Plan and Execution

Robert Bass
Department of Philosophy
Coastal Carolina University
Conway, SC 29528
rhbass@gmail.com

We act to achieve goals, to bring about outcomes that we prefer to known or imagined alternatives.¹ I wish to examine a special case of such goal-directed activity, in which a plan is adopted at one time to bring about an outcome which, for its successful completion, requires that steps be taken at a later time.  The issues in which I am interested have to do with a particular case in which the actions taken at the later time may or may not accord with the plan adopted. To isolate this type of case, I will distinguish it from three others.

To simplify, we can suppose the following: (1) that the plan is adopted at a time, t₀ – call this Adoption – in order to achieve an envisioned outcome and that a single action – call it the Step –  is necessary at a later time,  t₁, in order to execute the plan, (2) that the Step is selected solely as a means to achieve the outcome envisioned, (3) that once Adoption has occurred, the agent (at the time, t₀ ) strictly prefers that the Step be taken at t₁  to any non-Step alternative actions,² and (4) that the plan itself is well-conceived in the sense that its Adoption is reasonable or at least not unreasonable, given the agent’s knowledge and motivations at t₀.

The first sort of case to consider and set aside is that in which, at  t₁, the Step is strictly preferred to its alternatives.  This seems to pose no problems since there has been no relevant preferential change since Adoption nor has there been any relevant change in the information (available to the agent) upon which the plan was predicated.

The second kind of case is that in which the agent has acquired additional relevant information between t₀ and t₁.  Such information might show that some action other than taking the Step would lead to an outcome that would have been preferred, even at t₀ , had that information been available to the agent then.  Alternatively, it might involve the discovery that the Step will not in fact be effective or that something else will be more effective in bringing about the outcome for the sake of which the plan was undertaken.  If the information had been available earlier, a different plan, not entailing the Step, would have been adopted.  In such a case, it seems entirely reasonable for the agent to alter his plan and refrain from taking the Step.

The third variety of case is that in which the agent’s preferences with respect to the outcome have changed.  At the time of Adoption, the agent at least weakly preferred that outcome to available alternatives.  But it is possible that between t₀ and t₁, his preferences have changed though the possible outcomes to which his actions could lead have not.  It is no longer the case that he weakly or strictly prefers the selected outcome for the sake of which the plan was adopted to some other member of the set of possible outcomes.³ Again, in a case like this, it seems reasonable for the agent to alter the plan and refrain from taking the Step.⁴

The kind of case in which I shall be interested is that in which there has been no change in relevant information available to the agent nor has there been any unforeseen change in the agent’s preferences, but in which, at (or just before) t₁, the agent strictly prefers not to take the (necessary) Step.⁵ In addition, we can suppose that the preference change with respect to the Step was itself foreseen at the time of Adoption.⁶

Such situations are familiar.  An example might be deciding upon a diet.  There is an envisioned outcome which is ranked above other accessible future outcomes, losing weight, and a necessary step, such as refraining from between-meal snacks.  In addition, at the time the plan is adopted, it is recognized that there will be a temptation to snack between meals: when the Step must be taken, the agent will prefer snacking to sticking to the diet.  On one hand, it appears that the agent’s reasons for taking the Step are just the same as they were for the initial Adoption – no unanticipated information or preference has entered the picture.  If, as I have supposed, the plan was initially well-conceived, the agent ought to take the Step because the initial Adoption was reasonable.  On the other hand, now that the prospect of snacking is immediate, the agent does not prefer the outcome expected from refraining from the snack.  He would, right then, rather snack than lose weight.  Why must he be bound by his preferences of a few hours earlier?  If it is rational for him to guide his actions by his preferences, why are the preferences at t₀ decisive, while those at  t₁ are discounted – especially since it is the preferences at t₁ that are the ones he actually has at the time the choice to snack or not must be made?

Intuitively, most of us, I think – however difficult we find it to carry through in practice – suppose that the former argument is better: Having made a reasonable plan, and in the absence of relevant additional information not already taken into account in the formulation of that plan, it is reasonable for a person to take the necessary steps to implement the plan, even if those necessary steps are dispreferred at the time they must be taken. 

