Is it Rational to be Bayesian Rational?

Most economists and many decision theorists equate the notion of rationality with Bayesian rationality. While the assumption that individuals actually are Bayesian rational has been largely disputed and is now virtually rejected, the conviction that Bayesianism defines the normative standard of rational behavior remains fairly entrenched among economists. However, even the normative relevance of Bayesianism has been questioned. In this post, I briefly survey one particular and interesting kind of argument that has been particularly developed by the decision theorist Itzhak Gilboa with different co-authors in several papers.

First, it is useful to start with a definition of Bayesianism in the context of economic theory: the doctrine according to which it is always rational to behave according to the axioms of Bayesian decision theory. Bayesianism is a broad church with many competing views (e.g. radical subjectivism, objective Bayesianism, imprecise Bayesianism…) but it will be sufficient to retain a generic characterization through the two following principles:

Probabilism: Bayesian rational agents have beliefs that can be characterized through a probability function whose domain is some state space.

Expected Utility Maximization: The choices of Bayesian rational agents can be represented by the maximization of the expectation of a utility function according to some probability function.

Gilboa’s critique of Bayesianism is uniquely concerned with probabilism though some of its aspects could be easily extended to the expected utility maximization principle. Probabilism can itself be characterized as the conjunction of three tenets:

(i) Grand State Space: each atom (“state of nature”) in the state space is assumed to resolve all uncertainty, i.e. everything that is relevant for the modeler is specified, included all causal relationships. Though in Savage’s version of Bayesian decision theory, states of nature where understood as “small worlds” corresponding to some coarse partition of the state space, in practice most economists implicitly interpret states of nature as “large worlds”, i.e. as resulting from the finest partition of the state space.

(ii) Prior Probability: Rational agents have probabilistic beliefs over the state space which are captured by a single probability measure.

(iii) Bayesian updating: In light of new information, rational agents update their prior to a posterior belief according to Bayes’s rule.

While the third tenet may be disputed, included within the realm of Bayesianism (see for instance Jeffrey’s probability kinematics or views entertained by some objective Bayesians), it is the first two that are targeted by Gilboa. More exactly, while each tenet taken separately seems pretty reasonable normatively speaking, problems arise as soon as one decides to combine them.

Consider an arbitrary decision problem where it is assumed (as economists routinely do) that all uncertainty is captured through a Grand State Space. Say, you have to decide between choosing to bet on what is presented to you as a fair coin falling on heads and betting on the fact that the next winner of the US presidential will be a Republican. There seem to be only four obvious states of nature: [Heads, Republican], [Heads, Democrat], [Tail, Republican], [Tail, Democrat]. Depending on your prior beliefs that the coin toss will fall on Heads (maybe a 1:1 odd) and that the next US president will be a Republican (and assuming monotonic preferences in money), your choice will reveal your preference for one of the two bets. Even if ascribing probabilities to some of the events may be difficult, it seems that the requirements of Bayesian rationality cannot be said to be unreasonable here. But matters are actually more complicated because there are many things that may causally affect the likelihood of each event. For instance, while you have been said that the coin is fair, maybe you have reason to doubt this affirmation. This will depend for instance on who has made the statement. Obviously, the result of the next US presidential elections will depend on the many factual and counterfactual events that may happen. To form a belief about the result of the US elections not only you have to form a belief over these events but also over the nature of the causal relationships between them and the result of the US election. Computationally, the task quickly becomes tremendous as the number of states of nature to consider is quite huge. Assuming that a rational agent should be able to assign a prior over all of them is normatively unreasonable.

