Are Plans Necessary?

Are Plans Necessary?Author(s): Michael McDermottSource: Philosophical Studies: An International Journal for Philosophy in the AnalyticTradition, Vol. 138, No. 2 (Mar., 2008), pp. 225-232Published by: SpringerStable URL: http://www.jstor.org/stable/40208870 .

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Philos Stud (2008) 138:225-232 DOI 10.1007/sl 1098-006-9033-4

ORIGINAL PAPER

Are Plans Necessary?

Michael McDermott

Received: 25 April 2006 / Accepted: 26 June 2006 /Published online: 30 August 2006 © Springer Science+Business Media B.V. 2006

Abstract According to classical decision theory, an agent realises at time t the option with maximum expected utility (determined by his beliefs and desires at f), where the relevant options are possible actions performed at f. I consider an alternative according to which the relevant options are in general plans, complex courses of action extending into the future.

Keywords Decision theory • Options

Decision theory typically concerns itself, as Pollock has recently noted (2003, 2005), with actions, which are to be performed "now". But, Pollock complains, deliberation takes time, so the actions must be at least a little bit in the future. So wouldn't it be better to face up to this fact and consider the issues that arise when the actions are definitely in the future - even far in the future? Or (while we are about it) when we have to choose between complex courses of action spread out over a range of future times?

Pollock's conception of the aims of decision theory, and the rules of the game, is not everyone's. He appeals pretty frequently and uncritically to the common-sense metaphysics of the mental. He assumes that there are such mental acts as deliber- ating, considering, deciding and so forth, and that the aim of decision theory is to give good advice on how to go about the performance of these mental acts. He attaches great importance to certain common-sense "facts" about the mind, such as the fact that we cannot consider a very large number of alternative actions, or attend to all the logical consequences of our beliefs.

Some of us are more interested in decision theory as part of a response to scep- ticism about the mental. The project is to show that folk psychology, or central parts of it, can be reconstructed as a properly empirical theory, explaining and predicting observable behaviour by positing currently unobservable states and events. Each such posit would need to be justified by its contribution to the explanatory power

M. McDermott (E3) Department of Philosophy, University of Sydney, Sydney NSW 2006, Australia e-mail: [email protected]

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and systematic virtues of the theory as a whole. The project is not yet very far advanced. The most promising candidates for initial positing seem to be, roughly speaking, beliefs and desires. We have the glimmerings of an idea of some general principles by which observable interactions between subject and environment could affect beliefs and desires, and by which beliefs and desires could jointly cause observable behaviour. The last is where decision theory comes in. The glimmering of an idea is that people act pretty much as it is rational to act, given their beliefs and desires. The main thing on the agenda at the moment is to develop these hints and see how much real explanatory work a theory of beliefs and desires can do. Even- tually we may be able to see whether deciding, willing, intending and so on are reducible to belief and desire, and if not, whether that shows a deficiency in the framework of beliefs and desires, or a deficiency in those further concepts. For the time being, we shall simply refrain from assuming anything mental beyond beliefs and desires. At this early stage our discussion will naturally be highly schematic and over-simplified; illustrations from real life must be taken with a grain of salt.

I want to consider the question of future actions from this rather uncommon- sensical standpoint.

It seems clear that a man's beliefs and desires today cannot directly affect his behaviour tomorrow. If they affect his behaviour tomorrow at all, it is because they affect his beliefs and desires tomorrow. The step in the causal chain where we go from mental states to behaviour must be a step to current behaviour. Then how can options which can only be realised later possibly be relevant? The idea I want to explore is that current behaviour might be explained by its being part of a plan which extends into the future. Why does John buy a book today? Because the plan 'Buy the book today and read it tomorrow' seems good to John - better than its competitors.

Beginning with Lewis's causal decision theory (1981), I develop a framework which allows for the admission of plans. I then argue that we can just as well do without them.

1

Classical decision theory says that an agent realises an option which has at least as much expected utility as any other option. For short: he realises the option with maximum expected utility.

