L. A. Paul on transformative experience and decision theory I

I have never eaten Vegemite---should I try it?  I currently have no children---should I apply to adopt a child?  In each case, one might imagine, whichever choice I make, I can make it rationally by appealing to the principles of decision theory.  Not according to L. A. Paul.  In her rich and fascinating new book, Transformative Experience, Paul issues two challenges to orthodox decision theory---they are based upon examples such as these.

(In this post and the next, I'd like to tryout some ideas concerning Paul's challenges to orthodox decision theory.  The idea is that some of them will make it into my contribution to the Philosophy and Phenomenological Research book symposium on Transformative Experience.)


The experience of eating Vegemite for the first time is, in Paul's terminology, an epistemically transformative experience:  that is, it is an experience that teaches you something that you can only learn by having an experience of that type; what it teaches you is what it is like for you to taste Vegemite.  This raises an apparent problem for orthodox decision theory.  Suppose that, like me, you have never tried Vegemite.  And suppose that you are faced with a decision problem---a choice between a number of alternative actions---where at least one of the possible outcomes of at least one of the alternative actions involves you eating Vegemite: for instance, you might have the choice whether or not to try Vegemite; or you might be offered a bet where the stake is three jars of the stuff.  Then, contends Paul, you will not be able to use orthodox decision theory straightforwardly to make your choice.  The problem is that, in orthodox decision theory, in order to decide between alternative actions, we need at the very least a set of possible states of the world and a utility function that assigns utilities to those states of the world.  However, in the case of the decision problem that features Vegemite, you do not have access to your utility function:  after all, one of the states of the world involves you eating Vegemite at some point in the future; but you don't know what it's like to eat Vegemite, and the phenomenal character of an experience is often important in determining the utility you assign to having that experience.  Thus, there are decision problems that an agent might face where it seems that orthodox decision theory cannot provide the action-guiding advice that is one of its central purposes.

Some claim that the experience of becoming a parent is also an epistemically transformative experience:  before you do it for the first time, you cannot know what it is like to do so.  But it can also be what Paul calls a personally transformative experience:  that is, it is an experience that can change your values in such a way that your utility function after the experience is different from your utility function before the experience.  This raises another apparent problem for orthodox decision theory.  Suppose that, like me, you have not been a parent.  So there is a chance that, if you were to become a parent, your utility function may change.  Let us suppose that there is in fact no problem of epistemic access to your current or future utility functions in this case: you know what your current utility function is and you know what your future utility function would be if you were to become a parent and what it would be if you were not to become a parent.  And suppose that one thing you know about you current utility function and your hypothetical utility function were you to become a parent is that they are different---you know that, before becoming a parent, you will value the company of your friends more than the company of your hypothetical offspring; afterwards, this will be reversed.  According to orthodox decision theory, you make any decision by appealing to your current utility function.  But in a situation in which at least one of the actions between which you must choose may lead to a change in your utility function, this seems to ignore an important vantage point, namely, the vantage point of your future self after the choice has been made---indeed, the part of your self that will in fact have the experiences you're choosing between.  If I know that becoming a parent will give me less time to spend in the company of my friends and more time in the company of my hypothetical child, and if I currently value the former more than the latter but will come, upon becoming a parent, to value the latter more than the former, then it would seem irrational to make the decision by appealing only to my current utilities.  As before, there seem to be decision problems that an agent might face where it seems that orthodox decision theory cannot provide the action-guiding advice that is one of its central purposes.

In the sequel, I will argue that epistemically transformative experiences pose no special problem for orthodox decision theory---I'll deal with this in the present post.  Personally transformative experiences, on the other hand, do.  I will offer an extension to orthodox decision theory designed to accommodate decisions that involve personally transformative experiences---I'll deal with this in the second post.

Orthodox decision theory

Let us begin by describing orthodox decision theory.  In this post, I'll take a very simple non-causal, non-evidential decision theory.  All of the problems we're considering arise for this version, and nothing new arises when we move to the causal version.  In the next post, where I deal with personally transformative experiences, we will consider causal decision theory; but in fact no new problems arise for it---the challenges Paul raises could be raised for a non-causal theory.