An obvious answer (at least for economists and behaviorists-minded philosophers) is to remark that prior beliefs need not be “in the mind” of the decision-maker. What matters is that the betting behavior of the decision-maker reveals preferences over prospects that can be represented by a unique probability measure over as larger a state space as needed to make sense of it. There are many things to be said against this standard defense but for the sake of the argument we may momentarily accept it. What happens however of the behavior of the agents fail to reveal the adequate preferences? Must we conclude then that the decision-maker is irrational? A well-known case leading to such questions is Ellsberg’s paradox. Under a plausible interpretation, the latter indicates that most actual agents reveal through their choices an aversion for probabilistic ambiguity which directly led to the violation of the independence axiom of Bayesian decision theory. In this case, the choice behavior of agents cannot be consistently represented by a unique probability measure. Rather than arguing that such a choice behavior is irrational, a solution (which I have already discussed here) is to adopt the Grand State Space approach. It is then possible to show that with an augmented state space there is nothing “paradoxical” in Ellsber’s paradox. The problem however with this strategy is twofold. On the one hand, many choices are “unobservable” by definition, which fits uneasily in the behaviorist interpretation of Bayesian axioms. On the other hand,  it downplays the reasons that explain the choices that actual agents are actually making.

To understand this last point, it must be acknowledged that Bayesianism defines rationality merely in terms of consistency with respect to a set of axioms. As a result, such an approach completely disregards the way agents form their beliefs (as well as their preferences) and – more importantly – abstains from making any normative statement regarding the content of beliefs. “Irrational” beliefs are merely beliefs that fail to qualify for a representation through a unique probability measure. Now, consider whether it is irrational to fail or to refuse to have such beliefs in cases where some alternatives but not others suffer from probabilistic ambiguity. Also, consider whether it is irrational to firmly believe (eventually to degree 1) that smoking presents no risk for health. Standard Bayesianism will answer positively in the first case but negatively in the second. Not only this is unintuitive but it also seems to be pretty unreasonable. Consider the following alternative definition of rationality proposed by Gilboa:

A mode of behavior is irrational for a decision maker, if, when the latter is exposed to the analysis of her choices, she would have liked to change her decision, or to make different choices in similar future circumstances.

This definition of rationality appeals to the reflexive abilities of human agents and, crucially, to our capacity to motivate our choices through reasons. This suggests first that the axioms of Bayesian decision theory can be submitted both as reasons to make specific choices but also has the subject of the normative evaluation. This also indicates that whatever may be thought of these axioms, Bayesianism lacks an adequate account of beliefs formation. In other words, Bayesianism cannot pretend to constitute a normative theory of rationality because it does not offer any justification neither for the way an agent should partition the state space nor for deciding which prior to adopt. The larger the state space is made to capture all the relevant features explaining an agent’s prior, the lesser it seems reasonable to expect rational agents to be able or to be willing to entertain such a prior.


Behavioral Welfare Economics and the ‘View from Nowhere’

As Richard Thaler has just received a well-deserved ‘Nobel prize’ for his pioneering contribution in behavioral economics and behavioral finance, many commentators are reflecting over the scientific and ethical significance of Thaler’s work and more generally of behavioral economics regarding policy matters. Thaler is of course well-known for having developed with legal scholar Cass Sunstein the whole nudge idea as well as the seemingly oxymoronic “libertarian paternalism” notion. In a somehow challenging review of Thaler’s contribution, Kevin Bryan expresses some worries regarding the ethical implications relating to the nudging practice:

“Let’s discuss ethics first. Simply arguing that organizations “must” make a choice (as Thaler and Sunstein do) is insufficient; we would not say a firm that defaults consumers into an autorenewal for a product they rarely renew when making an active choice is acting “neutrally”. Nudges can be used for “good” or “evil”. Worse, whether a nudge is good or evil depends on the planner’s evaluation of the agent’s “inner rational self”, as Infante and Sugden, among others, have noted many times. That is, claiming paternalism is “only a nudge” does not excuse the paternalist from the usual moral philosophic critiques! Indeed, as Chetty and friends have argued, the more you believe behavioral biases exist and are “nudgeable”, the more careful you need to be as a policymaker about inadvertently reducing welfare. There is, I think, less controversy when we use nudges rather than coercion to reach some policy goal. For instance, if a policymaker wants to reduce energy usage, and is worried about distortionary taxation, nudges may (depending on how you think about social welfare with non-rational preferences!) be a better way to achieve the desired outcomes. But this goal is very different that common justification that nudges somehow are pushing people toward policies they actually like in their heart of hearts. Carroll et al have a very nice theoretical paper trying to untangle exactly what “better” means for behavioral agents, and exactly when the imprecision of nudges or defaults given our imperfect knowledge of individual’s heterogeneous preferences makes attempts at libertarian paternalism worse than laissez faire.”