However, according to standard decision theory, this misdescribes the situation.  It is not exactly that the first argument is invalid, but that it rests on a false premise.  In standard decision theory, the only reasons we have are based on preferences and expected consequences (subject to a budget constraint) at the time a choice is made.  A decision cannot rationally depend – except insofar as this affects current preferences and expectations – upon a past event such as having adopted a plan.  Thus, if the step needed to carry out the plan is such that one would prefer not to take it at the time of choice (i.e., when the step must be taken or not), then one has reason at that time not to take the step.  But if this fact was really foreseen when the plan was adopted, the plan fails to be reasonable because its execution depends upon the taking of a step which it is not reasonable to take.  One who accepts the rationality-defining postulates of standard decision theory should either not have formulated a plan aiming at that goal or should have made provision that every step that would have to be taken would be preferred to its alternatives at the time the steps actually have to be taken.⁷ We can put this somewhat differently by saying that, for standard decision theory, reasonable plans are constrained by the requirement that they contain nothing but feasible steps, where feasible steps are all at least weakly preferred,⁸ at the time at which they must be taken, to their alternatives.  If that requirement is not met, then the plan wasn’t reasonable in the first place.

This seems an unsatisfactory state of affairs.  If standard decision theory is correct about situations of this sort, there may be an outcome that an agent would like to achieve and a plan that, if executed, would achieve that outcome, and it may be that if the plan were executed and the outcome achieved, the agent would be glad that she had adopted the plan and taken all the necessary steps, but nonetheless, the agent cannot rationally adopt the plan because it incorporates infeasible steps.  Her best available options are to either give up seeking that outcome or to undertake special arrangements to make sure that all the steps are feasible.  Either option represents some cost, either in the form of giving up the chance to obtain one’s most preferred outcome or in the form of making special provisions to avoid having to take infeasible steps.  (A further concern is that those provisions might themselves be so costly that, if they are necessary to achieve the outcome, then the outcome is not worth achieving.)

Putting matters in this way suggests that the agent is confined to second-best choices, at least if she is rational.  What is best but not available to her would be to adopt and execute the plan, “infeasible” steps included. At this point, though, we may notice a loophole.  The agent cannot take her best option because that would be irrational.  But the sense in which “irrationality” is involved here is that of standard decision theory.  What reason does the agent have to care about that – especially if by being “irrational” she could achieve either a better outcome or the same outcome at a lower cost to herself?  On the face of it, there seem to be two possible answers to that question.  It could be that being irrational in the requisite way is not motivationally possible to the agent or that it would entail other costs that outweigh any likely gains.  If the first of these is the case, then “being irrational” in the requisite way is not a real option, while if the second obtains, that seems a sufficient reason for the agent to avoid such action even if it is motivationally possible to her.

A more interesting issue arises, though, if neither of these is the case.⁹ Then, it seems that the charge of irrationality is empty.  An approach more consonant with the spirit if not the letter of decision theory is to rethink our notions of rationality.  An improved account of what rationality is may enable us to say that the agent can be rational in adopting and executing plans that include infeasible steps.¹⁰

The Coordination Model

An interesting approach to this complex of issues is suggested by E. F. McClennen.  On his view, it is useful to model the kind of situation we have been discussing as a problem in interactive choice:

There is an obvious and important analogy between the single decision maker faced with making a sequence of decisions over time and a group of persons faced with coordinating their actions.  The situation analyzed ... is the intrapersonal counterpart to one that is the focus of the theory of interpersonal interaction, that is, game theory.  In the latter situation, different individuals have different preference orderings over possible jointly attainable outcomes, and the task becomes, given the strategic structure of the game in which they are participants, to determine a rational choice for each, on the assumption that each other participant also chooses rationally.¹¹

Briefly and in outline, the picture he proposes is this:  We can define different utility functions for the agent at t₀ and at t₁.  At t₀, the agent prefers that the Step be taken at  t₁ and the envisioned outcome achieved.  At t₁, the agent prefers that the Step not be taken even if that means that the envisioned outcome is not achieved.  Since the utility functions are different, we can view the agent at t₀ and the agent at t₁ as separate time-defined selves.¹² The question that faces us then is how or whether the actions of the time-defined selves can be coordinated.  We can, in principle, hope to shed light on a problem in individual decision-making by looking at results in the theory of interactive choice.

