Archive for the ‘economics’ Category

Strong Independence in Decision Theory

Thursday, 21 July 2016

In the course of some remarks on Subjective Probability by Richard C. Jeffrey, and later in defending a claim by Gary Stanley Becker, I have previously given some explanation of the model of expected-utility maximization and of axiomata of independence.

Models of expected-utility maximization are so intuïtively appealing to some people that they take one of these models to be peculiarly rational, and deviations from any such model thus to be irrational. I note that the author of a popular 'blog seems to have done just that, yester-day.[0]

My own work shows that quantities cannot be fitted to preferences, which pulls the rug from under expected-utility maximization, but there are other problems as well. The paradox that the 'blogger explores represents a violation of the strong independence axiom. What I want to do here is first to explain again expected-utility maximization, and then to show that the strong independence axiom violates rationality.


A mathematical expectation is what people often mean when they say average — a probability-weighted sum of measures of possible outcomes. For example, when a meteorologist gives an expected rainfall or an expected temperature for to-morrow, she isn't actually telling you to anticipate exactly that rainfall or exactly that temperature; she's telling you that, given observed conditions to-day, the probability distribution for to-morrow has a particular mean quantity of rain or a particular mean temperature.

The actual mathematics of expectation is easiest to explain in simple cases of gambling (which is just whence the modern, main-stream theories of probability itself arose). For example, let's say that we have a fair coin (with a 50% chance of heads and a 50% chance of tails); and that if it comes-up heads then you get $100, while if it comes-up tails then you get $1. The expected pay-out is .5 × $100 + .5 × $1 = $50.50 Now, let's say that another coin has a 25% chance of coming-up heads and a 75% chance of coming-up tails, and you'd get $150 for heads and $10 for tails. Its expected pay-out is .25 × $150 + .75 × $10 = $45 More complicated cases arise when there are more than two possible outcomes, but the basic formula is just prob(x1m(x1) + prob(x2m(x2) + … + prob(xnm(xn) where xi is the i-th possible outcome, prob(xi) is the probability of that i-th possible outcome, and m(xi) is some measure (mass, temperature, dollar-value, or whatever) of that outcome. In our coin-flipping examples, each expectation is of form prob(headspayout(heads) + prob(tailspayout(tails)

One of the numerical examples of coin-flips offered both a higher maximum pay-out ($150 v $100) and a higher minimum pay-out ($10 v $1) yet a lower expected pay-out ($45 v $50.50). Most people will look at this, and decide that the expected pay-out should be the determining factor, though it's harder than many people reälize to make the case.

With monetary pay-outs, there is a temptation to use the monetary unit as the measure in computing the expectation by which we choose. But the actual usefulness of money isn't constant. We have various priorities; and, when possible, we take care of the things of greatest priority before we take care of things of lower priority. So, typically, if we get more money, it goes to things of lower priority than did the money that we already had. The next dollar isn't usually as valuable to us as any one of the dollars that we already had. Thus, a pay-out of $1 million shouldn't be a thousand times as valuable as a pay-out of $1000, especially if we keep in-mind a context in which a pay-out will be on top of whatever we already have in life. So, if we're making our decisions based upon some sort of mathematical expectation then, instead of computing an expected monetary value, we really want an expected usefulness value, prob(x1u(x1) + prob(x2u(x2) + … + prob(xnu(xn) where u() is a function giving a measure of usefulness. This u is the main-stream notion of utility, though sadly it should be noted that most main-stream economists have quite lost sight of the point that utility as they imagine it is just a special case of usefulness.

A model of expected-utility maximization is one that takes each possible action aj, associates it with a set of probabilities {prob(x1|aj),prob(x2|aj),…,prob(xn|aj)} (the probabilities now explicitly noted as conditioned upon the choice of action) and asserts that we should chose an action ak which gives us an expected utility prob(x1|aku(x1) + prob(x2|aku(x2) + … + prob(xn|aku(xn) as high or higher than that of any other action.

If there is a non-monetary measure of usefulness in the case of monetary pay-outs, then there is no evident reason that there should not be such a measure in the case of non-monetary pay-outs. (And, likewise, if there is no such measure in the case of non-monetary pay-outs, there is no reason to suppose one in the case of monetary pay-outs, where we have seen that the monetary pay-out isn't really a proper measure.) The main-stream of economic theory runs with that; its model of decision-making is expected-utility maximization.

