find that R is for each agent the AU-right act. As it happens,
T All this is in contrast to the usual assumptions of game theorists who generally specify rational agents seeking to maximize their utilities, each agent equipped with full knowledge of the structure of the game as well as of the rationality of his opponents and their utility functions. Gibbard assumes none of this. On the other hand, he does specify how his agents will and would act, whereas (other) game theorists rarely explore issues that call for such specification.
S Gibbard, op. cit., p. 214.
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each man will do what he AU-ouglat to do ) Consider T. Were T to do p the outcome would have a relative value of 1, whereas were T to do R the outcome would have a relative value of 2: since the outcome of T's doing R would be better than that of his doing P (the only alternative T has to R) , R is T's AU-right act. By parallel argument, R is also J 's AU-right act. Observe that in arriving at these conclusions the numbers and the asterisks have been decisive. The dictates of AU are in fact in every case controlled by the subjunctive conditional propositions conveyed by the asterisks in conjunction with the numbers. (The indicative proposi- tions conveyed by the arrow are in no case relevant to AU.)
Turning now to RU, on condition that the RU-ideal set of rules exists and that there is an RU-right act for each man (it will emerge below that this condition, the problematic character of which Gibbard fails to notice, is in fact not satisfied), the RU-right act for each man is P. The following argmnent shows this: We take as a condition that there is exactly one RU-ideal set of rules. Let C be a set of rules that does not call for P in structure I worlds. Now suppose that C is RU-ideal. Then, if C' differs from C only in that C' calls for P in structure I worlds, for each logically possible social world general conformity with C' would have at least as good an outcome as would general conformity with C. From which it follows that C' is RU-ideal and (since, by the condition, there is only one RU-ideal set of rules) that C is not RU-ideal which is contrary to the initial supposition. The conclusion is that if there is exactly one RU-ideal set of rules, this set of rules cannot fail to call for P in structure I worlds. Observe that the dictates of RU are in no way affected by the information conveyed by either the asterisks or the arrow. The dif- ference between AU and RU can be expressed most simply as follows: though both the numbers and the asterisks are relevant to AU, only the numbers are relevant to RU. Given this difference it is not at all surpris- ing that AU and RU can conflict. (Note that the arrow is relevant to neither AU nor RU) .
Since, in structure I worlds, each man will do what he AU-ought to do it might seem that we are free to assume that the agents in structure I worlds are AU-agents with full knowledge of their situations and each other. But I doubt that this is so. For suppose that Gibbard's agents were possessed of full knowledge and were committed to AU. Then we could apparently say of his agents the following three things: (i) What each agent ought to do depends upon what the other agent is going to do and thus would do in any event. (Remember that Gibbard's agents are in isolation booths and thus would do in any event whatever they will do.) (ii) What each agent is going to do and thus would do in any event depends upon what he thinks he ought to do. (iii) Each agent knows all this and knows that the other knows all this. Given these three things it is not easy to see how either agent could decide ~o do anything, or do anything. And yet, in the case, each will act, if only by default. And so it is good that Gibbard does not make assumptions con- cerning the moralities, psychologies, or knowledge of his agents. He makes assumptions regarding only what they will and would do, not why. The specifications for his cases are thus in no danger of being inconsistent.
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In summary, in structure I cases each agent will do the AU-right thing. namely, R. And if an RU-right act exists, then P is for each agent RU- right. Thus, if an RU-right act exists, then the possibility of structure I cases refutes (1) and (2) as well as (3). Further, if no act is RU-right, then, of course, (1) and (2) are false, though the status of (3) is unclear and will be left undetermined in this essay. Suffice it to say that, in view of the possibility of structure I social worlds, (1) and (2) are false whether or not RU-right acts exist. Since (1) constitutes one-half of Brandt's reduction thesis, the possibility of structure I worlds refutes this thesis. (Because Gibbard never doubts the existence of RU-right acts he finds it possible to state his conclusions in connection with his structure I case more simply and less guardedly than I have stated mine.)