I think that McClennen’s proposals on this are both interesting and important.  He seeks to reconfigure the theory of rational choice and, in the process, reject some of the axioms that have defined standard decision and game theory.  I shall not enter into this in detail since I think he is correct about the need for recasting standard decision and game theory.  What I do wish to consider is whether, if we accept his recasting of standard theory, it really helps with the kind of issues involved here.  To do that, some digression is necessary to say something about how his account differs from the standard theory.

On McClennen’s view, it is a mistake to view problems of interactive choice, as most game theorists have viewed them,  as somehow reducible to special cases of maximization with respect to a given set of parameters.  That overlooks or discounts the fact that one is dealing with other rational agents and leads to familiar puzzles such as the fact that if all agents in a given interaction adopt this approach, they will often all be worse off than if they had adopted some different approach.

The point can be put this way: There is no general solution to the problem of joint maximization of two or more distinct utility functions.¹³ Instructing agents, in a situation of interactive choice, to always act on the assumption that each may treat others’ expected actions and choices as parameters against which to maximize amounts to assuming that there is a general solution to the problem of jointly maximizing multiple utility functions.¹⁴ Since that is not true, such maximizing agents often end up, by virtue of their interaction, in defeating one another’s attempts to maximize.¹⁵ A better model would view rational agents (in non-strictly competitive games) as trying to coordinate upon a Pareto-superior solution (in which, at least some and preferably all, are better off than they would be apart from such coordination, and in which none are worse off).  That, for McClennen, sets the relevant metric in terms of which agents should attempt to maximize in non-strictly competitive games.  They are seeking not the best possible score in terms of each of their utility functions, considered apart from the interactive context, but the best possible coordination.

To return now to the problem which we were considering, that of an agent executing a plan when his preferences at the time of execution are different than those at the time of Adoption due to distaste for a necessary Step, when that is modeled as an interactive choice between two time-defined selves, McClennen would say that each time-defined self should view itself as seeking an optimal coordination with its counterpart.

The best game-theoretic model for the kind of interaction that could occur between time-defined selves is, as McClennen notes, an ultimatum game.  In an ultimatum game, there is a first and a second player, and the second player makes her choice knowing both what the first player has chosen and the possible consequences attendant upon any choice she makes, given the first player’s choice.  As an example, we can consider a case in which the first player has a choice as to how to divide ten dollars between the two players, while the second player can accept or reject the proposed division.  If the second player accepts, the money will be divided as proposed, while if the second player rejects the proposed division, neither player will receive anything.  Standard decision theory would counsel the first player to propose a division that takes the largest possible share for himself and leaves the minimum share to the second player.  If, for simplicity, we assume that divisions can only occur in whole-dollar increments, the first player should propose that he receive nine dollars and that the second player receive only one.  The second player, in turn, should accept this division because the alternative is to receive nothing.  By accepting the division, the second player is better off by a dollar than she would be if she rejected it.¹⁶

Now, it is well-known that people playing such a game, whether they occupy the roles of the first or the second player, do not in fact typically act in the way that standard decision theory counsels.  First players are far more likely to propose equal divisions or divisions that are moderately favorable to themselves (say, six dollars to four dollars).  And second players, when offered a nine dollar to one dollar division are far more likely to reject than to accept the offer.¹⁷

To some extent, this fact can be accommodated within standard decision theory without charging the players with irrationality.  On behalf of second players, we can suppose that they are concerned not just with payoffs that will accrue to them in particular ultimatum games but with reputation effects and the impact that those will have upon offers made to them in subsequent ultimatum games.  Second players may reason that if it is known to potential first players that they will reject nine-one offers, such offers will not be made to them.  They will instead receive more favorable offers and the prospect of receiving and accepting those more favorable offers will outweigh the loss incurred when the (rare) nine-one offer is rejected.  For similar reasons, first players may expect nine-one offers to be rejected and therefore choose to make more favorable offers to begin with.

Such explanations go some way towards reconciling observed behavior with standard decision theory, but not far enough.  Even when arrangements are made to insure the anonymity of the participants, so that there are no possible reputation effects, the same patterns of behavior described above, though less pronounced, are still observed.¹⁸  There is still a significant likelihood that nine-one offers will not be made and, if made, will not be accepted.¹⁹  Of course, standard game theorists could simply recognize this and say that, since their theory is supposed to be normative rather than descriptive, it is possible that many or most people are playing irrationally.