The model does not require that people have a conscious measure of usefulness, and certainly does not require that they have a conscious process for arriving at such a measure; it can be taken as a model of the gut. And employment of the model doesn't mean that the economist believes that it is literally true; economists across many schools-of-thought regard idealizations of various sorts as approximations sufficient for their purposes. It is only lesser economists who do so incautiously and without regard to problems of scale.


But, while expected-utility maximization may certainly be regarded as an idealization, it should not be mistaken for an idealization of peculiar rationality nor even for an idealization of rationality of just one variety amongst many. Expected-utility maximization is not rational even if we grant — as I would not — that there is some quantification that can be fitted to our priorities.

Expected-utility maximization entails a proposition that the relevant expectation is of potential outcomes which are taken themselves to be no better or worse for being more or less probable. That is to say that what would be the reälized value of an outcome is the measure of the outcome to be used in the computation of the expectation; the expectation is simply lineär in the probabilities. This feature of the model follows from what is known as the strong independence axiom (underscore mine) because Paul Anthony Samuelson, having noticed it, conceptualized it as an axiom. It and propositions suggested to serve in its stead as an axiom (thus rendering it a theorem) have been challenged in various ways. I will not here survey the challenges.

However, the first problem that I saw with expected-utility maximization was with that lineärity, in-so-far as it implies that people do not benefit from the experience of selecting amongst discernible non-trivial lotteries as such.[1]

Good comes from engaging in some gambles as such, exactly because gambling more generally is unavoidable. We need practice to gamble properly, and practice to stay in cognitive shape for gambling. Even if we get that practice without seeking it, in the course of engaging in our everyday gambles, there is still value to that practice as such. A gamble may become more valuable as a result of the probability of the best outcome being made less probable, and less valuable as a result of the best outcome becoming more certain. The value of lotteries is not lineär in their probabilities!

It might be objected that this value is only associated with our cognitive limitations, which limitations it might be argued represented a sort of irrationality. But we only compound the irrationality if we avoid remedial activity because under other circumstance it would not have done us good. Nor do I see that we should any more accept that a person who needs cognitive exercise to stay in cognitive shape is thus out of cognitive shape than we would say that someone who needs physical exercise to stay in physical shape is thus out of physical shape.


[0 (2016:07/22)] Very quickly, in a brief exchange, he saw the error, and he's corrected his entry; so I've removed the link and identification here.

[1] When I speak or write of lotteries or of gambling, I'm not confining myself to those cases for which lay-people normally use those terms, but applying to situations in which one is confronted by a choice of actions, and various outcomes (albeït some perhaps quite impossible) may be imagined; things to which the term lottery or gamble are more usually applied are simply special cases of this general idea. A trivial lottery is one that most people would especially not think to be a lottery or gamble at all, because the only probabilities are either 0 or 1; a non-trivial lottery involves outcomes with probabilities in between those two. Of course, in real life there are few if any perfectly trivial lotteries, but a lot of things are close enough that people imagine them as having no risk or uncertainty; that's why I refer to discernible non-trivial lotteries, which people see as involving risk or uncertainty.

It's the Water

Sunday, 5 June 2016

In the '70s or earlier, it was noticed that, in America, academic departments of economics that were located at or near the Atlantic or Pacific Ocean tended to have one set of attitudes about macrœconomics, while those away from the oceans and in particular near the Great Lakes tended to have another. From this, they were grouped as saltwater and as freshwater (or as sweetwater), respectively.

The distinction was most widely recognized in macrœconomics, with the freshwater departments arguing for founding macrœconomics in micrœconomics considerations (especially in the theory of individual decision-making under uncertainty), for using dynamic models, and for quantification. However, though (or perhaps because) they emphasized the importance of micrœconomic considerations for the development of macrœconomic theory, the freshwater schools seemed more content with standard micrœconomic theory than were the saltwater schools, where non-standard decision-theory was more investigated (while being regarded as less important to macrœconomics).

It has been claimed that the distinction between these groups has faded to irrelevancy, with younger economists having adopted insights from both, and with older disputants having departed. However, since the on-set of the most recent financial crisis, old-fashioned Keynesians have become more vociferous, if not actually much more numerous. (Paul Krugman no longer takes any water with his salt.)