It is perhaps natural to feel that Gibbard's first case is objectionable just because it includes assumptions concerning what agents will and would do. But this can be no objection since it is obvious that such assumptions are essential to the application of AU; without such assumptions the dictates of AU could not be determined and thus could not be compared with those of RU. Nor is it an objection that in this case it is assumed that the agents will, in any event, do the AU-right thing. RU addresses itself to all sorts of agents even such 'incorrigible' ones. Furthermore, that the agents will in any event do the AU-right thing, though a feature of the first case, is not a feature of any of the others below, some of which are equally decisive against (1) and thus Brandt's reduction thesis (though of course none tell against (2)) .
In order to refute (3) Gibbard constructs a world of the following structure:
II
Agents Relative values of outcomes.
T J
- - >
P P* 3
P* R* 1
R P 1
R* R 2
If an RU-right act exists, the RU-right act for each agent in a structure II world is P. But R would be the AU-right act .for T. Thus, if an RU-right act exists, the possibility of structure II worlds refutes (3) as well as (1). Of course, if no act is RU-right, (1) is false, though as has been said the status of (3) is unclear and will be left undetermined. Thus, given the possibility of structure II worlds, (1) is false whether or not RU-right acts exist. However, since it is neither the case that every
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action done will be RU-right (J will do R though P is the RU-right action if one exists) nor the case that every action done will be AU-right (J will do R though P would be his AU-right action), the possibility of structure II worlds does not bear on either (4) or (2). (Again since he never doubts the existence of RU-right acts, Gibbard's conclusions from his structure II case are stated categorically and more simply than mine.)
Against (4) Gibhard offers a world of the following structure:
III
Agents Relative values of outcomes.
T J
P P* 2
P* R* 1
R P 1
R* R 2 Gibbard argues that in worlds of this structure, both P and R would be RU-right: Sets of rules that call for P in such cases are in this connection unimprovable, and the same holds of sets of rules that call for R. From this Gibbard infers that in these eases, each agent will do an RU-right action. And since neither agent will do what for him would be the AU- right action, Gibbard concludes that the possibilitity of structure III worlds refutes (4).
But in fact his analysis of the significance for RU of structure III cases is unsound. It is true that RU and AU will not coincide in dictates in structure III cases, but this is not for the reasons given by Gibbard. What the possibility of structure III worlds entails is that RU has no dictates in structure I cases, but this is not for the reasons given by Gibbard. What worlds entails that no actions are RU-right, that a unique RU-ideal set of general prescriptions does not exist. This fact of course refutes Brandt's reduction thesis, which is Gibbard's primary objective, but it also shows that RU is radically defective, a fact which Gibbard fails to notice. Let us see how the possibility of structure III cases entails that no actions are RU-right.
RU supposes or presupposes that exactly one set of rules satisfies a certain condition. RU involves a reference to the set, G, of general pre- scriptions that satisfies the condition, K, that for each logically possible social world, S, if every member of S were to conform to G on each occasion of action, then the outcome would be at least as good as it would be were every member to conform on each occasion of action to some other set of general prescriptions. (Brandt's formulation involves a refer- ence to that set of general prescriptions that satisfies the above condi-
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t ion . ) lo In o rde r to de tach f rom R U a conclusion of the fo rm (where x is some ac t ion)
x is right. one needs a t rue p ropos i t ion of the form,
The set of general p rescr ip t ions that satisfies K calls for x. But if a unique set of general prescr ip t ions sat isfying K does not exist,
then no propos i t ion of this fo rm is true. A n d the poss ibi l i ty of s tructure I I I wor lds entai ls that a unique set of rules sat isfying K does no t exist. Le t C be a set of rules that satisfies K. C will cal l in s t ructure I I I wor lds e i ther for P, for R, or indifferently for e i ther P o r R. I f C cal ls for P; then, if C ' differs f rom C only in tha t C ' calls for R, C ' also satisfies K. I f C calls for R; then, if C ' differs f rom C on ly in that C ' calls for P, C ' a lso satisfies K. A n d finally, if C calls indifferent ly for e i ther P o r R ; then, if C ' differs f rom C only in tha t C ' cal ls specifically for P o r specifically for R, then C ' also satisfies K. In any case, C is no t the only set of rules that satisfies K, and so a unique set of rules sat isfying K does not exist. 11 A n d f rom this it follows that, where x is some action, no p ropos i t ion of the form,
The set of general prescr ip t ions tha t satisfies K calls for x. is true, and thus no p ropos i t ion of the form,
x is right. can be de tached f rom R U . T h a t is, no ac t ion is RU- r igh t since the R U - ideal set of rules does n o t exist.
