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How to choose between two equally desirable things?


An unusual situation in practical reasoning is the problem of equipollent preference. When given the choice between two things, an agent finds both things equally desirable. The problem of equipollent preference involves an agent who:

  1. is able to choose only one option, x or y;

  2. prefers neither x nor y in comparison to the other; and

  3. prefers having at least one of x or y to having none.

Philosophers have called the problem of equipollent preference “Buridan’s Ass” (See Nicholas Rescher 1969 for a nice overview of the problem). As the story usually goes, an ass stands equidistant between two equally appetizing bales of hay. Unable to decide between the two bales of hay, the ass starves. Absurd consequences seem to ensue when there is a choice between two equally powerful motivations.


The aim of this paper is to offer a possible resolution to the problem of equipollent preference. In particular, I would like to argue that rational agents possess the ability to solve the problem of equipollent preference and do so regularly. First, I will need to review an argument between two contemporary philosophers, Donald Davidson and Michael Bratman, regarding their theories of intention and how their theories supposedly solve the problem. Then, I will show how each theory’s solution is somewhat deficient. Finally, I will conclude that the problem of equipollent preference is solvable if we synthesize Davidson’s and Bratman’s theories of intention.


In “Davidson’s Theory of Intention,” Michael Bratman (1999) argues that Davidson’s theory faces a pair of difficulties, which are the result of his overly weak conception of the role of intentions and plans in practical reasoning. On the one hand, Davidson’s theory seems unable to accommodate the possibility of a future intention in the face of equally desirable future options, and, on the other hand, his theory cannot ensure that rational intentions are agglomerative. Upon further examination, however, Davidson’s theory is not an overly weak conception since he does seem to consider the role of plans in practical reasoning. Even including the role of plans in practical reasoning fails to solve the seemingly insoluble problem of equipollent preference.


Bratman uses an example to exemplify the problem. He supposes that an agent, S, may stop at one of two bookstores, but S cannot go to both. S finds both options equally attractive, and S judges all-out that any act of stopping at bookstore A would be just as desirable as any act of stopping at bookstore B. Does it follow from Davidson’s account that S has both intentions or that S has neither intention? This question, according to Bratman, emphasizes that Davidson’s discussion of all-out desirability judgment is unclear.


Bratman believes Davidson’s account of an all-out desirability judgment in favor of A-ing is implicitly comparative. Comparisons may be either weak or strong. A weak comparison would see A-ing as “at least as desirable as its alternatives,” while a strong comparison would see A-ing as “strictly more desirable than its alternatives” (Bratman 1999, p. 219). Which type of comparison does Davidson’s theory require?


According to Bratman, if Davidson’s theory requires for future intentions the weaker type of comparison, then S both intends to go to bookstore A and intends to go to bookstore B. This seems wrong since S knows he cannot go to both stores. On Davidson’s view, then, it seems that S can intend to A and intend to B without, at the same time, intending both A and B. Bratman believes this violates a natural constraint that rational intentions should be agglomerative. Rational intentions are agglomerative if an agent, at the same time, rationally intends to A and rationally intends to B, then it should be both possible and rational for the agent to intend A and B. Accordingly, Davidson’s theory cannot require for future intentions the weaker type of comparison since intentions will not be agglomerative.


For Davidson’s theory of intention to require the stronger type of comparison, S must hold a strong comparative evaluation in favor of A. To return to the bookstore example, S can decide on which bookstore to go to, but continue to see each option as equally desirable. This decision, however, provides S with an intention that does not correspond to a strong comparative evaluation. For S to decide to go to bookstore A even though he does not judge all-out that so acting would be strictly more desirable than going to bookstore B, the intention does not satisfy the demands of a strong comparative evaluation.


Bratman believes that the difficulty of equipollent preference and future intentions are the result of Davidson’s conception of what facts a theory of future intention must include. Davidson attempts to extend the materials present in his account of intentional action, i.e. appropriate belief/desire pair, to an account of future intention, but this is a thin conception of the role of intention in practical reasoning, according to Bratman, because a theory of future intention must explain why we bother to form them. Bratman believes forming future intentions is a part of larger plans whose role is to aid coordination of our activities over time. Future intentions require the formation of further intentions and constrain the formation of other intentions, and they play a crucial role in the “on-going creation and adjustment of our plans” (Bratman 1999, p. 223) which is exactly what Davidson neglects in his theory.