It occurs to me that, for one group of heterodox economists, we might refer to the Wien, or … to the Danube. So … blue-water? (Blauewasser?) Indeed, as one branch of that school-of-thought tends to represent itself as definitive for the whole school, perhaps blue-water could be the more inclusive term.

Meanwhile, through Cambridge runs the River Cam. There's something in that water. Something bad.

On the Concept of Ownership

Monday, 23 May 2016

I have long and often encountered discussion that implicitly or explicitly involves notions of property or of ownership, which discussion is rendered incoherent from a failure to consider what it means for something to be property, what it means to own something.

Some confusion arises because we have come often to use the word property casually to mean an object (physical or more abstract) to which some sort of ownership may apply, without our considering whether the object is well conceptualized for purposes of considering property rights,[1] and without considering that actual ownership associated with that object might be distributed in some complicated ways amongst multiple parties.

One might, for some reason, associate a plot of land with an object imagined as beginning at the center of the Earth and extending to some sort of limits of the atmosphere (or beyond); from such an association, and then from a presumption that the whole object were property, farmers were once known to shoot at airplanes as trespassing vehicles. Yet other folk would assert that owning a plot of land as such only entitled one to control things to lesser depths and heights, in which case the rights could be associated with a smaller object, representing a sub-object as it were. One person might be thought to have the right to farm the aforementioned land, and another to extract its mineral resources so long as he didn't thereby interfere with the farming. Possibly others would claim peculiar easements, allowing them to travel through some or all of the object without thereby trespassing. There might be purported rights entitling still others to flows of resources such water, air, and electromagnetic radiation travelling through the object. In the case of sunlight (an electromagnetic radiation), the rights would typically be presumed to involve only some space above the soil, and the farmer might both have claims against her neighbors doing things that reduced her sunlight and be constrained by similar claims for her neighbors.

If we are thinking in terms of one object, and then change to thinking of an object within it, previously relevant rights of ownership may become irrelevant. If we instead think in terms of an object of which our original object is but a part, then new claims may become relevant. Two objects, neither of which is completely contained in the other, may share some third object as a part; so that any thorough consideration of ownership involving these two objects containing the third may involve rights that are literally identical and rights that are different. The minimal object relevant to describe some asserted set of property rights might not be sufficient to describe other rights none-the-less associated with that object. The minimal object in each of the previously mentioned cases (of farming, of easement, of mineral extraction, and of unobstructed resource flow) is somewhat different from the minimal object in the other cases.

A farmer who somehow forfeits her right not to have sunlight artificially obstructed may still be imagined to own the plot of land on which she grew her crops, yet she doesn't own what once she owned. Likewise, a house-holder who somehow surrenders his right to come and go from the plot on which the house sits doesn't own what once he owned. And, though it would perhaps seem very unsual, one might imagine these rights not transformed into claims for those who have prior rights to surrounding spaces, but instead coming into possession of third parties. For example, perhaps I speculate that I can buy whatever rights I need to build a skyscraper, on the assumption that I can buy a right to block the sunlight to a neighboring farm; I could purchase that latter right first, then discover that I am thwarted as to other purchases. This might work nicely for the farmer, but she no longer has a right that she once had; she no longer owns something that she once owned.

We can still express what things are owned as if they are objects, but we must then select our objects to match our rights of use. And our discourse can become strained and unnatural if we insist on always treating the thing owned as a distinct object rather than as a right of use. For example, if Timo is exclusively entitled to inhabit a cabin in the Winter and james is likewise entitled to inhabit it in the Summer, and we must express them as owning distinct objects, then we must treat the cabin in Winter as one object and the cabin in Summer as another. Indeed, we will surely have to be far more contrived in our construction of objects to account for what the two jointly do not own of the cabin! On the other hand, we can say that each has a right to use the cabin in some way without necessarily specifying how other rights of use are distributed; the concept of the cabin is available without first settling questions of ownership.

I don't propose that we generally stop using the word property as in the ordinary sense of a piece of property, merely that we understand that this everyday use may be misleading. Nor would I suggest that we should somehow stop thinking in terms of objects when we carefully consider ownership. But we must be alert to the fact that our choice of objects with which to think is largely taxonomic and to some degree arbitrary, and we should not take results that are no more than artefacts of that taxonomy as anything more profound.