As Noah Smith however rightly notes, that is not a problem that is peculiar to the nudge approach nor more generally to behavioral welfare economics:

“There are, indeed, very real problems with behavioral welfare economics. But the same is true of standard welfare economics. Should we treat utilities as cardinal, and sum them to get our welfare function, when analyzing a typical non-behavioral model? Should we sum the utilities nonlinearly? Should we consider only the worst-off individual in society, as John Rawls might have us do?
Those are nontrivial questions. And they apply to pretty much every economic policy question in existence. But for some reason, Kevin chooses to raise ethical concerns only for behavioral econ. Do we see Kevin worrying about whether efficient contracts will lead to inequality that’s unacceptable from a welfare perspective? No. Kevin seems to be very very very worried about paternalism, and generally pretty cavalier about inequality.”

According to Robert Sugden, what standard and behavioral welfare economics have in common is that they endorse – if implicitly – the ‘view from nowhere’ in ethics. The latter – whose name has been coined by Thomas Nagel – is the view that goodness or rightness is to be judged according to criteria set by some exogenous impartial or benevolent dictator. In welfare economics, the criteria imposed by the benevolent dictator are instantiated through a (Arrowian or Bergsonian) social welfare function (SWF). An SWF is itself traditionally obtained through the definition of the relevant informational basis (which kind of information should be taken into account in the normative analysis) and aggregation rule (how to use this information to make social evaluations and comparisons).

In this perspective, it is right that standard and behavioral welfare economics share a feature that some may regard as problematic: the very definition of the relevant SWF is left to a putatively impartial and benevolent being who is thought to lay outside the group of persons to whom the normative evaluation is addressed. The problem with the view from nowhere is that it creates a divide between the one making the impartial ethical judgments and evaluations and the persons whose welfare, rights and so on, are the objects of these judgments and evaluations. That means that welfare economics as a whole is somehow paternalistic in its very foundations.  Arguably there is a difference between standard and behavioral welfare economics: the latter is more restrictive regarding the relevant informational basis. In the classical preference-satisfaction account of welfare that most welfare economists endorse (including most but not all behavioral economists), preferences whatever their content are considered as relevant from a welfare point of view. Behavioral welfare economists argue however that it is legitimate to ignore preferences that are revealed by choices resulting from cognitive biases, lack of awareness, errors and so on. This only contributes to strengthen the paternalistic tendencies of welfare economics. In other words, the difference between standard and behavioral welfare economics is not one of nature but rather “merely” of degree.

Ultimately, it is important to acknowledge that welfare economics as a whole is not fitted to discuss most issues related to (libertarian) paternalism, especially the problems of manipulation and autonomy. Welfare economics is nowadays essentially a theoretical framework to make social evaluations given exogenous welfare criteria but cannot be a substitute for moral and ethical reasoning (though the related social choice approach can be a way to reflect on ethical problems).

Parfit on How to Avoid the Repugnant Conclusion (And Some Additional Personal Considerations)

Derek Parfit, one of the most influential contemporary philosophers, died last January. The day before his death, he submitted what seems to be his last paper to the philosophy journal Philosophy and Public Affairs. In this paper, Parfit tackles the famous “non-identity problem” that he has himself settled in Reasons and Persons almost 35 years ago. Though unachieved, the paper is quite interesting because it appears to offer a way to avoid the not less famous “repugnant conclusion”. I describe below Parfit’s tentative solution and also add some comments on the role played by moral intuitions in Parfit’s (and other moral philosophers’) argumentation.