The same conclusion can be r eached by a different argument . Cons ider w o r d W1 (see Section One a b o v e ) . Assume tha t h is tory (1 ,6 ,12 ) would have a be t te r total ou tcome than would any o the r poss ible h is tory of Wl . Le t C be an ideal set of rules: let C be a set of rules such that , for each
ao It is indeed a little strange that Brandt should in his formulation of RU employ a definifi~ reference to that set that satisfies a certain condition, K, thus requiring a unique set, and then, when stating the condition, K, require of this set only that conformity to it produce at least as much good as con- formity to any other, a condition which does not seem calculated to select exactly one set. His formulation of RU seems somewhat at cross purposes with itself. And so, though I assume that he intends the uniqueness require- ment since his formulation does. entail it, it is possible that he did not form an intention on this point. But then it is also possible that he did intend the uniqueness requirement and meant the test to be such that the 'ideal set' would be with respect to some possible societies better than and with respect to all possible societies at least as good as any other. If this test were made fully explicit in RU, the result would be an Rid more of a piece on its face. But it would still be defective in 'the way I explain in the text.
xa This e0nelusion would follow even if we were to make 'mixed' strategies avail- able to the agents. Only one case needs to be considered, the general ease: For any p (where 0 < p < 1), if C satisfies K and requires that an agent in a structure III would set himself the probability p of doing P and the pro- bability (1 - p) of doing R; then, if C' differs from C only in that C' calls Specifically for P or specifically for R, then C' also satisfies K and thus a unique se~ of rules satisfying K does not exist.
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possible social world, W, any history of W generated by general conformity by all agents at all times to C would have at least as good a total outcome as would any other possible history. C would generate history (1,6,12) in W1. Now consider: How would C resolve situation S~ in world W~? We have not said and, what is more to the point, it does not matter. If C' differs from C only in the way in which C' would resolve S~ in Wx, then since C is an ideal set of rules, so is C'. C and C' are to differ only in the way they resolve S] in W~, but S ] is a situation that does not come up to W1 if everyone at all times conforms to either C or C', and the status of a set of rules as RU-ideal is not affected by how the set of rules would handle cases that wouldn't come up were everyone always con- forming to its rules. (For example, if one of an ideal set of rules were, 'Keep promises', then it wouldn't matter what the set said about situations that arise only if promises are broken.) So, for two separate reasons, the RU-ideal set of rules does not exist and no action is RU-right. As first noticed, RU fails to take into account the fact that some rules have equally good alternatives. And this over-sight is significant: since many important systems of rules apparently contain arbitrary elements, there are in the case of many important systems of rules equally good alternative systems. This seems true, for example, of rules for traffic, contract, and property. And as just noticed, RU is indifferent with regard to those situations that would not arise were men, on its terms, always well-behaved. Again this is significant and odd. Many hard situations are created by bad-acting and rule-breaking. Some would say for example that situations that present punishment decisions are by definition created by bad-acting and rule-breaking. One expects moral theories and theorists to be concerned with such situations and to care how they are resolved.
Brandt contends that RU is a specious form of rule-utilitarianism, and indeed it is, but not for the reason he thinks. RU is specious not because it always coincides in its implications for action with AU, but because it has no implications for action at all and as a consequence never coincides with AU. It has no implications at all for action since on its terms there is no such thing as the ideal set of rules.
It is worth noting that the problem that infects RU turns up in only slightly altered form to embarrass the principle that Brandt contends pre- sents a credible form of rule-utilitarianism, viz.: an act is right if and only if it conforms with that learnable set of rules the recognition of which as morally bindingwroughly at the time of the act--by everyone in the society of the agent, except for the retention by individuals of already formed and decided moral convictions, would maximize instrinsic value. 1~
Consider a society, S, and a time, t, such that for S at t there exist equally good alternative sets of rules covering cases not covered by the
12Brandt. op. tit., p. 139.