I won’t discuss the adequacy of this response, but it is worth considering how McClennen would counsel rational players of the ultimatum game to play.  I think he would accept most of what standard theorists have to say about the impact of reputation effects on prospects with respect to future games (where those are relevant).  However, since he views rational agents as seeking an optimum coordination in interactive situations, he would advise first players to make non-lopsided offers initially to maximize the likelihood that those offers will be accepted.²⁰ This, of course, presupposes that it is rational for second players to reject offers that are significantly lopsided in favor of first players, because if it were not rational for second players to reject those offers, it would not be irrational for first players to make them.

If we apply this to the case of time-defined selves involved in executing a plan, it appears that McClennen would hold that there is an additional, heretofore unrecognized (or at least unmentioned) condition on the rationality of adopting a plan.  The plan must be such that there is a reasonable distribution of the benefits from its execution between the earlier and the later time-defined selves (allowing “reasonable distribution” to stand in for whatever the optimal coordination between time-defined selves would be in a fully specified case).  If this condition is not met, the later time-defined self has no reason to carry through the plan initiated by the earlier time-defined self, and the earlier time-defined self has, in the absence of a reasonable expectation that the later time-defined self will carry through, no good reason for adopting the plan.

This seems plausible, but I think we ought to consider how far the analogy with the interpersonal case extends here, for, though there are similarities, there are also some, possibly significant, differences. 

We can begin to see what the differences are by asking what could be meant by a benefit to a time-defined self.  Does it make sense to say that the earlier time-defined self receives some benefit if the later time-defined self executes its plan?  In one sense, it is plain that it does not.  There is no experienced benefit for the earlier time-defined self because it no longer exists; it has been superceded by the later time-defined self.  If it is experienced benefit that is crucial, it can be argued that earlier time-defined selves should adopt plans that maximally favor themselves while they persist, but should take no account of whether a later time-defined self will go along, since, once the later time-defined self arrives, there will be no further experience for the earlier time-defined self.  This is hardly promising as an account of coordination between time-defined selves.

Let us suppose instead – and I think this is what McClennen had in mind – that something counts as a benefit to a time-defined self if it satisfies preferences that the time-defined self had, whether or not those preferences are satisfied in the experience of the time-defined self.  If an earlier time-defined self prefers a given future outcome to its alternatives, then that preference is satisfied if the given future outcome occurs.  If we understand benefits to time-defined selves in this way, we can make sense of a distribution of benefits between time-defined selves and, therefore, of a reasonable distribution.

Still, there are some further disanalogies between the intrapersonal and the interpersonal coordination cases.  One that is obvious is that, though there is no anonymity between time-defined selves, there seems also to be no room for reputation effects to play the role they evidently do in interpersonal examples of the ultimatum game.  There is no way that the behavior of a later time-defined self can affect the future play of an earlier time-defined self because the earlier time-defined self, by definition, no longer exists.  If McClennen is to argue that rational time-defined selves will coordinate upon a reasonable distribution of benefits, he will have to rely entirely upon his claims about the conditions under which coordination between selves is rational without any augmentation from the reputation effects to which, for the interpersonal case, orthodox game theorists can appeal.

It was noted above, with regard to the interpersonal ultimatum game, that for it to be rational for first players to refrain from making offers that lopsidedly favor themselves, it must be rational for second players to reject those offers.  Accordingly, for the intrapersonal case, for it to be rational for earlier time-defined selves to refrain from making plans that lopsidedly distribute benefit to themselves, it must be rational for later time-defined selves to refuse to execute those plans.

The question that now arises is: How can it be rational for a later time-defined self to refuse to execute any plan that distributes some, otherwise not obtainable, benefit to itself ?  If the plan is executed, it obtains some benefit, however small.  If the later time-defined self does not execute the plan, it does not receive that benefit.  It is, of course, true that refusal to execute the plan will cost the earlier time-defined self its intended benefit also, but it is unclear why that should matter to the later time-defined self since it will have no impact on the non-existent future behavior of the earlier time-defined self.  When the later time-defined self must choose between receiving a benefit or not, how can it be rational to reject the benefit, however small it is?  It appears that the constraint upon rational plans that McClennen proposes is very modest indeed.  Rational plans may quite lopsidedly favor earlier time-defined selves because later time-defined selves cannot rationally reject an offered benefit, however small.