In fact, the right of use may be recognized as itself an object of an abstract sort, but the right to use a right of use is not distinct from simply that right of use, and thus cannot be dissociated from it.[1.5]


My laboring of the relationship of ownership to objects and their uses isn't quibbling nor pirouetting. People who imagine an object as such to be owned tend all too often to imagine it somehow being owned beyond any of its various possible uses. They thus imagine that it can remain the property of one person or group even as another party — most often those in control of the state — appropriate its use, and even as this second party seizes every right of use. It then also becomes absurdly thinkable that one person might retain every right of use that she had, associated with an object, yet transfer ownership to some other party. Ownership would be reduced to absolutely nothing more than something such as a formal title.

When the state regulates property, it is taking rights of use and hence ownership. This transfer is relevant to questions of compensation (as in the case of the guarantees of the Fifth Amendment to the US Constitution[2]), and of whether state regulation of the means of production is a form of socialism.


[1] The word object comes from the Latin ob-iacere, meaning throw-before, and referred originally to that thrown before the mind. What we now call objects are, however, mental organizations of what is thrown before us. Thus, to use a classic example, we can talk about my hand as an object, and my fist as an object; they seem to be the same object, yet only sometimes. (We may still, in good conscience, use the word objective for perceptible external reality. And extending it to include unperceived and imperceptible external reality shouldn't cause more than mild discomfort; the rightful demands of etymology are not unlimited.)

[1.5] This paragraph was added on 24 May.

[2] That Amendment (with an underscore by me) reads

No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a grand jury, except in cases arising in the land or naval forces, or in the militia, when in actual service in time of war or public danger; nor shall any person be subject for the same offense to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation.

Reänimation

Wednesday, 18 May 2016

The extended quiescence of this 'blog has largely been an artefact of my limiting of various activities as I bore-down on critiquing Production of Commodities by Means of Commodities, a work of heterodox political economy by Piero Sraffa. The task has been thoroughly unpleasant, because there is so very much wrong with his work and because he writes in an obscure manner. At the same time, I have been dealing with depression intensified by personal circumstances. Had I allowed myself to step away from the project more than I did, I might never have finished it.

I have not, indeed, finished it; but, on Wednesday morning, I completed a first draft of the article. That draft is now in the hands of some of the other economists whom I know. (Naturally, I have since found things that I want to change, though none of these represent a major issue.) So I think that I will be back to writing more entries here.


One of the economists who has graciously said that he would take a look at the article (not-withstanding that it is monstrous in size!) asked me what motivated my writing of it.

Over many years, I have repeatedly been annoyed by encounters with those who draw upon PoCbMoC. More recently, I have been concerned by increased popular support for administrating economies (which support happens to be egalitarian or quasi-egalitarian); and this book is part of the infrastructure of the experts who defend such administration.

Further, at the time that I finally began actually working on this article, I felt stalled-out in my paper on the axiomata of qualitative probability. (That paper was and is a rat's nest, in which the basic propositions are not currently each perfectly orthogonal to all others.) In a sense, then, this article on Sraffa's book was intended as a break, though I quickly discovered that the task was going to be far more onerous than I had presumed.

Production of Commodities by Means of Commodities is the central text of neo-Ricardian economics, and a core text of post-Keynesian economics; it is also an important source for a variant form of Marxism that would abandon the labor theory of value. If I can get my article published in a reputable journal, that publication will eventually be the death of neo-Ricardianism and of the aforementioned variant of Marxism; I don't know enough about post-Keynesianism to know how well they might do without PoCbMoC. Some of my criticisms are relatively minor, but some of them strike at the heart of the work.

(It took rather a long time to develop my article, but reading it offers the impression a nearly continuous rain of blows, some dreadful.)

I say eventually because I wouldn't expect the present admirers to acknowledge how hard they'd been hit, but I'd expect a virtual end to the winning of converts. I don't know that I can find a journal to publish the article because

  • it is quite long;
  • the mainstream of economists are unfamiliar with PoCbMoC so that
    • editors and reviewers may think it insufficiently significant, and
    • those reviewers most likely to feel sufficiently competent to examine my article are admirers of Sraffa.