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moral rules received in S at t, cases not covered and settled by already formed and decided moral convictions. ( I recall here only the first of the two arguments presented above to show that there is not a unique RU- ideal set of rules.) For S at t, Brandt ' s rule-utilitarianism reduces to the un- critical endorsement of the incomplete and perhaps objectionable received mora l i ty of S. For S at t, the 'utilitarianism' in Brandt 's theory drops out. A n d for S at t, his theory is incomplete in a way I believe Brandt would find objectionable. His theory would not speak to all of the cases that could arise in S at t, and in some of these not-covered cases it would matter what was done, there would be right and wrong courses of action. So, for S at t, Brandt ' s theory would be incomplete in the sense that not 'all true ethical statements [could] be deduced f rom it'. 13 R U demands a unique ideal set of rules, but there cannot be one on its terms. Brandt 's own theory makes a similar demand which for most actual societies is probably never satisfied. In fact, similar defects mar many rule-utilitar- ianisms that refer the issue of r ight action on at least some occasions to systems of ideal rules rather than systems of actual and useful rules. 1" But not every ' ideal-rule' theory suffers from this defect. The following mixed ideal-rule and act-utilitarian theory is specifically designed to avoid it:
M U : Where B is t h e intersection of those sets of rules that satisfy K, an act, x, is right for an agent if and only if x would not be in violation of B and x would have at least as good conse- quences as would any other act open to the agent that would not be in violation of B.
This mixed theory h a s implications for action provided only that sets of rules that satisfy K exist. 1~ Given the existence of such sets of rules, their
XSRiehard B. Brandt, Ethical Theory (Prentice-Hall: Englewood Cliffs, New Jersey, 1959), p. 5.
14 For the distinction between actual-rule and ideal-rule rule-utilitarianisms, see Brandt, 'Utilitarianism', section 2, and J. J. C. Smart, An Outline of a Utilitarian System of Ethics (Melbourne University Press: Melbourne, 1961), pp. 4-5.
15 It is I think important to realize that it is at least not obvious that any sets of rules satisfy K. We have seen that if at least one set satisfies K, then more than one set satisfies K. But it is possible that no set satisfies K. One might attempt to argue along the following lines for this negative conclusion: (1) Each rule in a set of rules must be statable and thus finite. (2) The set of rules to be tested by K must be finite. Here one would have to show that this restriction ought to be a part of K whether or not it is an intended part of K. (3) Every finite set of finite rules will, in at least some conceivable worlds, be improvable from the standpoint of the consequences of general con- formity: no definite set of finite rules will satisfy K. The argument here might have two parts. First one might try to show that all sets of rules containing only 'teleological' rules, such as the act-utilitarian rule, will be improvable, and that in fact as long as 'teleological' elements are present a set will be im- provable. Next one would attempt to show that given any finite set of finite
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intersection of course exists and is unique. Furthermore, this theory may be 'complete'. Since. it yields directives for all conceivable cases, it is possible that it yields all the proper ones. And finally, MU has the pos- sible virtue of not always coinciding with AU. The possibility of structure I and I I worlds, as well as certain worlds of structure IV to be described below, entails this last point. ( I f the four theses set out in Section One are changed so that they are about M U rather than RU, then the possi- bility of these several sorts of cases would refute all four theses provided only that at least one RU-ideal set of rules exists.) But I do not claim that MU has any further virtues. Nor do I claim that it is in any sense a correct normative theory. In fact I think that it is most certainly not in any sense a correct normative theory, and that it ought not to appeal either to those who seek a rule-utilitarian reform or to those (like my- self) who feel that act-utilitarianism properly formulated is in an im- portant sense correct. M U ought not to satisfy the reformists since it would have A U control in many areas in which co-ordination and rules are needed. And M U ought not, of course, to satisfy the conservatives since it does after all include an element of rule-utilitarianism and would have a n agent, x, sometimes n o t do the best action open to him (and not do it just because ideal rules call for something else, i.e., just because it would be better for everyone to do something else than for everyone to do what i t would be best for x to do) .