The agent's options are propositions which he "can act at will" to make true. They are understood to be his narrowest options: there cannot be two ways of realising an option A which have different consequences.

What is expected utility? The agent divides his credence between various dependency hypotheses. A dependency hypothesis K is a complete account of "how the things he cares about do and do not depend causally on his present actions."1 He assigns a value V(W) to each possible world W, determining a credence-weighted expected value V(A^ for every proposition X. Then the expected utility of the option A is given by

\J(A) = I/c(Credence (K). V(AK)).

1 The restriction to things he cares about may be dropped without affecting anything important (as Lewis notes), and for simplicity I shall do so.

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It is plausible to suppose that for any option A, a dependency hypothesis must entail AO-+W for some world W. (That is, Conditional Excluded Middle holds for options: for any option A, and for any proposition X, a dependency hypothesis entails either A\J->X or AD-> not-X) Lewis, however, thinks that rational inde- terminists often give no credence to any such dependency hypotheses: even though a dependency hypothesis is a complete account of how things depend on the agent's narrowest options, >4D-> X and AD-^not-X may both be false if the link between A and X is chancy. He assumes only that for any option A and world W a dependency hypothesis must entail AD-> Chance (W) = q for some q. I think Lewis is wrong about this,2 and will proceed on the simpler assumption. If you agree with Lewis, regard what follows as being about the psychology of convinced determinists. The way to build chance back in will be obvious enough.

Given our assumption, we have

\J(A) = lyy (Credence (AO-*W) . V(W)).

Now if options are to include plans extending into the future, the first thing that must be changed is the basic principle connecting belief and desire to action. In general, an agent realises the current part of the option with maximum expected utility. What else must be changed?

The agent's options were said to be propositions, which he "can" act at will to make true. Is the present tense appropriate, or should it now be 'can, or will be able to'? Let us keep it in the present, to emphasise that our topic is his options now, leaving it open that he might have new options tomorrow.

A more important question is whether the relevant notion of possibility is to be

objective or subjective. Is it a matter of what the agent really can do, or of what he thinks he can do? If future actions can be parts of options, there seems to be good reason to make the notion subjective. Suppose that John will actually die tonight (although John gives no credence to this proposition). That does not seem to be relevant to our explanation of his present behaviour. He buys the book because he thinks that buying it today and reading it tomorrow is possible.

It seems, indeed, that an agent must be certain that a plan is possible, for it to be

among his options. Suppose John does give some credence to the hypothesis that he will die tonight. On that hypothesis, what should he believe about the consequences of the plan? If the agent is not certain that a plan is possible, it seems to have no determinate expected utility.3 So I shall assume that an agent is certain that each of his options is possible.

Assuming that X\3-+Y implies that Y is possible if X is, a dependency hypothesis implies that many further propositions are possible. The agent's beliefs about these further possibilities can fall short of certainty. If John gives some small credence to the hypothesis that his buying the book would please its author, and is certain that

buying it is possible, he may give some small credence to the proposition that

pleasing the author is possible.

2 McDermott (1999). 3 We might get a determinate expected utility by looking at consequences given possibility (as Pollock seems to do), but then rational action would be affected by likelihood of possibility, as well as expected utility.

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If options must be certainly possible, they must sometimes be partly conditional. In the case where John suspects he may die, the partly conditional plan 'Buy the book today and read it tomorrow if I'm still alive' can still be an option. Assuming that John is certain that if he is alive he will be aware of that fact, he can be certain that the realisation of this plan is possible. And its realisation has determinate consequences on each of the hypotheses 'I die' and 'I don't die'. There seems to be no reason why the conditional element in the plan need be anything other than d, and hence no reason to doubt that it has a determinate truth value on the hypothesis 'I die'. If, having bought the book, John dies in the night, the plan will be effortlessly realised. (So will the plan 'Buy the book today and eat it tomorrow if I'm still alive'. These are different options - they have different consequences on some dependency hypotheses - but they can be realised together. Lewis assumed that an agent's options are a partition - exactly one of them must be realized - but if options can be future we should make that at least one.)

