Murray Rothbard’s theory of demonstrated preference is not explicit enough for my taste, and hence I hereby endeavor to make it more explicit. The goal of Rothbard’s theory is to develop a weak, operational notion of preference which can be used to ground utility and welfare judgments in a “value-free” way, without importing a heavy metaphysics or ethics, but still delivering important economic welfare theorems such as “voluntary trade leaves all participants better off”, etc. The theory comes from his awesome paper, “Toward a Reconstruction of Utility and Welfare Economics”.
This blog post records the main results of an enlightening conversation I had with Jade, who led me to notice that the precisification was needed and pointed out the oddity about exchange and the vagueness of “disturbance”, as well as the core idea of the HDRT.
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| Infographic based on this blog post (Nano Banana) |
Contents:
Rothbard’s statement
As stated by Rothbard, the concept is as follows (p. 2):
Human action is the use of means to arrive at preferred ends. Such action contrasts to the observed behavior of stones and planets, for it implies purpose on the part of the actor. Action implies choice among alternatives. Man has means, or resources, which he uses to arrive at various ends; these resources may be time, money, labor energy, land, capital goods, and so on. He uses these resources to attain his most preferred ends. From his action, we can deduce that he has acted so as to satisfy his most highly valued desires or preferences.
The concept of demonstrated preference is simply this: that actual choice reveals, or demonstrates, a man’s preferences; that is, that his preferences are deducible from what he has chosen in action. Thus, if a man chooses to spend an hour at a concert rather than a movie, we deduce that the former was preferred, or ranked higher on his value scale. Similarly, if a man spends five dollars on a shirt we deduce that he preferred purchasing the shirt to any other uses he could have found for the money. This concept of preference, rooted in real choices, forms the keystone of the logical structure of economic analysis, and particularly of utility and welfare analysis.
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| Comic based on the core argument of Rothbard’s paper (Nano Banana) |
Preliminary objections dismissed
Even before making it more precise, it may seem that this concept of preference is simply wrong, and cannot serve as a foundation for determining utility or welfare.
- Regrets: People often do things that, in natural language, we would say that they did not prefer to do, in view of the fact that afterwards, they regretted doing them.
- Addiction: Addicts are said to make choices “compulsively”, which means they don’t really want to do them in some sort of true way which is more important than whatever sort of ‘wanting’ governs their actual action.
- Ignorance: Even if people are always doing the best action they can think of, sometimes there are actions that they simply don’t know are possible, and which they would choose to do if they knew about them, and it seems that those better possible actions are the actions that they really prefer to do, rather than the ones that they actually do.
- Weakness: Sometimes people already know of better actions that they would do if they could do them, but they don’t do those actions because they lack the resources, or the physical strength, or some other prerequisite for the action, and hence it seems that those actions-lacking-means are the actions that are truly preferred, rather than the actions-actually-done.
- Equal outcomes: It seems that the way that we speak of actions in natural language allows for situations where the same world-state W can be caused either by an action A being done, by an action B being left undone, or by an action C being done in violation of someone’s preference. If the outcome is the same, the action-preference structure can seem irrelevant to whether anyone prefers the outcome, and it can seem that action-preferences cannot be really as important as outcome-preferences.
These five objections are dismissed rather than answered because the demonstrated-preference economist will only answer them with a confession of poverty. The demonstrated-preference economist admits that such phenomena do exist in the world as described by natural language, and that they are not accounted for by his demonstrated-preference theory. Nevertheless, it is the demonstrated-preference economist’s assessment that there is no better, richer theory that can capture all of these phenomena without importing heavy metaphysical or ethical assumptions that are not suitable for value-free economic theory. So the demonstrated-preference economist simply confesses our poverty regarding the pursuit of a richer theory that can capture all of these phenomena, and gives up on such a pursuit. Nevertheless, the demonstrated-preference economist finds that his theory can derive many true and interesting theorems about the satisfaction of preference so-understood, which motivates his continued enterprise. However, in order to continue the demonstrated-preference enterprise in such a way as to be explicit enough for Thiago’s taste, a precisification of the theory is in order.
Precisification
Before stating the concept, Rothbard repeats his usual action axiom, that “human action is the use of means to arrive at preferred ends”. In doing this, I take him to be, among other things, taking the distinction between voluntary and involuntary behavior as a primitive, where only voluntary behaviors can be actions. Then we might think that demonstrated preference is exhausted by the following condition:
VBDP: If, at time T, an agent S exhibits a behavior B voluntarily, then S demonstrates a preference for engaging in B at T.
Rothbard clearly accepts VBDP, but as stated, VBDP does not suffice to get the conclusions Rothbard wants. For Rothbard certainly wants it to follow from the definition of demonstrated preference that aggression leaves the victim worse off, and there is nothing in VBDP that allows deriving this. So I think Rothbard needs to supplement VBDP with an additional condition:
PPDP: At every time T, every agent S demonstrates a preference for continuing to possess, without any unconsented disturbance from any other agent, all goods that S currently legitimately owns and is not currently in the process of giving away, trading away, or throwing away.
And I think that that’s enough to get Rothbard’s intended results, as I will show next, but it also raises some questions, as I will show after that.