In an attempt to move beyond this, I shall suggest something which may (I am unsure) represent what McClennen has in mind and explain why I think it is still unsatisfactory.  At the end, I shall say a few words that attempt to diagnose more generally what (I think) goes wrong McClennen’s proposal.

Why might the plan of an earlier time-defined self include more than a minimal benefit for a later time-defined self?  We have noted already that there is an asymmetry that favors the earlier time-defined self in settling upon a plan.  Not only does it alone have the opportunity to select the plan from among the available options, it may also expend resources on behalf of the plan’s execution or irrevocably commit²¹ them in its behalf.  To this extent, the later time-defined self is constrained in ways that the earlier is not.  It may have fewer resources at its disposal and cannot, in any case, make a different plan, more satisfactory to itself, at the earlier time (since it does not exist at the earlier time).  The later time-defined self’s options are limited to either executing the original plan or abandoning it in favor of something else.

However, we should also note that there is an asymmetry that runs in the opposite direction.  If the plan adopted by the earlier time-defined self is to be executed at all, then the later time-defined self must cooperate and carry out its part.  Though the later time-defined self had no direct voice in selecting the plan, it is still true that it is active (and the earlier time-defined self is not) at the time of necessary steps involved in the plan’s execution, so it alone may scuttle the plan, thereby turning any expenditures or commitments that the earlier time-defined self had made for the sake of the plan’s execution into uncompensated losses.

If we leave aside the possibility that the later time-defined self simply maliciously aims at the frustration of the earlier time-defined self’s preferences (the rationality of which is dubious), then, since the later time-defined self is active when the plan must be executed, its decision may presumably be expected (by the earlier time-defined self) to be based upon the attractiveness of the alternatives available to it at the time that it acts.  (Upon what other basis might the earlier time-defined self form an expectation about how the later will act?)  If we conceive of the situation in this way, then the earlier time-defined self may formulate a plan that offers more than a minimal benefit to the later time-defined self because it must, in effect, “bid against” the attractive alternative options that may be available to the later time-defined self. 

We can illustrate what might be involved in this by returning to the earlier example of selecting and sticking to a diet.  The fastest and most effective way to achieve the earlier time-defined self’s objective of losing a certain amount of weight might be to fast for several days.²² However, undertaking such a fast is likely to be met with resistance by the later time-defined self: if the choice is to continue the fast or give in to the temptation to eat normally, it is likely to give in.  If the earlier time-defined self is to formulate a plan that is likely to be executed, it would be well-advised to make allowance for such weaknesses by selecting a diet that makes provisions for lowering net calorie consumption without making large motivational demands upon the later time-defined self – for example, one that includes low-calorie snacks.

I don’t think this amounts to a real advance on what can be said by standard decision theory for two reasons.  First, it seems that the considerations that are actually appealed to are, though more richly specified, of the same sort as are appealed to by the standard theory.  The reason the earlier time-defined self offers more than a minimal benefit can be cashed out entirely in terms of the future pay-offs to the earlier and to the later time-defined selves considered separately.  The earlier time-defined self makes a more than minimal offer because, without it, it does not expect its plan to be executed.  The later time-defined self, with its differing utility function, goes along (if it does) because that is its best option.  There is no reconfiguration of either utility function to coordinate with the other.  Or, to put matters differently, the earlier time-defined self does not make a more than minimal offer: we have only discovered an additional constraint on what qualifies as offering a minimal benefit to the later time-defined self, namely, one that is better for the later time-defined self, in terms of its independently specified preferences, than the other options that may be available to it.

            Second, I think the proposal fails to capture what we typically take to be the rational weight or importance of following through upon plans.  This requires a little spelling out. Normally, we take having settled on a plan to provide some reason for following through upon it. This reason amounts to no more than a presumption in favor of taking the steps necessary to execute the plan, and, as a presumption, it can in various ways be outweighed, over-ridden or defeated.²³ But this reason is also no less than a presumption in favor of taking the necessary steps.  If it is to be reasonable not to take those steps, the reason needs to be outweighed, over-ridden or defeated.