The concept of possibility we want is that of something which is within the agent's power; it will be realised if he chooses appropriately; it is true on one of his options. I use OX to mean that X is possible in this sense. DX =df not O not-A" - X is true on every option.

We now have two modal concepts which we are ascribing to agents: possibility, and the counterfactual conditional. We can get along with just the first, I think. We have assumed that a dependency hypothesis entails, for each option A, exactly one counterfactual of the form AD-^W. We may assume, further, that it entails no further counterfactual information: a dependency hypothesis says how things depend causally on the agent's current options. But A\3r*W appears to be equivalent to (A^W). For, suppose AD- W - W is true on the option on which the agent does A; then, on every option, either not-A or W. Conversely, suppose that Az>W is true on every option; then it is true in particular on the option on which he does A, and hence so is W.

2

Given this shared framework, let us say that a Classical theorist is one who confines options to present actions, while a Planning theorist does not. The question now is whether the Planning theory has any additional explanatory power.

We cannot hope to maintain that an agent always acts with no thought to his possible future actions. But that does not show that he needs plans. If an agent's options are wholly in the present, he can still be moved by his beliefs about his future actions, as with any other future events, qua consequences of his present actions.

Consider the simplest case: John buys the book today (with no thought that he might die in the night); it is agreed that he would not buy it but for the value he places on reading it tomorrow (or on the consequences of reading it). That is all the Planning theorist needs: John has three options - Buy & Read, Buy & not-Read, not-Buy; the one with maximum expected utility is Buy & Read; so he buys. But with one more fact about John, the Classical theorist can also explain the behaviour. He ascribes to John a belief that he would read the book if he bought it. His explanation then is that of John's two options, Buy and not-Buy, the first has greater expected utility, so he buys.

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If John is certain that he would read the book if he bought it, then U(Buy), as calculated by the Classical theory, is equal to U(Buy & Read), as calculated by the Planning theory. In general, the Classical theory will make the same predictions of behaviour as the Planning theory whenever the following condition holds:

(C) The agent is certain that his future actions would maximise expected utility. However, there are cases in which the agent clearly is not certain of any such

thing. And in some such cases it may seem that there is rational behaviour which can only be explained by the Planning theory.

Consider the following variant of the case of John. The Classical theorist and the Planning theorist both accept the following:

Credence ( ((Buy & Read => W10) & (Buy & not-Read z>Wi) & (not-Buy z> W9))) = 1; V(W10) = 10, V(WX) = 1, V(W9) = 9.

According to the Classical theory, John has two options, Buy and not-Buy. Let Credence (D(Buy => Read)) = r. Then Credence ( (Buy z> not-Read)) = 1 - r. So Credence (D(Buy d Wl0)) = r and Credence (D(Buy z> Wt)) = 1 - r. So U(Buy) = 9r+l. Also U(not-Buy) = 9. So he buys the book iff r > 8/9. But (let us suppose) we have reason to believe that r is low - below 1/2, say. Although John thinks that buying and reading would be better than buying and not reading, he has sufficient insight into his own character to think that he would probably fail to read, if he bought.

If John does not buy the book, well and good for the Classical theory. Well and good also for the Planning theory. It has scope to treat future actions as parts of current options, but does not have to do so, so it can just agree with the Classical explanation in this case.

But if John does buy the book, the Classical theory seems to be in trouble. His behaviour seems to be explicable only on the Planning theory: its three-option explanation still applies.4

As an argument to show that we need the Planning theory, this leaves some-

thing to be desired. Is the behaviour that only the Planning theory can explain clearly rational behaviour? We need not pursue this question, however, because there is a more fundamental weakness in the argument. We supposed that we have reason to believe that r is low - reason acceptable on the Classical theory. (On the

three-option Planning explanation, of course, r = 0, since Buy & not-Read is one of the options.) What could the reason be?