Social worlds can be constructed that would refute (1) and (2) even if RU-right acts existed. And if some actions were RU-right, cases exist that would refute (3 ) . On this hypothesis, structure I cases would refute all three of these theses, and structure I I cases would refute theses (1) and (3) . Finally, cases exist which, on this hypothesis, would refute (4) . I f RU-right acts existed, certain cases of structtwe IV below would refute (4) as well as (1) and (3) . (Gibbard, of course, does not address him- self to the conditional issue or present a case of the following structure.)
and non-forward-looking rules, it will always be possible to conceive of eases that call for further exceptions and refinements. The conclusion, if (1), (2), and (3) could be established, would be that no (finite) set of (finite) rules satisfies K (since any such set would be improvable).
Perhaps such an argument can be articulated and shown to be correct. If so, then ideal-rule theories including RU and Brandt's own theory are defective in a more profound way than I have maintained, and MU is also radically defective. I am inclined to think that no set of rules satisfies K, and that these further conclusions are correct, but I am not sure. This much can be said. If a theory commits itself to the existence of a unique ideal set of rules, one should examine its test for a set's being ideal to determine not only whether exactly one set satisfies it, but also whether even one set satisfies it. And the latter question is probably in most cases the more important one.
1 1 ~ r
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IV Agents T J
P P P* R R P* R* R*
Relative value of outcomes.
1 3 3 2
Structure IV cases are marked by full interchangeability of roles: 'T ' and 'J' can be interchanged without changing anything that is said of either T or J. Thus we are free to assume that T and J possess identically the same 'abstract properties' (Brandt's term).16 Let us make this assumption and confine our attention to structure IV cases in which the agents are identical with respect to 'abstract properties'. If we also assume, as Brandt would want us to, that the general prescriptions of RU must 'make no reference to individuals, but [be] concerned only with [abstract] properties, 1T then no set of general prescriptions exists general conformity with which would, in the structure IV cases in ctuestion, definitely and with certainty yield either (P ,R) or (R,P) . Sets of general prescriptions will, for these structure IV cases, have to require the same thing of each agent. Thus, if C were the set of general prescriptions that satisfies K, then C would call in structure IV cases either for P, for R, or indifferently for either P or R. (I do not assume that every set of rules will, for example, call for P 'straight out' or in a simple way. Thus, a set might contain the rule 'when in a situation of the type,
Relative value of outcomes Agents x y
P P 1 P R 3 R P 3 R R 2
do R unless the other man would do R if you did P in which case do P'. with certainty yield either (P ,R) or (R,P) . Sets of general prescriptions 'Do P'. Every set of general.rules, however complex its application to structure IV cases in which the agents are identical in all 'abstract proper- ties', will, in these cases, say to each of the two agents either 'Do P' 'Do R', or 'Do either P or R' . )
If C existed, what would C call for in the structure IV cases at issue? It is clear that C would call for P. But before the issue of whether or not C will call indifferently for either P or R can be properly addressed, several adjustments in the discussion are required. First, the numbers in the structure IV table need to be replaced by numbers which, while leaving the same order are separated by differences which are related differently:
aa Brandt, Ethical Theory, pp. 12-20. ar Brandt, Ethical Theory, p. 19. See also pp. 253-254 and 396-397.
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I V '
Agents T J
R u l e - U t i l i t a r i a n i s m
Utilities of outcomes
P e 1 P* R 10 R P* 10 R* R* 9
Second, these new numbers need to be interpreted as expressing not only the value ranks of the outcomes but their u t i l i t i e s : 8 Third, the test for ideal rules needs to be refined: I now assume, for purposes of the present structure IV discussion, that the ideal set of rules will be that set, G, of rules that satisfies the condition, K r, that for each logically possible social world, W, every member of W's conforming to G on each occasion of action would have at least as great an expected utility as would their conforming on each occasion of action to any other set of rules. (An expected utility here is the sum of the utilities of the possible outcomes weighted by their probabilities under the given hypothesis concerning what the members of W do.) It can now be shown that if C exists it will not be indifferent between P and R but will call definitely for R in the class of structure IV cases being considered. Suppose C were indifferent between P and R. Then we can assume that, given general conformity to C, P and R would each have the probability 1 /2 and the expected utility would be,
1 / 4 ( 1 ) + 1 /4 (10 ) + 1 / 4 ( 1 0 ) + 1 / 4 ( 9 ) = 30 /4 = 7½. In contrast, if C required R, then, given general conformity to C, the expected utility would be,
0 (1 ) + 0 (10) + 0 (10 ) + 1(9) = 9. It follows that C will not be indifferent between P and R. And since C will certainly not call for P, it follows that C will call for R in the structure IV worlds under consideration (namely, structure IV' worlds in which the agents are identical in 'abstract properties').19 All assuming, of course, what is not the case, that C exists and that RU-right acts exist.