Davidson’s theory seems to neglect future intentions as a part of larger plans that aid coordination of activities over time; however, Bratman may have overlooked a key element of Davidson’s theory of intention. In particular, textual evidence in Davidson’s article, “Intending” (2001, pp. 83-102), shows that he leaves room for plans in future intentions. In several places, Bratman implies that Davidson has placed restrictions on what may reasonably be considered in forming an intention. Davidson, however, never places such a restriction on his theory. An all-out judgment should take account of all an agent’s relevant beliefs and desires. Davidson writes, “A present intention with respect to the future is in itself like an interim report; given what I now know and believe, here is my judgment of what kind of action is desirable… My intention is based on my present view of the situation; there is no reason in general why I should act as I now intend if my present view turns out to be wrong.” A rational judgment, then, will enlist all of the agent’s relevant desires. Some of these relevant desires may be plans that an agent formulates in an intention. Bratman seems wrong to restrict what Davidson can and cannot include in forming an intention. Davidson’s theory, thus, considers the role of plans in practical reasoning even though he does not explicitly set out a theory of intention based on planning. What remains is whether taking account of the role of plans in practical reasoning can solve the problem of equipollent preference.


Bratman uses plans and planning in a theory of intention, which he thinks avoids the problem of equipollent preference. Bratman believes that reason says an agent is able to choose either option, bookstore A or bookstore B. The agent, then, can form the intention to go to bookstore A even though the agent does not see going to bookstore A as more desirable than going to bookstore B. Once the agent has formed the intention to go to bookstore A, the agent will, other things being equal, actually go to bookstore A, since intentions are conduct-controlling pro-attitudes. Conduct-controlling pro-attitudes are different than desires because they include plans which do not merely influence an agent’s conduct, but control it (See Bratman 1983 for a good discussion of conduct controlling pro-attitudes). Davidson’s theory cannot account for intentions in the same way because he fails to recognize intentions as conduct-controlling pro-attitudes. Davidson believes intentions are all things considered judgments. All-things considered judgments cannot be conduct-controlling pro-attitudes. All things considered judgments are merely conduct-influencing pro-attitudes. This type of pro-attitude merely influences the way one acts, but it does not control whether or not one will perform some action (See Bratman 1983, p. 273). While it is possible to have two all-things considered judgments of the form “A is all things considered optimal” and “B is all-things considered optimal,” it is impossible to have both of the following conduct-controlling pro-attitudes: “I will A (which means I cannot B)” and “I will B (which means I cannot A).” All-things considered judgments do not prevent a rational agent from holding two equally desirable intentions, which the conduct-controlling pro-attitudes apparently do prevent.


Plans may not solve S’s problem. S may settle in advance to go to bookstore A, and actually go to bookstore A later, but this seems wrong since S judges any act of going to bookstore A is just as desirable as any act of going to bookstore B. No plan seems able to get around the question: how can you rationalize a choice when the options are equipollent? It seems that neither Davidson’s nor Bratman’s theory can adequately answer this question. If we “settle in advance on one of several options judged equally desirable” (Bratman 1999, p. 224), such a decision does not seem to show why we believe the chosen option is the correct option.Just deciding on one or the other option fails to demonstrate the desirability of that option. The importance of co-ordinating roles of future intentions and plans in practical reasoning circumvents the problem of equipollent choices, rather than actually offering an answer to it. Davidson escapes Bratman’s accusation that his conception of future intentions is overly weak because it cannot account for the role of intentions and plans in practical reasoning, but even accounting for the role of intentions and plans as Bratman’s theory does cannot escape the problem of equipollent options.