Derivation of Rothbard’s results
I contend that together, PPDP and VBDP exhaust Rothbard’s concept of demonstrated preference, and they get the results Rothbard wants:
- Aggression Result: All aggression leaves the victim worse off, via PPDP.
- Trade Result: Voluntary trade leaves all participants better off, via VBDP.
This suffices to get Rothbard’s laissez-faire result as soon as the Unanimity Rule is added, namely (p. 23):
Unanimity Rule: We can only say that “social welfare” (or better, “social utility”) has increased due to a change, if no individual is worse off because of the change (and at least one is better off).
The Aggression Result and the Trade Result, combined with the Unanimity Rule, yield the Laissez-Faire Result:
- Laissez-Faire Result: All-and-only actions that do not interfere upon legitimate private property can be said to increase social utility.
And this was the intent.
Questions, oddities, and worries
However, the precisification leaves us with some questions, oddities, and worries.
VBDP oddity: Interpersonal exchange not better than autistic exchange?
One oddity about the Trade Result is that while it says trade leaves everyone better off, it seems to make it illegitimate to say voluntary trade leaves you more better off than voluntarily refraining from engaging in trade. After all, either kind of choice is a voluntary behavior, and by VBDP, increases welfare; and as Rothbard emphasizes, there are no magnitudes of preference to be compared. But certainly there seem to be economic theorems to the effect that trading is a better means to people’s ends than refraining from trade; so I should like to see a reconciliation of this.
PPDP questions and worries
The clarification that PPDP is needed for the results also leaves us with some questions that Rothbard did not raise or address:
1. Legitimately owned goods
PPDP introduces a concept of “legitimately owned goods”. It is necessary to talk about legitimate ownership rather than mere possession, or else Rothbard’s laissez-faire result does not follow as he intended it. Is this concept legitimate in economics? Is it precise enough, and is it wertfrei?
2. Consent and disturbances
PPDP introduces a concept of “unconsented disturbance”. This requires further precisification of “disturbance” and “consent”. These concepts seem to be vague and, to a large extent, culturally relative. Can they be made precise enough for economics?
3. Harmless Death Ray Theorem
We should also like an adequately formal theory of how actions play out in time, so as to avoid what I’ll call the Harmless Death Ray Theorem (HDRT), as follows. Suppose time is discrete, i.e., for the temporal ordering relation ≺, we have forward-discreteness [∀x∀y(x ≺ y → ∃z(x ≺ z ∧ z ⪯ y ∧ ¬∃u(x ≺ u ∧ u ≺ z)))] and backward-discreteness [∀x∀y(y ≺ x → ∃z(z ≺ x ∧ y ⪯ z ∧ ¬∃u(z ≺ u ∧ u ≺ x)))]. Suppose further that over this discrete temporal order, we have “atomic actions”: at time t1 the action has not yet begun, and at the immediately next time t2, the action has already been completed. Then if we allow that acts of aggression can be atomic actions (for color, we can call an atomic act of aggression a “death ray”), it seems that PPDP cannot allow there to be a preference against these atomic acts of aggression, since at t1 the destroyer has not yet done anything, and at t2 the victimized owner cannot demonstrate a preference for owning his property, which is already gone (so paradoxically, the “death ray” is proved “harmless”, since it does not reduce welfare). Clearly we do not want the HDRT to follow. Is preference theory committed to the density of time, and the non-existence of atomic actions? Or should we instead reformulate the preference conditions to be forward-looking rather than at-an-instant? Does this not, in some way, reintroduce the constancy assumption which Rothbard dreaded?
4. Irrelevance worries
PPDP seems to raise some worries about demonstrated preference having nothing to do with preference in natural language, making any concept of welfare derived from it dubious as being truly a concept of welfare as we would think of it in natural language.
Some of these worries are mere restatements of the preliminary objections that we had dismissed earlier, which tend to resurface when PPDP is stated. For instance, suppose that relinquishing your property requires performing some action, call it an act of forfeiture, which, for whatever reason, you haven’t been able to afford to do recently, but which you will do as soon as you can afford to. Is it fair to say that you demonstrate a preference to hold onto your property at every moment until you manage to perform the act of forfeiture? Aren’t you instead glad it was taken off your hands, if it was?
But others of these worries are independent of the preliminary objections and exclusive to PPDP. For instance, owners can own property that they are far away from, and currently not consciously aware of. Can they really be demonstrating any preference regarding their property just by the fact that they own it? Aren’t you instead making a forward-looking constancy assumption that, since they own the property now, then it must be true that, later, when they find out that their property was harmed, they will feel bad about this?
Conclusion
I hope to, at some point, develop a version of demonstrated-preference theory that comes with a solution to the questions, oddities, and worries above. For now, the goal was simply to record my precisification and the fact that these worries are raised from it. Rothbard’s paper was very inspiring and interesting, and I should like to see it developed into a truly reconstructed welfare theory, vindicating the Laissez-Faire Result and its wertfrei nature, if that can be done.
Postcript: Admittedly, it would be closer to the text if we could somehow derive PPDP from VBDP. I am not sure how to do this, but assuming private property is conceived of in Rothbard’s libertarian way, I think maybe it can be done by means of an ontology of “purposes”, as sketched here. For prior work on analysis of demonstrated preference, see this paper, which was pointed out to me by Dabchick.
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