In this simple decision theory, we model a decision problem as follows:

• $\mathcal{S}$ is a set of propositions each of which describes a different possible state of the world;
• $\mathcal{A}$ is a set of propositions each of which describes a different possible action that our agent might perform and states that in fact she does perform that action;
• $U$ is a function that takes a conjunction of the form $AS$, where $A$ is in $\mathcal{A}$ and $S$ is in $\mathcal{S}$, and returns the utility that the agent would obtain were that conjunction to hold---that is, the utility she would obtain if she were to perform that action in that world;
• $p$ is a subjective probability function (or probabilistic credence function) over the states of the world $S \in \mathcal{S}$.

Given this, we can define the value of an act as follows:
$$V(A) := \sum_{S \in \mathcal{S}} p(S)U(AS)$$ Finally, we can state the main decision rule of simple decision theory:

Maximize value If there is an action with maximal value and $A$ does not have maximal value, then choosing $A$ is irrational.

In this statement of the decision rule, it gives a requirement of rationality.  But it can also be stated as advice-giving:  Don't choose an action if it has less value than an action of maximal value.  It is this advice-giving principle that is the primary target of Paul's challenges.

Epistemically transformative experience

Now let us turn to the apparent challenge to this orthodox version of decision theory that arises from epistemically transformative experiences.  In order for an agent to use the advice-giving principle stated at the end of the previous section, it seems that she must be able to calculate the value $V(A)$ of each action $A$ that is available to her; and, in order to do that, she must have access to her own subjective probability function $p$ and utility function $U$.  Thus, it seems, when an agent faces a decision problem in which the utility she assigns to a particular possible outcome of one of the possible actions is not accessible to her, she cannot follow the advice-giving principle of causal decision theory.  This is exactly the situation created by epistemically transformative experiences: if you face a decision problem in which one of the possible outcomes involves such an experience, you have no access to the phenomenal character of that experience, and since the phenomenal character of an experience in an essential factor in determining the utility you assign to it, you have no access to the utility you assign to that outcome.  Thus, you cannot follow the advice-giving principle of causal decision theory and you are unable to make the decision in a rational way.  Or so Paul contends.

In order to explore this challenge to orthodox decision theory, I'd like to consider a simpler sort of decision problem; one that doesn't involve epistemically transformative experiences, but which does involve apparently inaccessible utilities.  We'll see how causal decision theory can accommodate this simpler decision problem and ask whether we might use a similar technique to accommodate the sorts of decision problems that Paul has in mind.

Here is the decision problem: 

Room of Unknown Outcome  You must choose whether or not to enter the Room of Unknown Outcome.  In this room you will either be given £5, or £5 will be taken from you, but you do not know which.  If you do not enter, you will be given nothing and nothing will be taken away from you.

Thus, there are two actions: Enter and Don't Enter.  And, at least as we will initially frame the decision problem, there is just one state of the world---while it might seem that there is uncertainty, the initial framing of the problem locates that uncertainty as uncertainty about which utility function you have, rather than uncertainty about the way the world is.  Thus, the value you assign to Don't Enter is 0, while the value you assign to Enter is either the utility you assign to £5 or the utility you assign to -£5, but you do not know which, since you don't have access to your utility function---in order to know the utility that you assign to Enter, you must know what the outcome of entering the room will be.