Neither Bratman’s nor Davidson’s theory of intention seem to provide sufficient means for a resolution of the problem of equipollent preference. An example will show how each theory is deficient. Suppose Colleen wants a 20-oz. Pepsi-Cola and she believes that going to Balboni’s package store will enable her to purchase a Pepsi, thus satisfying her thirst. At Balboni’s, she finds two rows of 20-oz. Pepsi-Cola bottles in the refrigerator. Colleen knows that she can only choose one of the 20-oz. Pepsi-Cola bottles and that anyone of the 20-oz. Pepsi-Colas will quench her thirst. Should Colleen choose a bottle in the left row or a bottle in the right row? Should she choose one from the middle or back of either row? What Pepsi should Colleen choose? Why should she choose that one over the other bottles? Colleen finds herself in the middle of a dilemma of equipollent preference.


Davidson could offer a solution to Colleen’s dilemma in two ways. First, according to Davidson, Colleen can intend to purchase the Pepsi in the left row (“PL”) as well as intend to purchase the Pepsi in the right row (“PR”). Intending to purchase PL is at least as desirable as intending to purchase PR; however, since Colleen knows it is not possible to purchase both PL and PR, she cannot intend to purchase both. This account violates the notion of agglomerativity. Second, Davidson may believe that Colleen can intend to purchase PL if she holds a strong comparative evaluation in favor of purchasing it. But, she does not hold a strong comparative evaluation in favor of purchasing PL because Colleen believes purchasing PR is equally desirable. Davidson’s theory encompasses too much and ultimately leads the agent into an indecisive situation. Colleen is unable to decide between PL and PR. Thus, Davidson’s theory seems unable to resolve Colleen’s dilemma.


Bratman’s theory, on the other hand, is too narrow. Even though plans are supposed to avoid deliberation at the time of action and aid in the coordination of our activities over time, Colleen’s dilemma demonstrates that such a theory of intention does not avoid deliberation at the time of action or aid in the coordination of our activities over time. According to Bratman’s theory of intention, reason says Colleen can choose either option, PL or PR, even though Colleen does not see purchasing PL as more desirable than purchasing PR. Once Colleen has formed the intention to purchase PL, Colleen ought to purchase PL since intentions, according to Bratman, are conduct-controlling pro-attitudes. What if there are no Pepsi’s in the left row? Bratman says that Colleen may abandon her original plan and formulate a new one. Then, what is the purpose of the plan if it can be abandoned at the time of action? If Colleen can abandon a plan at the time of action, then it seems useless for her to formulate the plan in the first place. This type of problem renders Bratman’s theory inoperable in these types of cases. To carry out Bratman’s theory, either Colleen would have to randomly choose a Pepsi at the time of action or Colleen would have to form an intention so specific that she would be hard-pressed to find a situation in which she could execute the action.


An adequate resolution of the problem of equipollent preference will require synthesizing Bratman and Davidson’s theories of intention. Such a resolution will include the employment of unfamiliar terminology. There needs to be a distinction between choosing, picking, and selection (See Morgenbesser 1977). First, choosing among alternatives occurs when the act of taking or doing one of the actions is determined by the differences in the agent’s preferences over them. Second, when an agent is strictly indifferent with regard to the alternatives, the act of taking or doing one of them is an act of picking. Finally, selection is meant as a generic term, neutral with respect to choosing and picking.


We encounter choosing situations all the time. For example, Kathy may prefer to go to the movies more than going to the park. Kathy has a clear preference for going to the movies. These are the less interesting situations since Kathy has a clear preference of one action over the other. The more interesting situations occur in cases like Colleen’s dilemma, which is described above. In this type of situation, Colleen has no clear preference between PL and PR because her preference is symmetrical.


There are curious situations where an agent has a clear preference of one course of action over another, but s/he is unable to choose that alternative because the selection that will yield the preferred outcome is inaccessible to the agent. For instance, suppose that Colleen has the choice between PL and PR, but one of the two options is poisoned. Colleen has a clear preference of one course of action. She prefers to drink the Pepsi not laced with poison; however, since PL and PR are indistinguishable (besides the fact that one is actually poison), Colleen does not realize that she actually prefers one of the two options.