One possibility is that John has often in the past bought books and failed to read them, so he has good reason to give low credence to Buy z> Read, and hence to D(Buy 3 Read). But it would still be reasonable for the Classical theorist to

argue that John's current behaviour shows that his credence is higher than his

4 Hammond (1976, 1988) discusses a case analogous to an extreme version of our present case -

John is certain that he would not read the book. Hammond's interest is in "Consequentialism", a normative doctrine which would advise John to buy the book and read it. (Hammond's case involves an agent whose options are, in descending order of value, (i) take one taste of a drug, decline further offers, (ii) abstain completely, (iii) take one taste, then another,...; but he is certain that if he took one taste he would not decline further offers. Hammond says the agent fears addiction, which

suggests that (i) is not an option; but that is not Hammond's intention.) Our case is similar also to Jackson and Pargetter's case of Procrastinate (1986). They defend "Actualism", which says that an

agent objectively ought to do A if A has greater utility that what the agent would do if he did not do A. On their view, if John really would not read the book if he bought it, it is true that he should not

buy it, and also that he should buy it and read it.

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evidence warrants: given the agreed facts, his buying the book shows that he thinks it probable, despite the evidence, that D(Buy 3 Read).

Could there be evidence that r is low from current behaviour, say betting behaviour? Can we suppose that John would bet on the proposition (Buy z> Read) only at favourable odds? But D(Buy 3 Read) is a modal proposition; how could John bet on it at all? Perhaps like this: as soon as he has bought the book, he bets that he will read it. Suppose John is offered such a bet. He gave, and presumably still gives, credence r to D (Buy 3 Read) and credence 1-r to (Buy 3 not-Read). He is certain that he has just bought the book, and can't change that fact: Credence ( Buy) = 1. So presumably Credence ( Read) = r and Credence ( not- Read) = 1 - r, so Credence (Read) = r, so the odds at which he is just prepared to bet on Read should give us r. So let us suppose that John declines an even-money bet on the proposition Read; doesn't that show that r < 1/2?

Well, there is a hitch. Perhaps John gives some credence to the proposition that his reading the book is causally dependent on whether he bets.5 Therefore Credence (D(Buy 3 Read)) may no longer be r, now that John's options are Bet and not-Bet, rather than Buy and not-Buy. (The '' refers to John's current options.) And Cre- dence ( (Buy 3 not-Read)) may no longer be 1 - r. So we cannot be sure that Credence (Read) = r. Moreover, even if Credence (Read) is equal to r, we cannot assume that John's preparedness to bet on Read depends on Credence (Read). In general, the credence relevant to a bet on X is Credence (D(Bet 3 Win)); this equals Credence (X) only if the agent is sure that the truth of X is not dependent on whether he bets.

However, it would be implausible for the Classical theorist to argue that John thinks he would be less likely to read the book if he bet on Read. And if Credence (D(Bet 3 Read)) now (relevant options Bet and not-Bet) is even as big as Credence ( (Buy 3 Read)) was before (relevant options Buy and not-Buy), it would seem impossible to explain John's declining the bet. So the hitch does not seem to help the Classical theorist.

Or perhaps we can avoid the problem by stipulating that John is certain that he will have no memory of the bet tomorrow, and hence certain that his reading is not dependent on his betting. Or by stipulating that the stakes are too small to affect his reading. Or ...

So the Classical theorist does seem to be in trouble. The case is: John buys the book; but, offered an even-money bet on the proposition that he will read the book, he declines. This behaviour does not seem to be explicable on the Classical theory.

But, I reply, it is not explicable on the Planning theory either. According to the Planning theory, John will bet on Read, at any odds! For since both Buy & Read and Buy & not-Read were certainly possible (according to the Planning theory explanation), his buying the book did not close off the options of reading and not reading; so when offered the bet, he has four options - Bet & Read, Bet & not-Read, not-Bet

5 This would seem to be a possibility even if John always knew that he would be offered the bet if he bought the book.

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Philos Stud (2008) 138:225-232 231

& Read, not-Bet & not-Read; and of these the first is clearly the best - it has all the advantages of Read over not-Read, plus his winnings from the bet.6

So both sides should agree that the described behaviour is incoherent: the case does not discriminate.