There is no epistemically transformative experience involved in Room of Unknown Outcome: you have had experiences in the past that are similar enough to gaining £5 and losing £5 that you know what it would be like to have one of those experiences again.  The problem is that you do not know which of those two experiences you will have.  Nonetheless, the example shares with Paul's examples the lack of access to the agent's utility function.  How might we accommodate Room of Unknown Outcome 1 in orthodox causal decision theory?  The standard move is to reframe the uncertainty in the problem as uncertainty about the state of the world, rather than uncertainty about the utility function.  That is, we reframe the decision problem as follows.  There are still two actions: Enter and Don't Enter.  But there are now two states of the world: the first is the state in which you receive £5 upon entering the room (denote this Prize is £5); the second is the state in which you are divested of £5 upon entering the room (denote this Prize is -£5).  You then assign subjective probabilities to these two states.  Since the antecedents have no influence on the consequents--whether or not you enter the room has no effect on what the prize is--these amount to subjective probabilities over the consequents Prize is £5, Prize is -£5, etc.  Finally, you assign utilities to the conjunctions Enter & Prize is £5, Don't Enter & Prize is £5, etc.  Whereas there was uncertainty about the utilities that attached to the various act-state conjunctions in the original framing of the problem, there is no such uncertainty in this framing: for instance, $U$(Enter & Prize is £5) = $U$(£5), and you know the latter quantity since you've had the experience of gaining £5 before.  In this way, you might use orthodox decision theory to choose between Enter and Don't Enter.  For instance, if you are equally confident in Prize is £5 and Prize is -£5--so $p$(Prize is £5) = $p$(Prize is -£5) = 0.5--and if your utility is linear in money--so $U$(Enter & Prize is -£5) = $-U$(Enter & Prize is £5)$--then the expected utility of Enter is 0, which is the same as the expected utility of Don't Enter.  Thus, their values are the same and both actions are permissible.

Now, you might wonder how we can possibly set our subjective probabilities in Prize is £5 and Prize is -£5.  After all, the description of the example gives us so little information that it would seem that no particular probabilities are warranted.  This is a genuine problem; but it is not a new problem.  It is simply the problem of setting credences in the presence of very limited evidence.  Extreme subjective Bayesians say that, in such a situation, almost any probability function is permissible.  At the other end of the spectrum, objective Bayesians say that we should apply the Principle of Indifference and assign equal credence to each of the possibilities---thus, we assign a credence of 0.5 to Prize is £5 and to Prize is -£5.  Both approaches have their problems, but they are not peculiar to cases of ignorance about utility.  If I tell you that I have a handkerchief in my pocket that is blue or red, you must set your credence in each possibility in the presence of similarly impoverished evidence.

So we accommodate Room of Unknown Outcome in orthodox decision theory by considering a more fine-grained space of possible states of the world:  the crucial feature of this new space is that, in each of the new fine-grained states, enough information is specified in each of them that we know the utility we assign to act-state conjunctions $AS$.  We then use standard Bayesian techniques to set our credences in these new states and we apply orthodox decision theory.  We call this fine-graining strategy a redescription strategy, since it involves redescribing the decision problem so as to make it amenable to treatment within orthodox decision theory.  Might we use a similar strategy to accommodate decision problems that use epistemically transformative experience?  Let's take a simple example:

Vegemite You must choose whether or not to try Vegemite.

We assume that you haven't eaten Vegemite before.  So one of the possible actions---namely, the action of eating Vegemite---will result in an epistemically transformative experience.  As a result, before you make the choice, you will not know what it is like to eat Vegemite and thus you will not know the utility you assign to eating Vegemite.  We initially frame the problem, as we did above in the case of Room of Unknown Outcome, as involving ignorance about your utilities.  Thus, there is just one possible state of the world; there are two possible actions, Eat and Don't Eat; and while you know the utility of Don't Eat (conjoined with the one possible state of the world), you don't know the utility of Eat (conjoined with that state).  Thus, you cannot assess the value of Eat, and so cannot use orthodox decision theory to make your choice.  Or so Paul contends.

Inspired by the redescription strategy used above, we might try to reframe Vegemite as a case of ignorance about the world.  In Room of Unknown Outcome, we did not know what the prize would be; but, for each possible prize, we knew the utility of that prize; so we fine-grained the states of the world to specify the prize in that state.  In Vegemite, we do not know what the taste will be; but, you might hope, for each possible taste, we know the utility of experiencing that taste; so we fine-grain the states of the world to specify the taste in that state.  But things are not so straightforward.  In Room of Unknown Outcome, the possible prizes were specified in the original description of the decision problem, and they were all prizes of which we'd had similar experiences before.  This is not the case in Vegemite.  When we fine-grain the states of the world in Vegemite, which tastes should we include as possible?  Yahoo! Answers suggests the following for Vegemite: "fermented yeast that have puked and died", "salty beyond belief", "sucking on a rusty nail that has been soaking in salt water for over a year", "a little bit of salty heaven".  But even if we have had sufficiently similar experiences to these to know the utilities we would assign to them, we can't be sure that these are all of the possibilities; and we can't be sure that there aren't possibilities whose utilities we do not know because we have never had an experience that is sufficiently similar.  After all, there are two types of epistemically transformative experience:

• (Type I) You have in fact had an experience in the past that is phenomenologically similar to eating Vegemite. You know this, but you don't know which of your past experiences it is.  In this case, the experience of eating Vegemite is epistemically transformative because it teaches you which of your past experiences is phenomenologically similar to eating Vegemite.
• (Type II) You have not had an experience in the past that is phenomenologically similar to that of eating Vegemite.  You know this might be the case.  In this case, the experience of eating Vegemite introduces you to a completely new phenomenological experience and teaches you that eating Vegemite gives rise to that experience.

While it is clear how we can accommodate Type I epistemically transformative experiences using the fine-graining strategy, it is not so clear how to do that for Type II cases.  In a Type I case, we know the range of possible experiences to which eating Vegemite might give rise: so we can specify the range of fine-grained states of the world over which to distribute our probabilities; and these states of the world now specify enough detail for us to know the utilities that we assign to conjunctions of an action with one of those states.  In a Type II case, we do not know this range: so we cannot even specify the fine-grained possible states of the world, let alone distribute probabilities over them.

However, all is not lost.  Consider again the definition of the value of an act given above:$$V(A) = \sum_{S \in \mathcal{S}} p(S) U(AS)$$  And note that this may be rewritten as follows:$$V(A) = \sum_{u \in \mathrm{ran}(U)} u \times p(\mbox{Utility for $A$ is $u$})$$ where

• $\mathrm{ran}(U)$ is the range of the utility function $U$; that is, it is the set of values that $U$ takes;
• The proposition My utility for $A$ is $u$ is true at all and only those states $S$ such that $U(AS) = u$.

Thus, even if we cannot use the first definition of $V(A)$ to calculate its value because we don't know all the possible states of the world---perhaps because we don't know all the different possible experiences to which the action $A$ might give rise---we can nonetheless use the second definition of $V(A)$ to calculate its value providing we can assign probabilities to propositions of the form My utility for $A$ is $u$.

There are two issues to address before we can be confident that we have accommodated epistemically transformative experiences in orthodox decision theory.  The first we have met already: it is the worry that there is no rational way to assign probabilities to each of the possible states of the world when they are specified in this way.  How, for instance, am I to assign a probability to the proposition My utility for tasting Vegemite is 5?  As I said, we've met this problem before, at least in the case in which I have no evidence that bears on these propositions.  In such cases, some Bayesians will permit a large range of different probability functions, whereas others will specify a unique rational response to this paucity of evidence.

You might think that one of the usual problems with the latter response--namely, the language dependence objection to the Principle of Indifference--is particularly acute in the present case.  The Principle of Indifference says (at least) that an agent who lacks any evidence should distribute their credences equally over all the possibilities.  However, as is often pointed out, this gives rise to different credences depending on how you present the possibilities:  if you know that the handkerchief in my pocket is red or blue, you might apply the Principle of Indifference to the possibilities Red, Blue, in which case you'd assign 1/2 to Red; or you might apply that principle to the possibilities Red, Light Blue, Dark Blue, in which case you'd assign 1/3 to Red.  You might think that this problem is particularly apparent in the present case, where we are assigning probabilities to propositions such as My utility for $A$ is $u$, where we don't know how many states of the world make that proposition true.  For instance, suppose I know that my utility for tasting Vegemite is either -100, -50, 10, 20, or 30.  The Principle of Indifference tells me to assign a credence of 1/5 to each of these possibilities.  But I don't know how many possible tastes correspond to each of these possible utilites.  For all I know, it could be that there is just one possible taste that corresponds to a utility of -100, but fifteen possible tastes that correspond to a utility of -50.  If this were the case, you would wish my probability for -50 to be fifteen times greater than that for -100.

All of this is true.  But, again, it is not a new problem for Bayesian epistemology.  When I assign a probability of 0.5 to Red and 0.5 to Blue in the handkerchief case, I am well aware that these propositions are unlikely to carve nature at its joints; they are unlikely to respect the true symmetries in the world; I am well aware that, if one considers the true possible states of the world---if such a notion even makes sense---there may be twice as many at which Blue is true as there are at which Red is true.  But the mere existence of this possibility does not seem to undermine my assignment of 0.5 to each in this case.  Nor, I claim, should it undermine my assignment of 1/5 to each of -100, -50, 10, 20, 30 in the Vegemite case.