If RU-right acts existed R would be RU-right in the structure IV cases in question, and so each agent would be doing the RU-right thing. Of course neither agent will do the AU-right thing. And so, if RU-right actions existed, the possibility of the indicated class of structure IV societies would refute (4) as well as (1) and (3) , assuming that the replacement of K by K' is allowed as it seems it should be. s° Since no
is For the concept of a utility measure see Luce and Raiffa, op. cit., Ch. 2. The measure developed by Luce and Raiffa is specifically a measure of rational preference; we can assume a similar measure for value or proper preference.
19This conclusion, that C (were it to exist) would call for R in structure IV' cases in which the agents are identical in 'abstract properties', would no t follow were we to make available to the agents 'mixed' strategies. See the Appendix to this section.
s0 An analogous conclusion follows even if 'mixed' strategies are available to the agents. See the Appendix to this section.
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actions are RU-right, a result entailed by the possibility of structure IH worlds, the status of (4) is, in fact, unclear, as is the status of (3).
The discussion of cases can be summarized as follows: If the RU-ideal set of rules existed, (1), (2), (3), and (4) would be refuted by the possibility of certain sorts of social worlds. Structure I cases would refute (1), (2), and ( 3 ) . Structure II cases would refute (1) and 3). And certain structure IV cases would refute (1), (3), and (4). But since the RU-ideal set of rules does not exist, a fact entailed by the possi- bility of structure III worlds, (1) and (2) are certainly false, but the status of (3) and (4) are unclear and have been left undecided.
Appendix to Section Two
Gibbard's agents must choose between 'pure' strategies: Each can either press a button or refrain from pressing it. Neither can choose to make the depression of his button dependent on some controlled chance pro- cedure. Neither can, for example, choose to make it .9 probable that his button will be depressed. They can make depression a certainty or give it no chance at all; they cannot hedge. Since their choices are restricted in this way, the rules that speak to their situations are similarly restricted and can either order P, or R, or either P or R. The restriction to 'pure' strategies is natural and corresponds to usual real-life conditions: we seldom are in fact able to tie our actions irrevocably to chance devices. In the text of Section Two, I followed Gibbard and assumed the same restriction. However, since 'mixed' strategies are of interest in general game theory, and since it can at least be argued that under certain con- ditions reasonable men would, if they could, employ 'mixed' strategies, I will now consider certain consequences of making all 'mixed' strategies available, where a mixed strategy is a course of action (e.g., the spi~nlng of a pointer wired to the button) that results in a probability assignment to each member of an antecedently specified set of actions or strategies, the probabilities assigned summing to 1. (Note that if 0 and 1 count as probability assignments then a pure strategy can be viewed as a special mixed strategy in which the probability assigned to each except one of the antecedently specified strategie~ is 0. When the distinction amongst types of mixed strategies is important I will from now on speak of pure as opposed to non-pure strategies.) In what follows I consider the effects in only two connections of admitting all mixed strategies. Two conclusions drawn in Section Two are re-examined: the first no longer holds when mixed strategies are admitted, but an analogue of the second does still hold. Both conclusions concern a class of type IV cases.
