Rule-Following and Constitutive Rules: A Reconciliation (Working paper)

I have finished a working paper on the topic of rule-following and constitutive rules. This is not an economic paper at all but rather one about social ontology and it makes use of some of the material I have posted on this blog. Comments are welcome of course!

The paper is here:

Rule-Following and Constitutive Rules: A reconciliation


Is the Choice of a Welfare Criterion a Matter of Opinion?

Noah Smith has a post on Gul and Pesendorfer’s 2005 much-discussed manifesto on the methodology of economics, especially regarding the rise of neuroeconomics. Philosophers of economics tend to compare Gul and Pesendorfer’s essay to Friedman’s 1953 article which provides an instrumentalist defense of the rationality assumption. Their article has generated a significant literature, notably a book edited by Schotter and Caplin. A recent discussion of the significance of Gul and Pesendorfer’s essay regarding the relationship between economics and psychology is provided by Don Ross in book Philosophy of Economics.

Noah Smith highlights two points. First, Gul and Psendorfer’ claim that only choice data are relevant in economics. Second, they argue against the idea that neuroeconomics and behavioral economics are relevant for welfare economics. Regarding the second point, he writes (my emphasis):

To be blunt, all welfare criteria seem fairly arbitrary and made-up to me. Data on choices do not automatically give you a welfare measure – you have to decide how to aggregate those choices. Why simply add up people’s utilities with equal weights to get welfare? Why not use the utility of the minimum-utility individual (a Rawlsian welfare function)? Or why not use a Nash welfare function? There seems no objective principle to select from the vast menu of welfare criteria already available. The selection of a welfare criterion thus seems like a matter of opinion – i.e., a normative question, or what GP call “social activism”. So why not include happiness among the possible welfare criteria? Why restrict our set of possible welfare criteria to choice-based criteria? I don’t see any reason, other than pure tradition and habit.

The notion that the choice of a welfare criterion is a matter of “opinion” seems to me somewhat odd. This is even more the case when “opinion” seems to be synonym with “normative question”. Are all normative issues matter of opinion? Is normative economics devoid of any objective or scientific basis? Or is science as a whole nothing but a matter of opinion?

This issue is even more difficult to discuss in the context of Gul and Pesendorfer’s essay because the latter are somehow heterodox in their view of welfare economics. Contrary to the received view, Gul and Pesendorfer claim that standard welfare economics is not normative economics. Rather, welfare analysis is “a tool for analyzing economic institutions and models” (p. 25 in Caplin and Schotter’s book). They actually reduce the welfare analysis to revealed preference and the Pareto criterion because “it is the only criterion that can be integrated with positive economic analysis” (p. 25). According to them, economists “use welfare analysis to identify the interest of economic agents and to ask whether the understanding of the institutional constraints on policies remains incomplete. This use of welfare analysis requires the standard definition of welfare” (p. 25, my emphasis).

In other words, what Gul and Pesendorfer are doing is to completely ground welfare economics in positive, revealed preference analysis. Welfare economics has no justification outside positive economics. I said above that this is somewhat heterodox because the choice of a welfare criterion is generally regarded as outside the domain of positive economics, or at least this was the view of the pioneers of the “new” welfare economics like Samuelson. However, the suggestion that positive economics imposes constraints on the choice of a welfare criterion is not new: in the 1930’s, the rejection of the then standard Utilitarian view of welfare was made on the basis of a “positive” claim that interpersonal comparisons of utility were outside the realm of science but instead depend on “value judgments”.

As I understand it, Noah Smith’s claim that the selection of a welfare criterion is “a matter of opinion” is that we cannot tie the latter to scientific theories and facts. We can study facts on the basis of the scientific method and reject scientific theories on the basis of evidence but normative issues cannot be settled in this way. This sounds reasonable and indeed that has been the received view in the philosophy of science for decades. The problem is that this view relies on a distinction between the positive and the normative (or between facts and values) which is too strong. Consider Gul and Psendorfer’s argument that links welfare analysis to the revealed preference approach of positive economics. What is problematic or at least debatable is not the idea that welfare analysis should be coherent with or informed by positive analysis. The problem is the tacit presupposition that revealed preference and choice data are the only acceptable scientific input in the analysis (Noah Smith’s first point). What is the status of this presupposition? Well, at the most basic level, it is purely conventional in the sense that it reflects some consensus among economists. In itself however, it is not empirically testable and seems to be nothing more than “a matter of opinion”.

Now, consider the other way around: can (and should) normative economics inform and constrain positive economics as Amartya Sen (among others) contends? Given the fact that positive economics is also grounded on conventional choices, there is absolutely no reason to reject this possibility. But wait: if everything is a matter of opinion (i.e. is conventional), what remains of science? The answer is simply that we must recognize that the scientific endeavor is constituted by values and conventional choices. The point is that these choices are not totally arbitrary though and that we are constantly arguing about them (philosophers of economics more explicitly than others). From this point of view, the choice of a welfare criterion is no more a matter of opinion than the choice of the relevant data for positive analysis. But this is or should be  a “justified” or “reasonably argued” opinion based on facts and theories, but also on ethical considerations. This is no more “social activism” (Gul and Pesendorfer’s term) than a methodological manifesto like Gul and Pesendorfer’s one.

Rules and Possible Worlds

Following my discussion of the rule concept that I started in previous posts, I will here briefly explore an intriguing possibility consisting in conceptualizing rules on the basis of “possible worlds” semantics. More specifically, I will define rules as (soft) constraints on possible worlds. For the intereste reader, this approach is pursued in more details in several papers by the philosopher Jaap Hage (see here and here).

