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Straight Versus Constrained Maximization

Published online by Cambridge University Press:  01 January 2020

Jordan Howard Sobel
Jordan Howard Sobel*
Affiliation:
Scarborough College, University of Toronto, Scarborough, ON, Canada, M1C 1A4
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Extract

David Gauthier stages a competition between two arguments, each of which purports to decide once for all transparent agents which is best, being a straight or being a constrained maximizer. The first argument, which he criticizes and rejects, is for the greater utility, on a certain weak assumption, of straight maximization for all transparent agents. The second, which he endorses, is for the greater utility on the same weak assumption of constrained maximization for all transparent agents.

In Section I, Gauthier’s account of constrained maximization is presented, and his use in the two arguments of the idea of choosing a disposition to choose actions is noted. Section II is about the unfortunate argument that Gauthier criticizes. This argument is flawed in ways additional to those he notices, but a less ambitious form of reasoning can, for individuals whose probabilities and values are right, be good for the greater expected utility of straight maximization. Section III takes up the argument that Gauthier endorses and maintains that it is wrong in a way specific to it as well as in ways closely related to all of the first argument’s noted flaws. An Appendix features a three-person prisoners’ dilemma and includes demonstrations of principal conclusions reached in the body of this paper.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 23 , Issue 1 , March 1993 , pp. 25 - 54
Copyright
Copyright © The Authors 1987

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References

1 The stated issue is how best to choose in strategic contexts in which the actor takes himself to be one centre of action amongst others, ‘so that his choice must be responsive to his expectations of others’ choices, while their choices are similarly responsive to their expectations’ (MA 21). Straight maximizing is said to be ‘uncontroversially utility-maximizing’ (MC 90; MA 183) and best for parametric contexts in which the actor takes himself to be the sole centre of action, and regards ‘the actions of others as fixed circumstances’ (MA 85).

I will for the most part ignore this difficult distinction. I will not press, for example, that as drawn on MA 21, it makes prisoners’ dilemmas, though paradigmatic for Gauthier of problems that constrained maximization would meliorate, parametric contexts for their agents if they are straight maximizers. Confessing strongly dominates in a prisoners’ dilemma, and actions are certainly causally independent. So straight maximizers in a prisoners’ dilemma can identify confessing as utility-maximizing and choose without regard to their expectations concerning choices of other agents. Sobel, Cf. ‘Maximizing, Optimizing, and Prospering,’ Dialogue 27 (1988) 233-62CrossRefGoogle Scholar, at 250, n. 10. Perhaps Gauthier would say that though they are parametric contexts for straight maximizers, prisoners’ dilemmas are strategic contexts for constrained maximizers.

Page references to Gauthier’s ‘Maximization Constrained: The Rationality of Cooperation’ (in Campbell, R. and Sowden, L. eds., Paradoxes of Rationality and Cooperation: Prisoner’s Dilemma and Newcomb’s Problem [Vancouver: University of British Columbia Press 1985] 75-93Google Scholar) will be indicated by MC followed by the page number; references to Gautier’s Morals by Agreement (Oxford: Oxford University Press 1986) will be indicated by MA followed by the page number. The material in MC is from ‘ch. 6, sections 2 and 3 [of Morals by Agreement] with revisions made by David Gauthier’ (MC 75). Passages that appear in both texts seldom differ, but when they do, quotations are from MC.

2 I will not pursue my opposition to this underlying requirement, which expresses Gauthier’s pragmatism regarding rational choosing-dispositions. I will not repeat objections to the ideas that necessarily a choosing-disposition is rational for an individual if and only his having it is utility-maximizing (see my ‘Maximizing, Optimizing, and Prospering’), or his choosing it would be utility-maximizing (see my ‘Interaction Problems for Utility Maximizers,’ Canadian Journal of Philosophy 4 [1975]677-88). My focus is not on claims that straight and constrained maximization are rational, but on claims that they are utility-maximizing. Let me record, however, without developing it, my opposition to Duncan Macintosh’s related pragmatism regarding rational preferences (’Preference’s Progress: Rational Self-Alteration and the Rationality of Morality,’ Dialogue 30 [1991], at 4 & 10). Preferences, just as credences (pace William James), are rational, in my view, if and only if, during ideally exhaustive reflection exclusively upon their terms and objects, and not also on consequences of one’s having them, they would eventually be stable. I think, for example, that a desire for wealth can be rational for a person, even if this person is sure that only those who do not want it gain it. For even such a person might well want wealth for what it is and makes possible, and continue to want it no matter how long he thought about just it and what goes with it, as distinct and apart from what goes with wanting it. For any given credence or preference the issue whether or not it is rational, is distinct from the issue whether or not, supposing that one has a choice, maintaining it, or cultivating it, is rational.