Of course, in many cases like Vegemite, you would not be in the state of complete ignorance I have been considering.  For instance, you've heard the testimony of friends about their experience of Vegemite; you've read the Yahoo! Answers thread with its poetic descriptions; you've watched your friends' faces as they bite into their first piece of Vegemite on toast; in short, you've gathered data about the utilities that others assign to the experience of eating Vegemite.  Surely this will affect the subjective probabilities you assign to the different possible utilities that you assign to that experience.  I think that's right.  However, Paul has two concerns about this evidence.  The first is that, in some cases of epistemically transformative experience, the relevant testimony is not reliable.  Of course, people have no reason to misreport their utilities for eating Vegemite, so the testimony in that case is likely to be reliable.  But there is strong pressure in some societies to report high utilities for becoming a parent whether or not one's utility truly is high, so the testimony in that case is likely to be less reliable.  Again, this is all true.  But again Bayesians have ways of incorporating evidence that is less than completely reliable.  When we use Bayes' Theorem to compute the probability of a hypothesis given some evidence, part of our calculation involves the probability of the evidence given the hypothesis.  It is at this stage that we can incorporate our doubts about the reliability of the testimony: we simply note that the probability that a person testifies to assigning high utility to becoming a parent given that he in fact assigns low utility to becoming a parent is non-zero.

Paul's second concern about such testimonial or behavioural evidence is that, in order to extrapolate from that evidence to your own case, you must solve the notorious problem of the reference class.  After all, in order to set your probability that you assign utility -100 to eating Vegemite, you do not simply take the proportion of people who assign that utility amongst all people whose utilities you know.  Rather, you take the proportion of people who assign that utility amongst all people whose utilities you know and who are sufficiently similar to you.  You are unlikely, for instance, to consider people who have been eating Vegemite since childhood, since they are unlikely to have similar utilities to yours.  The problem of the reference class is the problem of determining who is and who isn't sufficiently similar to you.  Again, this is surely a problem.  But it is a problem that haunts Bayesian epistemology independently of its use in decision theory and certainly independently of its application to decision problems that involve epistemically transformative experiences.  The same problem is faced by a doctor trying to set her credence in the efficacy of a particular drug for a particular patient: she knows the frequencies of its efficacy amongst various groups of patients; what she doesn't necessarily know is which of those groups contains the patients most relevantly similar to their current patient--indeed, it is not clear that there is even a fact of the matter to know in this case.

In order to use this final version of the redescription strategy---the version in which we assign probabilities to propositions of the form My utility for $A$ is $u$---it seems that we must know the range of possible utilities.  Paul worries that, in cases of epistemically transformative experiences, that isn't always possible.  I certainly agree that, as we saw above, it isn't always possible to know the range of possible experiences that might result in a case of epistemically transformative experience.  That was the lesson of distinguishing Type I from Type II cases of such experience: in Type I cases, you know the range of possible experiences; in Type II cases, you don't.  But that doesn't prevent you from knowing the range of possible utilities that these experiences might have, even in the Type II case.  After all, utilities are measured by real numbers, so we know all the possible utilities for any given action at any given state of the world: they are simply the real numbers.  Indeed, in nearly all cases of transformative experiences, we can narrow the range significantly.  For instance, however unpleasant Vegemite tastes, it will be more valuable than experiencing severe pain; and however good it tastes, it will not be as valuable as seeing a loved one happy.  So it seems that there is no problem in assuming that we know the range of possible utilities that may attach to epistemically transformative experiences.

I conclude that, while epistemically transformative experiences give rise to problems for decision-makers who hope to use the advice-giving versions of orthodox decision theory to make their decisions, they are problems that Bayesian epistemologists face already, and they are problems that already arise for decisions that do not involve epistemically transformative experience.  As we will see in the next post, this is not the case for personally transformative experience: to accommodate that, we will have to extend orthodox decision theory substantially.