In the previous posts, I have concluded that Searle’s distinction between constitutive rules and regulative rules is a linguistic rather than an ontological one.[1] I have also suggested that Epstein’s frame principles are formally analyzable as rules, already on the basis of a (informal) possible worlds reasoning. As a reminder, Searle and Epstein respectively suggest the following syntax for their constitutive rules and frame principles:

SCR         This X counts as Y in circumstances C

EFP         For any z, the fact “z is X” grounds the fact “z is Y”

By contrast, regulative rules have the generic “if… then” form:

R              If X, then Y

One may be easily lead astray by the fact that though formally equivalent, these definitions leave several things implicit. Consider EFP first. Its statement includes what I will call an object (z), facts or states of affairs (“z is X” and “z is Y”) and properties (X and Y). Quite the contrary, SCR only contains objects (X and Y) as well as a set of conditions C (which is only implicit in EFP). Finally, R is only about facts, though there must be an implicit statement about the set of conditions where R obtains.

The disentanglement of objects, facts and properties is required to see the formal identity of these three definitions. If I use upper letters X, Y, Z to denote properties and small letters a, b, c to denote objects then we have something like

∀a[X(a) → Y(a)]

This statement reads as ‘for any object a, if a has property X then it has property Y’. Consider for instance these two examples:

(a) Pieces of paper that have been engraved by the Federal Reserve are money.

(b) John has made six fouls, therefore he is fouled out.

In example (a), objects are (some) pieces of paper and properties are ‘to have been engraved by the Federal Reserve’ and ‘being money’. In example (b), the object is John and properties are ‘to be ascribed six fouls” and ‘to be fouled out’. Moreover, each X(a) and Y(a) denotes a fact of the type ‘this object has this property’. Finally, both statement are expressed against a background of conditions (e.g. in (a), we assume that we are in the USA, in (b) that John participates to a basketball game). This indicates that rules only work as parts of larger institutions, i.e. are connected with other rules that may specify conditions and implications. For instance, the property “being fouled out” implies something like “one is forbidden to return on the court for the game”. Ultimately, all rules are reducible to statements about what is possible and necessary (and conversely, impossible). This is at this point that it is useful to introduce a possible world framework.

Informally, a possible world can be seen as an exhaustive description of some counterfactual reality[2]. More formally, a possible world corresponds to a set of sentences (propositions and formulae) describing states of affairs, each sentence being ascribed a truth value (e.g. in some world, it may be true that the Golden State Warriors are the 2015 NBA champions but false that the finalist were the Cleveland Cavaliers; both statements are of course true in the actual world). Several kinds of constraints may restrict the range of possible worlds[3]. The most obvious one are logical constraints: for instance, it is not possible to p and not-p to be both true in the same world. More generally, the logical constraints are defined by the various axioms that are imposed on the underlying syntax. Similarly, physical constraints (e.g. a piece of metal cannot being heated without expanding) and conceptual constraints (e.g. an object cannot be a triangle and a circle at the same time) may be imposed on possible worlds. The point is that a set of constraints determine whether or not two or several states of affairs are compatible in a given world. Now consider the general statement of a rule

∀a[X(a) → Y(a)]

Suppose we define an axiom such that if the statement is valid (i.e. the rule actually exists), then the whole sentence combining the antecedent and the consequent is necessarily true (i.e. true in all possible worlds). For instance, take the following rule which is supposed to hold in any official basketball game:

“Any player who makes six fouls is fouled-out”.

Because this sentence is necessarily true, then there cannot be a possible world where a player has made six fouls but is still playing the game. The combination of these two states of affairs is ruled out because we have imposed as an axiom that if the above rule exists, then they cannot hold together. We can be more subtle however by adding an accessibility relation between possible worlds. The interpretation of the accessibility relation depends on the kind of logic we are using but in the present, it would state that any world w’ that is accessible from a world w should have the same set of valid rules (but the reverse needs not to be true – it depends on the property of the accessibility relation). But worlds non accessible from w could have a completely different set of rules.

This formal approach is thus helpful to see that virtually all rules work as constraints on possible worlds irrespective of their syntax. It can also serve as a basis to study the conditions for a set of rules for being consistent (see the papers linked to above). This is an important issue if we acknowledge that institutions are sets of rules. It is likely that for any given institution, some rules cannot be changed easily at the risk of leading to inconsistency, while others may be modified without engaging the coherence of the whole institutional edifice.


[1] In his book Making the Social World, Searle suggests an alternative criterion for distinguishing between these two kinds of rules. Regulative rules are identified to “standing directives” while constitutive rules consist in “standing declarations”. The former have only for function to bring about some form of behavior, while the latter make something the case by representing it as being the case. The distinction is interesting as an account of the different ways rules may be generated. It is not so clear that is helpful to distinguish different forms of rules though, if we consider that being self-referential is more or less a necessary condition for any rule to holds.

[2] Philosophers disagree regarding the nature of possible worlds. David Lewis was the most prominent proponent of a realist account according to which possible worlds are true worlds that exist in some alternative reality and that can discovered. Others like Saul Kripke hold that possible worlds are theoretical constructions where it is stipulated what is true according to them.

[3] Because they are build on the basis of a truth value function, Possible worlds models are said to be ‘semantic’. Most of the time (but not so much in economics), they are combined with a language (a syntax) responding to a logic articulated around several axioms: modal logic, deontic logic, epistemic or doxastic logic are the most discussed.