Parfit is concerned with cases where we have to compare the goodness of two or more outcomes where different people exist across these outcomes. Start first with Same Number cases, i.e. cases where at least one person exists in one outcome but no in the other but where the total number of people is the same. Example 1 is an instance of such a case (numbers denote quality of life according to some cardinal and interpersonally comparable measure):

Example 1

Outcome A Ann 80 Bob 60 ——–
Outcome B ——— Bob 70 Chris 20
Outcome C Ann 20 ——— Chris 30


How should we compare these three outcomes? Many moral philosophers entertain one kind or another of “person-affecting principles” according to which betterness or worseness necessarily depend on some persons being better (worse) in an outcome than in another one. Consider in particular the Weak Narrow Principle:

Weak Narrow Principle: One of two outcomes would be in one way worse if this outcome would be worse for people.


Since it is generally accepted that we cannot make someone worse by not making her exist, outcome A should be regarded as worse (in one way) than outcome B by the Weak Narrow Principle. Indeed, Bob is worse in A than in B while the fact that Ann does not exist in B cannot make her worse than in A (even though Ann would have a pretty good life if A were to happen). By the same reasoning, C should be considered as worse than A and B worse than C. Thus the ‘worse than’ relation is not transitive. Lack of transitivity may be seen as dubious but is not in itself sufficient to reject the Weak Narrow Principle. Note though that if we have to compare the goodness of the three outcomes together, we are left without any determinate answer. Consider however:

Example 2

Outcome D Dani 70 Matt 50 ——– ——–
Outcome E ——— Matt 60 Luke 30 ——–
Outcome F ——— ——— Luke 35 Jessica 10


According to the Weak Narrow Principle, D is worse than E and E is worse than F. If we impose transitivity on the ‘worse than’ relation, then D is worse than F. Parfit regards this kind of conclusion as implausible. Even if we deny transitivity, the conclusion than E is worse than F is also hard to accept.

Given that the Weak Narrow Principle leads to implausible conclusion in Same Number cases, it is desirable to find alternative principles. In Reasons and Persons, Parfit suggested adopting impersonal principles that do not appeal to facts about what would affect particular people. For instance,

Impersonal Principle: In Same Number cases, it would be worse if the people who existed would be people whose quality of life would be lower.


According to this principle, we can claim that F is worse than E which is worse than D. Obviously, ‘worse than’ is transitive. What about Different Number cases (i.e. when the number of people who exist in one outcome is higher or lower than in another one)? In Reasons and Persons, Parfit originally explored an extension of the Impersonal Principle:

The Impersonal Total Principle: It would always be better if there was a greater sum of well-being.


Parfit ultimately rejected this last principle because it leads to the Repugnant Conclusion:

The Repugnant Conclusion: Compared with the existence of many people hose quality of life would be very high, there is some much larger number of people whose existence would be better, even though these people’s lives would be barely worth living.


In his book Rethinking the Good, the philosopher Larry Temkin suggests avoiding the repugnant conclusion by arguing that the ‘all things considered better than relation’ is essentially comparative. In other words, the goodness of a given outcome depends on the set of outcomes with which it is compared. But this has the obvious consequence that the ‘better than’ relation is not necessarily transitive (Temkin claims that transitivity applies only to a limited part of our normative realm). Parfits instead sticks to the view that goodness is intrinsic and suggests an alternative approach through another principle:

Wide Dual Person-Affecting Principle: One of two outcomes would be in one way better if this outcome would together benefit people more, and in another way better if this outcome would benefit each person more.


Compare outcomes G and H on the basis of this principle:

Outcome G: N persons will exist and each will live a life whose quality is at 80.

Outcome H: 2N persons will exist and each will live a life whose quality is at 50.