The First Conclusion. 'If a unique set, C, of general prescriptions were to exist that satisfied the condition, K', that for each logically possible social world, W, every member of W's conforming to C on each occasion of action would have at least as great an expected utility as would their conforming on each occasion of action to any other set of general pre- scriptions; then C would call for R in structure IV' worlds in which the
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agents were identical in abstract properties'. Once we make available to agents all mixed strategies, this conclusion can no longer be drawn: C no longer calls for R in these IV' cases. Nor would C call for R in any type IV case. This general negative result is most readily reached if we first replace the utility numbers in the type IV' table with variables standing for any utility numbers related in order as are 1, 3, 3, and 2, (the num- bers in the original ordinal table for type IV cases):
IV Agents Utilities of outcomes. T J
P P a P * R b a < c < b R P* b
> R* R* c Assuming general conformity with rules requiring each agent to set him. self the probability x of doing P and ( l -x) of doing R, and letting U be the expected utility,
U : ax 2 + b x ( 1 - - x ) + b(1 - - x ) x + c ( 1 - - x ) 2.
Simplifying, U : ( a - - 2 b + c)x ~ + ( 2 b - - 2 c ) x + c
U is a single-peaked function. Since, dU/dx = 2 ( a - 2b + c)x + ( 2 b - 2c),
U is maximum where, c - - b
X = a - - 2 b + c
And since, c - - b < 0 , a - - 2 b + c < 0, and a - - 2 b + c < c - - b ,
it follows that c - - b
0 < < .1. a - - 2 b + c
Thus, assuming the availability of mixed strategies, the set, C, of rules that satisfies K' (were C to exist), in structure IV societies in which the agents are identical .in 'abstract properties', would not call for R but instead would call for the mixed strategy, M, (c_u
a - - 2 b + c ' a - - 2 b + C
where the first term gives the probability for P and the second term the probability for R. As I have shown, neither of these probabilities will be equal to zero. In particular, the first probability would not be equal to zero and so C would not call for R.
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The Second Conclusion. 'If RU-right actions existed, then the possi- bility of structure IV' social worlds in which the agents are identical in abstract properties would refute (4) as well as (1) and (3), assuming that the replacement of K by K' is allowed'. The possibility of structure IV' cases is not now relevant to (4) : in all structure IV cases everyone will do R, but (4) is about cases in which everyone does the RU-right thing, and now, with the admission of all mixed strategies, the RU-thing is M rather than R. So the 'second conclusion' no longer follows. But an analogue of it does follow. It concerns a slightly different structure, and the argument requires a certain natural adjustment or refinement in AU. Here is the new AU:
AU: An act is right for an agent if and only if its expected utility would be at least as great as that of any other act open to the agent.
Consider first a new structure that would not refute (4). This structure is exactly like IV' except that each agent instead of doing R will employ the mixed strategy M1 no matter what the other agent does, where Mx is the strategy,
( 9 - - 1 0 9 - - 1 0 ) 1 - - 2 0 + 9 , 1 - - 1 - - 2 0 + 9
or more simply,
Were an RU-right act to exist, structure. (For the formula for
1 9 ) . 10 ' 10
M1 would be RU-right in cases of this Mx see the discussion above of the 'first
conclusion'.) In worlds of this structure, M1 will also be AU-right for each agent. In fact, in societies of this structure, every strategy will be AU-right for each agent: given that the other agent will in any event do M , it does not matter from the point of view of AU what a given agent does, Thus, were an RU-right act to exist, since M1 would be RU-right, though RU and AU would not coincide in their implications for action in these worlds, they would not be in full conflict. These worlds would not falsify (4) nor (3), though they do falsify (1). But consider the following structure and assume again that the agents are identical in 'abstract properties'.
V Agents
T J
P P P* R* R * P* R R
Utilities of outcomes
1 10 10 9
1 6 2
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Assume as part of the structure the following: (i) Each will employ M1. (ii) Each would employ the pure strategy R were the other to
employ the pure strategy P, and P were the other to em- ploy R. (This information is conveyed by the asterisks.)
(iii) Each would employ M1 were the other to employ any non-pure strategy.
(Note that the actions of T and J are here not completely independent. We could suppose that they can watch each other, that they are RU-men, but not very conscientious and inclined to back-slide into AU, that they are not very clever when it comes to figuring things out about mixed strategies and expected utilities, and that they know, perhaps they have been told, that M1 is the RU-right strategy and that it is in a sense the best non-pure strategy.)