To show that we need the Planning theory, we need a case in which a rational agent acts in a way which will maximise utility only if his future actions cooperate, but it is clear, on the Classical view, that he is not certain, or near enough to certain, that his future actions will cooperate. The problem is to find a case where this really is clear. The only remaining possibility appears to be to make the agent lack certainty because of conceptual poverty. Consider a chicken who crosses a road, at substantial cost, because she is thirsty and sees water on the other side. She assigns an expected utility of 10 to crossing and drinking, 1 to crossing and not drinking, 9 to not crossing. According to the Planning theory, she crosses because crossing is the current part of the best plan; no problem. According to the Classical theory, however, she crosses because the expected utility of crossing is greater than that of not crossing. The expected utility of crossing will be high enough if she assigns high enough credence to the proposition that she would actually drink if she crossed. But, lacking any knowledge of chook psychology, she seems to be in no position to predict her own behaviour. Even induction from her past behaviour seems to be impossible: how can she know that she has often drunk when thirsty in the past, when she lacks the psychological concept of thirst? And yet crossing the road seems, in the circumstances, to be a perfectly reasonable thing for a chicken to do.

I suggest, in reply, that condition (C) is true for agents without psychological knowledge. The belief that you will utility-maximise is a natural belief. It does not have to be based on evidence, or on a psychological theory.

When I say "the belief that you will utility-maximise" I do not mean to suggest that the chicken has the concept of utility. What she thinks is "I will drink if I cross", not "I will do what maximises utility."

Although this belief has, perhaps, no "cognitive" explanation (it is not obtained by reasoning, anyway), its presence need not be seen as miraculous. All the facts which make Drink the proposition with maximum expected utility, given Cross, are in the chicken's mind, after all. If there is a mechanism which reliably produces the action which has maximum expected utility, there could be a mechanism which reliably produces the belief 'I would do X when X is, as a matter of fact, the action which has maximum expected utility.

So the psychology of creatures without psychological concepts does not seem to require plans, either. Pending possible further considerations to the contrary, then, it seems simplest to stick with the Classical theory: an agent's options are wholly in the present; even those possible actions that may be options for him in the future are, for the present, seen merely as possible consequences of his present actions.

6 Spohn (1977) showed that the traditional equation between Credence (X) and fair betting quotient

gives no determinate value for events currently within the agent's control: his willingness to bet on such an event is determined by the potential gain, irrespective of the odds. Spohn inferred that Credence (X) then has no meaning. Levi (1991) agrees. Rabinowicz (2002) suggests that Credence (X) might still get meaning from some more subtle link to behaviour; but his particular suggestion depends on some other credences being indeterminate. For the purposes of this paper, we need not decide whether act credences are determinate or not.

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References

Hammond, P. (1976). Changing tastes and coherent dynamic choice. Review of Economic Studies, 43, 159-173.

Hammond, P. (1988). Consequentialist foundations for expected utility. Theory and Decision, 25, 25-78.

Jackson, F., & Pargetter, J. (1986). Oughts, options, and actualism. Philosophical Review, 95, 233-255.

Levi, I. (1991). Consequentialism and sequential choice. In Bacharach M., & Hurley S. (eds.), Foundations of decision theory, Oxford: Black well, pp. 92-122.

Lewis, D. (1981). Causal decision theory. Australasian Journal of Philosophy, 59, 5-30. McDermott, M. (1999). Counterfactuals and access points. Mind, 108, 291-334. Pollock, J. (2003). Rational choice and action omnipotence. Philosophical Review, 111, 1-23. Pollock, J. (2005). Plans and decisions. Theory and Decision, 57, 79-107. Rabinowicz, W. (2002). Does practical deliberation crowd out self-prediction?. Erkenntnis, 57,

91-122. Spohn, W. (1977). Where Luce and Krantz do really generalize savage's decision model. Erkenntnis,

11, 113-134.

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