This situation is similar to the normal case outlined in this paper, but Colleen has preference for one outcome. Due to the design, or structure, of the situation, however, the information as to which of the alternatives up for selection will yield the preferred outcome is inaccessible to Colleen. In other words, even though the selection alternatives are not identical, the selection alternatives are presented to Colleen in an identical guise so that she is unable to determine the identity of the preferred one. The situation puts an interesting twist on the original case. Thus, Colleen clearly prefers to drink the Pepsi without the poision, but, under the circumstances, she can do no better than pick one or the other.


From Colleen’s dilemma and cases like it arise simple picking situations. Colleen cannot select both Pepsis, and she is indifferent between PL and PR. It could be practically impossible for Colleen to select both Pepsis because she does not have enough money to purchase both or she has some reason against purchasing more than one soda pop in a 24-hour time frame. Whatever the reason may be, Colleen cannot select both Pepsis. She prefers the selection of one, PL or PR, whichever it may be, to the selection of none. This is an accurate characterization of a picking situation, but what remains is how to rationally defend Colleen’s picking one of the Pepsis over the other.


To rationally defend Colleen’s picking one of the Pepsis over the other is to distinguish between two different types of rational intention, what I will term general intentions and specific intentions. General intentions refer to those initial pro-attitudes in favor of actions in so far as they are of a certain type. For instance, Colleen has the general intention of purchasing a soda. General intentions refer to broad descriptions of future actions. Specific intentions, however, refer to pro-attitudes as a property of particular actions. For example, Colleen has a more specific intention in favor of purchasing a 20-oz. Pepsi-Cola bottle from Balboni’s package store. One can make an even more refined intention referring to the first 20-oz. Pepsi-Cola bottle in the left row of the refrigerator at Balboni’s package store, but such a specific intention runs the risk of Balboni’s being out of stock in the left row of Pepsis or some other unforeseen circumstance. That is a risk the agent must take and one that may also occur at a general level, i.e. Balboni’s may not carry Pepsi, Balboni’s may be closed, or a bus may strike Colleen on her way to Balboni’s. Regardless, general and specific intentions are representative of what Davidson termed all things considered judgments. They are not necessarily conduct-controlling pro-attitudes, but they certainly influence the way an agent acts.


Having distinguished between general and specific intentions, we now must show how these intentions assist in the execution of future action. Similar to Bratman’s theory of intention, there is a certain amount of planning involved. As Bratman has said, “we do not simply act from moment to moment” (Bratman 2000, p. 40). Rational agents settle in advance on future-directed plans of action. These plans of action play a basic role in support of the organization and coordination of our activities over time. Essentially, “plans provide a somewhat stable background framework that needs to be filled in appropriately with specifications of means and the like” (Bratman 2000, p. 41).


In terms of Colleen’s dilemma, she begins with a plan of action that includes a general intention to purchase a soda. She then plans a more specific course of action that includes a specific intention to purchase a 20-oz. Pepsi-Cola at Balboni’s package store. This is a choosing situation since it was Colleen’s preferential desire to purchase a soda pop over a Gatorade or some other fruit drink. Colleen possesses a conduct-influencing pro-attitude in favor of purchasing a Pepsi at Balboni’s. When she arrives at Balboni’s and finds that there are many different options – several Pepsis available for purchase – Colleen merely needs to pick one. All of the Pepsis will presumably quench her thirst, so she need only pick one of the Pepsis to purchase from the many Pepsis available. There is no need abandon her original plan since the content of that plan was general. Colleen may pick anyone of the several available Pepsis to fulfill that plan.


What I have tried to show is that we can overcome the problem of equipollent preference if we settle on a theory of intention that synthesizes Bratman’s notion of planning with Davidson’s causal theory of action. By distinguishing between general and specific intentions, the agent may form future intentions without worrying that such intentions will be rendered inoperable at the time of action. In addition, the agent should modify plans that accord with her general and specific intentions. In this way, if the agent ever has to face a situation like Colleen’s dilemma, then the agent will know that she will not suffer the same fate as Buridan’s ass.







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