But McClennen’s proposal fails to meet this condition, for if the proposal is correct, then if the distribution of benefits is such that the later time-defined self is indifferent between executing the plan and opting for the best available alternative instead, then the later time-defined self will be rationally indifferent whether the plan is executed or not.  The later time-defined self will lose nothing by executing the plan, since it has no better options available, but will also lose nothing by declining to execute the plan (in favor of the best of the alternatives available to it), for it has no better option.  So, in this kind of case, there is no consideration that outweighs, over-rides or defeats the presumption in favor of taking the necessary step.  If, as the current proposal requires, the later time-defined self is rationally indifferent between executing the plan and opting for its best available alternative instead, and therefore is not irrational if it declines to execute the plan in favor of its best alternative, that amounts to a denial that well-conceived plans have even presumptive reason-giving force.²⁴  Perhaps we will be driven to something like this in the end, but the fact that it conflicts with what we normally take to be the rational importance of following through upon plans is a strong prima facie reason against accepting it.

So far, I have expressed doubts about McClennen’s proposed model in which adopting and executing a plan is understood as a special case of a coordination problem between time-defined selves.  What he would like to say about this is analogous to his treatment of the interpersonal case, according to which agents in, e.g., an ultimatum game have a reason to adopt settling upon an optimal coordination as a basis for rethinking and, if necessary, altering their prior preferences.  I have said already that I think that plausible, so it is worth asking where the analogy breaks down.

We can make some progress by asking what sort of reason it is that the agents in the interpersonal case have for (possibly) reconfiguring their existing preferences in order to settle upon an optimal coordination.  The answer that I think McClennen would give is that the reason is pragmatic: Agents who are capable of taking “settling upon an optimal coordination” as a reason for reconfiguring their preferences will do better than agents who are not.  How will they do better?  The answer can be divided into two parts.  First, if two such agents are dealing with one another, there is a reduced likelihood that they will simply fail to coordinate (so that, in an ultimatum game, neither receives any benefit).  I don’t think that this goes very far because such agents will also be committed to rejecting sub-optimal offers.  But plainly, unless something else can be said about the bearing of the recommended strategy upon other cases, those who accept sub-optimal offers are better off than those who reject them.  Nor would it help to suggest that such agents, even on the assumption that they can identify one another, should adopt a strategy, in the role of second players, of accepting sub-optimal offers if tendered by agents who do not take settling upon an optimal coordination as a reason for adjusting their preferences, for that would reward – and therefore encourage – the adoption of the latter strategy.  The second way in which agents might do better by attending to optimal coordinations rather than to their independently specified preferences has to do with future impacts upon the behavior of others with whom they may interact. If it is known or becomes known that a particular second player always rejects sub-optimal offers, then potential first players would be irrational to make such offers to him.  The key point, for present purposes, is that the rationale for adopting McClennen’s recommended strategy has to do with future consequences of adopting it as compared to its alternatives.

The problem for time-defined selves is that the agents envisaged do not persist and accordingly cannot gain or suffer from any future consequences other than those that flow from their current actions or inactions.  A later time-defined self can’t have a reputation as one to whom it is best to offer optimal coordinations.  We can make this clearer by adjusting the interpersonal case so that it is closer to the intrapersonal case.  Suppose that the ultimatum game was to be played between two players who had never played before, either against each other or against anyone else, and who (it is known by both), immediately following their respective choices, would die.²⁵ Could there be any reason in a case like that for the first player to offer anything other than a division that lopsidedly favors himself or for the second player to reject such an offer?  If so, I do not see what it is.

What we need to do, if we are to avoid this kind of result, is to rethink the notion that all reasons derive ultimately from nothing but preferences with respect to outcomes.  The kind of agents who can do better for themselves by seeking to settle on optimum coordinations are already temporally extended.  To deal with problems of coordination between time-defined selves, where the time-defined selves have differing utility functions, we need to be able to think in terms of there being reasons to adopt a plan in the first place that are at least partially independent of the preferences of the time-defined selves adopting it, and accessible to both of the relevant time-defined selves.

References

Frank, Robert. 1988. Passions within reason: the strategic role of the emotions. New York: W.  W. Norton and Company.

McClennen, Edward F. 1990. Rationality and dynamic choice: foundational explorations. Cambridge: Cambridge University Press.

Skyrms, Brian. 1996. Evolution of the social contract. Cambridge: Cambridge University Press.

Comments? I'd love to hear.