I intend never again to pore over a work, even as short as PoCbMoC, when it is discernibly crack-pot. As I told a friend, I have been doing my time on the cross here; let someone else go after other such thinkers. I am capable of original work of significance, and that is how I intend to spend my remaining time qua economist.


This 'blog was begun as I left LiveJournal, appalled by its evolving policies under its second and then third owners. One might reasonably conceptualize this 'blog as a continuation of that which I had at LJ, and some of the entries of this 'blog are recyclings of entries from the earlier 'blog.

None-the-less, this 'blog has become very different from its predecessor. LiveJournal is a social-networking site; part of the reason that it has withered is that its users migrated to more successful social-networking sites. My present 'blog doesn't work that way. I have recurring readers, but there's nothing much like the Friends feed of LJ or of Facebook. There is no centralized connector of interests (as on LJ). I have regular readers, but they are likely to use an RSS aggregator (such as Flipboard) and less likely to comment (especially if they are using such an aggregator). I get far more irregular visitors, who are here by way of Google (or of some other search service), grabbing some information, and not so much as visiting any page here other than their entry pages.

So it doesn't feel appropriate to offer mundanities of the sort that I would relate to a neighbor or to a friend on the telephone. My public entries tend to be things that I imagine strangers would appreciate reading. The restricted entries (basically accessible to friends who followed me as I migrated from LJ) are almost entirely personal; but a reader is required to make a special effort to access them, so they are not about ordinary events; they are usually very personal.

With entries to this 'blog thus typically requiring more thought, there are generally fewer of them, and the 'blog becomes dormant when I cannot — or believe that I should not — give thought to those entries.

The State of My Paper on Sraffa

Wednesday, 16 March 2016

Piero Sraffa's Production of Commodities by Means of Commodities has 96 sections and four appendices. I've critiqued most of the first 85 sections, though I have for now skipped a few that draw-out conclusions from methods that I have shown to be fatally flawed. Along the way, I've also dealt with three of the appendices, the remaining one of which is bibliographical.

The final 11 sections that I've not discussed nor yet carefully read are concerned with what economists call land (not only space but resources such as ore) and with the significance of switching in methods of production. That last part is the most noted contribution from Sraffa, and widely considered to have merit across various schools of thought, though it has also been asserted that the contribution is not as novel as some have claimed. I withhold judgment until I go through it carefully.

The material over which I have so far pored is of no marginal value. I have come to loathe each resumption of my effort. But Production of Commodities by Means of Commodities is the core text of the neo-Ricardians, a central text of the Post-Keynesians (who have a significant academic and political foot-print in the UK), and the point of departure for an important variant of Marxism. So I should steel myself and complete the task.

After I get a first draft of the actual analysis done, before I write the other parts of the paper, I will begin making copies of the version in-progress available to those who can read these entries. And, after I have a more fully reälized working version, I might unrestrict my entries about this project, though that publicizing might wait upon my finding a journal that agrees to publish it.

Value Doesn't Work that Way

Tuesday, 12 January 2016

Many different conceptions of value are employed in different contexts, and more than one conception is employed in economics. But the notion of value that is most fundamental to economics is that of usefulness.

Usefulness isn't some attribute independent of context, nor does anything have the same usefulness to one person as it does to another. When context changes, value changes. When a thing that had value is moved, it does not carry its value with it; rather, it takes-on a new value associated with its new context. When a thing that had value moves from being the property of one person to being the property of another, its old value is not delivered to the new person; rather, it takes-on a new value associated with its new ownership.

Prices represent a somewhat different sort of value. Prices are quasi-quantified prioritizations, under which things may be exchanged. But, however prices are formed, they work only to the extent that they promote any exchanges that are useful to those potentially making the exchanges, and discourage any that are not. Ostensible prices that do not do so will be ignored in markets, and bring-about economic failure in other systems of allocation. Market values — prices established by markets — are those that conform to the priorities of the parties who choose to exchange. Market values, though different from usefulness, must be informed by usefulness, and thus must thus reflect the contexts of the things priced.

Prices are first-and-foremost rankings, and treating them as quantifications has limited heuristic value; a thing may be rationally priced at $1000 without its being 1000 times as useful as something rationally priced at $1. And, though the first thing may be rationally priced at $1000 in some context, if the context is changed radically, the thing may cease to have any usefulness, so that its price should be 0.