In a structure V world, were some act RU-ldght, M1 would be RU-right. But the AU-right acts for each man would be P and R. The expected utility of each of these strategies for T as well as for J is 10. For example, the expected utility of P for T is 10, for P would be answered by J with R. Clearly an expected utility of 10 cannot, in the case, be improved upon. So P and R are AU-right acts. What is more, P and R are the only AU-right acts. In particular, and this is all that needs to be seen, M1 is not AU-right: the expected utility of M~'for T as well as for J is 9 ~ since Mi would be answered by M1. Thus, in a structure V world, were some act RU-right, then since M~ would be the RU-right act, each agent would do the RU-right act though neither would do an AU-right act. Each will do M~ though the AU-right acts for each are P and R. The possibility of structure V worlds would (if some acts were RU-right) refute (4) as well as (1) and (3) (assuming of course the adjustments in RU and AU that introduce and make crucial expected utilities).
Section Three
RU and AU do not coincide in their implications for action. Since RU has no implications for action, these doctrines never coincide in their implications for action. And even if RU had implications for action, these doctrines would not always coincide in their implications for action. And that they wouldn't becomes the expected condition once it is noted that, while what other agents would do under various iiypotheses concern- ing what a given agent does is of relevance to the dictates of AU, such facts are always and necessarily irrelevant to the dictates of RU. In the language of the diagrammed structures, while both the asterisks and the numbers matter to AU only the numbers are significant for the application of RU. Brandt's reduction thesis is in error and would be in error even if the rule-utilitarianism under attack were not specious because vacuous;
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his thesis would be false even if it were about MU (which need not be vacuous even though RU is vacuous). What remains is to analyze the argument that leads Brandt to his reduction thesis in order that the initial plausibility of this thesis may be effectively explained away.
Brandt's argument is short, direct, and rests on an equivocation of a type endemic to contemporary discussions of utilitarianisms. He begins with the premise,
Q: If everyone always did the very best thing it was possible for him to do, the total intrinsic value produced would be at a maximum. 21
We note that it is true that if everyone always conformed to the act- utilitarian rule, viz.,
Perform an act, among those open to you, which will have at least as good consequences as any other.
then everyone would always do one of the best things it was possible for him to do. Relying on this truth, and ignoring the shift from 'one of the very best' in its consequent to 'the very best' in the antecedent of Q, Bran& deduces,
T: If everyone always conformed to the act-utilitarian rule, the total intrinsic value produced would be at a maximum.
And from T Brandt concludes that the set of general prescriptions, general conformity with which in each logically possible society would have at least as good consequences as would general conformity with any other set of general prescriptions, will either contain as its only member the act- utilitarian rule or will have identically the same implications for action as this rule.
But Q and T are both in a certain way ambiguous. Let us first make T explicit and unambiguous.
Tx: For each logically possible social world, general conformity with the act-utilitarian rule would have at least as good an outcome as would general conformity with any other rule (or set of rules).
T1 is what needs to be established if RU is to be reduced, as Brandt intends it to be, to AU. And T1 is supposed to follow from Q which in turn is supposed to be tautologically true. In fact, however, even if we adjust O so that contact with T is made (this can be done by replacing 'the very best thing' by 'one of the very best things'), the result, Q', is ambiguous between,
Qq: For each logically possible social world, a history in which each member at each moment of action did one of the best actions open to him would have at least as good an outcome as would any other history.
21 Brandt, 'Utilitarianism', p. 121.
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Q'2: For each logically possible social world, each member, A, and each moment of action, M, if A at M did one of the best actions open to him, then the outcome of A's doing this action would be at least as good as would be the outcome of his doing any other action.
Q' is ambiguous between a propostion, Q'I, about the outcomes of general conformities to the act-utilitarian rules, and a proposition, Q'~, about the outcomes of individual conformities to the act-utilitarian rules. Q'~ is of course true but of no relevance to T1. Q'I entails T1, but Q'~ is false; its falsity is entailed by the possibility of structure I worlds, which possi- bility of course also entails the falsity of T1. T1 cannot be established by deduction from Q' (or in any other way, since T1 is false), but the ambiguity in Q' just noted can help to generate a contrary appearance and is, I believe, the main source of Brandt's error.
University o/California, Los Angeles
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