According to the Wide Dual Person-Affecting Principle, G is better than H in at least one way because it benefits each person more, assuming that you cannot be made worse by not existing. H may be argued to be better than G on another way, by benefiting people more, at least on the basis of some additive rule. Which outcome is all things considered better remains debatable. But consider

Outcome I: N persons will exist and each will live a life whose quality is at 100.

Outcome J: 1000N persons will exist and each will live a life whose quality is at 1.


Here, although each outcome is better than the other on one respect, it may be plausibly claimed that I is better all things considered because the lives in J are barely worth living. This may be regarded as sufficient to more than compensate for the fact that the sum of well-being is far superior in J than in I. This leads to the following conclusion:

Analogous Conclusion: Compared with the existence of many people whose lives would be barely worth living, there is some much higher quality of life whose being had by everyone would be better, even though the numbers of people who exist would be much small.

This conclusion is consistent with the view that goodness is intrinsic and obviously avoids the repugnant conclusion.


I would like to end this post with some remarks with the role played by moral intuitions in Parfit’s reasoning. This issue had already came to my mind when reading Partit’s Reasons and Persons as well as Temkin’s Rethinking the Good. Basically, both Parfit and Temkin (and many other moral philosophers) ground their moral reasoning on intuitions about what is good/bad or right/wrong. For instance, Parfit’s initial rejection of impersonality principles in Reasons and Persons was entirely grounded on the fact that they seem to lead to the repugnant conclusion which Parfit regarded as morally unacceptable. The same is true for Temkin’s arguments against the transitivity of the ‘all things considered better than’ relation. Moral philosophers seem mostly to use a form of backward reasoning about moral matters: take some conclusions as intuitively acceptable/unacceptable or plausible/implausible and then try to find principles that may rationalize our intuitions about these conclusions.

As a scholar in economics & philosophy with the background of an economist, this way of reasoning is somehow surprising me. Economists who are thinking about moral matters are generally doing so from a social choice perspective. The latter almost completely turns the philosopher’s reasoning on its head. Basically, a social choice theorists will start from a small set of axioms that encapsulate basic principles that may be plausibly regarding as constraints that should bind any acceptable moral view. For instance, Pareto principles are generally imposed because we take as a basic moral constraint the fact that everyone is better (in some sense) in a given outcome than in another one make the former better than the latter. The social choice approach then consists in determining which social choice functions (i.e. moral views) are compatible with these constraints. In most of the case, this approach will not be able to tell which moral view is obligatory; but it will tell which moral views are and are not permissible given our accepted set of constraints. The repugnant conclusion provides a good illustration: in one of the best social choice treatment of issues related to population ethics, John Broome (a philosopher but a former economist) rightly notes that if the “repugnant” conclusion follows from acceptable premises, then we should not reject it on the ground that we regarded as counterintuitive. The same is true for transitivity: the fact that it entails counterintuitive conclusion is not sufficient to reject it (at least, independent argument for rejection are needed).

There are two ways to justify the social choice approach to moral matters. The first is the fact that we generally have a better understanding of “basic principles” than of more complex conclusions that depend on a (not always well-identified) set of premises. It is far easier to discuss the plausibility of transitivity or of Pareto principles in general than to assess moral views and their more or less counterintuitive implications. Of course, we may also have a poor understanding of basic principles but the attractiveness of the social choice approach is precisely that it helps to focus the discussion on axioms (think of the literature on Arrow’s impossibility theorem). The second reason to endorse the social choice approach on moral issues is that we now start to understand where our moral intuitions and judgments are coming from. Moral psychology and experimental philosophy tend to indicate that our moral views are deeply rooted in our evolutionary history. Far from vindicating them, this should quite the contrary encourage us to be skeptical about their truth-value. Modern forms of moral skepticism point out that whatever the ontological status of morality, the naturalistic origins of moral judgments do not guarantee and actually make highly doubtful that whatever we believe about morality is epistemically well-grounded.