3 This may not be Gauthier’s current position. He writes in continuation of the passage just quoted that the idea of a person’s choosing his conception of rationality or his choosing-disposition ‘invites further exploration’ (5). He may now be disposed to use this idea not merely as a heuristic device, but again quite literally in discussions of the merits of competing conceptions.

4 Straight and constrained maximization would yield different behavior for an individual in a situation if and only if: either this individual will be a straight maximizer in this situation and will do a certain thing, and if he were a constrained maximizer in this situation then he would do an incompatible thing; or he will be a constrained maximizer in this situation and he will do a certain thing, and if he were a straight maximizer in this situation he would do an incompatible thing.

5 The argument turns out to be about not only all expected situations in which the two dispositions would yield different behavior, but about all expected situations in which they could yield different behavior. It is about every situations such that either I will in s expect the others to base their actions on a joint strategy and the two dispositions would yield different behavior, or I will in s expect the others to base their actions on individual strategies, and the two dispositions would yield different behavior if I were ins expecting the others to base their actions on a joint strategy.

6 This point cuts through a nerve of Gauthier’s announced methodology. He writes that:

To demonstrate the rationality of suitably constrained maximization …. we consider what a rational individual would choose, given the alternatives of adopting straightforward … and … constrained maximization, as his disposition for strategic behavior …. Taking others’ dispositions as fixed, the individual reasons parametrically to his own best disposition (MC 81; MA 171).

And he reports that:

We have defended the rationality of constrained maximization as a disposition to choose by showing that it would be rationally chosen. Now this argument is not circular; constrained maximization is a disposition for strategic choice that would be parametrically chosen (MC 90; MA 183).

But, I am now asking, what if, as may be, an agent sees dispositions of certain other agents as not fixed independently of his own? What if he does not take his choice of a choosing-disposition for strategic behavior ‘to be the sole variable in a fixed environment’ of such choosing-dispositions? (MA 21)

7 As it happens, 3.5 is also Column’s expected utility for the interaction of individual strategies in which Row uses his pure strategy ∼ C, and Column uses his mixed strategy (1/2 C, 1/2 ∼ C).

8 Bargaining theories are framed for situations in which cooperative surpluses, benefits from agreements, are envisioned. Some reconceptualization, or at least relabeling, is needed for situations devoid of potential profit and gain, situations in which agreed cooperation can only minimize losses. In such situations not all parties, perhaps no parties, can by an agreement take away from the table as much as they bring to it. To adapt Gauthier’s theory to these ‘down-scaling’ problems, one is tempted to assign to what parties, for example, labor and management, ‘bring to the table’ the rôles of his ‘initial claims,’ and to take (as usual) for ‘initial bargaining positions’ no-agreement expected utilities (e.g., for plant-closures, and losses of jobs all round).

9 It is thus false that: ‘Failing to exclude straightforward maximizers from the benefits of cooperative arrangements … ensures that the arrangements will prove ineffective, so that there are no benefits to share’ (MC 88; MA 180).

10 Not so for Row or for Column. Consider Row. His expected utility for basing his action on the cooperative outcome ( ∼C,∼C,∼C), given that Column will do that and Level will do C, is 3. What if Row were a straight maximizer? Then he would do C; doing C being strongly dominant and actions being certainly causally independent, doing C would maximize. Column would also do C. Since Column would be sure that both Row and Level were doing C, Column’s expected utility for basing his own action on the cooperative outcome and doing ∼C would be 1. That is less than his expected utility 2 for the free-for-all outcome (C,C,C). Condition (ii) of the rule for constrained maximization would not be satisfied for Column, and he would ‘behave as a straightforward maximizer’ (MC 80; MA 169) — he would do C. Therefore, were Row a straight maximizer he would doC along with not only Level but also Column. Row’s expected utility for straight maximization is thus 2, which is less than his expected utility 3 for constrained maximization. And this even though, under the current interpretation of constrained maximization, straight maximizers are not excluded from terms of agreements and cooperative arrangements.

11 Our world-case features a mixed population, one straight maximizer and two constrained maximizers. The reader might be interested in verifying that most of our conclusions could have been based on a case like this one except that all agents are constrained maximizers who will not confess.

12 I am grateful to Richmond Campbell, David Gauthier, Duncan Macintosh, Wlodzimierz Rabinowicz, Willa Freeman Sobel, and to readers and an editor for comments and criticisms.