A great deal of the wealth in to-day's world is in the form of financial claims that have no meaning what-so-ever outside of the context of a market. If the market is eliminated, then these claims would have no usefulness and hence a rational price of 0. If the markets in which these claims might be used were somehow preserved, but the claims were seized and redistributed, then their new contexts would correspond to greatly diminished usefulness, and their rational prices would then be much smaller.

The great fallacy of popular notions that poor and middle-income people might be significantly enriched by a large-scale seizure and implicit or explicit redistribution of wealth from billionaires or from the 1% or whatever is the notion that the present prices of the seized wealth reflect an intrinsic economic property of the things seized, which property will be delivered with the things as they are transferred. Instead, the old value will evaporate, and the new value will often be 0.

This point is true even in cases in which the assets seized are not financial instruments. Imagine a community given a Lamborghini Diablo. It had more value than a Honda Fit to the millionaire who owned it; but, for the community, the Honda Fit could be more useful than a Lamborghini Diablo. The respective prices prior to redistribution were plainly poor reflections of what would be the values in the new context.

Wealth is destroyed not only when things of value are seized from the very wealthy and given to those less wealthy, but when there is any sort of large-scale redistribution; including that from the lower- and middle-income groups to the very wealthy. But further indiscriminate redistribution, as by income group, will not restore the wealth lost to past redistribution, and even in hypothetical cases in which only actual perpetrators are penalized and actual victims are compensated, there may be further loss of wealth as such.

So, no. There isn't enough money for the dreams of the Occupation movement nor for the promises made by candidates such as Bernie Sanders, because money doesn't work that way. And there isn't enough wealth, because wealth doesn't work that way. The accountings that claim otherwise are crack-pot.

Money 101*

Tuesday, 5 January 2016

The Nature and Origin of Money

[Read more.]

The Equation of Exchange and the Price Level

[Read more.]

The Inflationary Process

[Read more.]

Commodity-Based Money

[Read more.]

The Nationalization of Money and Fiat Money

[Read more.]

Partial-Reserve Issuance — the Charge of Fraud

[Read more.]

The Effects of Inequality in the Accumulation of Money

[Read more.]


* Years ago, when I had a 'blog at LiveJournal, one of my Friends there had started or was about to start taking an introductory course on macrœconomics. I banged-out an entry from which this one is derived.

Crime and Punishment

Thursday, 31 December 2015

My attention was drawn this morning to What Was Gary Becker's Biggest Mistake? by Alex Tabarrok, an article published at Marginal Revolution back in mid-September.

Anyone who's read my paper on indecision should understand that I reject the proposition that a quantification may be fit to the structure of preferences. I'm currently doing work that explores the idea (previously investigated by Keynes and by Koopman) of plausibility orderings to which quantifications cannot be fit. I'm not a supporter of the theory that human behavior is well-modelled as subjective expected-utility maximization, which is a guiding theory of mainstream economics. None-the-less, I am appalled by the ham-handed attacks on this theory by people who don't understand this very simple model. Tabarrok is amongst these attackers.

Let me try to explain the model. Each choice that a person might make is not really of an outcome; it is of an action, with multiple possible outcomes. We want these outcomes understood as states of the world, because the value of things is determined by their contexts. Perhaps more than one action might share possible outcomes, but typically the probability of a given outcome varies based upon which action we choose. So far, this should be quite uncontroversial. (Comment if you want to controvert.) A model of expected-utility maximization assumes that we can quantify the probability, and that there is a utility function u() that takes outcomes as its argument, and returns a quantified valuation (under the preferences of the person modelled) of that outcome. Subjective expected-utility maximization takes the probabilities in question to be judgments by the person modelled, rather than something purely objective. The expected utility of a given action a is the probability-weighted sum of the utility values of its possible outcomes; that is p1(au(o1) + p2(au(o2) + … + pn(au(on) where there are n possible outcomes (across all actions), oi is the i-th possible outcome (from any action) and pi(a) is the probability of that outcome given action a.[1] (When oj is impossible under a, pj(a) = 0. Were there really some action whose outcome was fully determinate, then all of the probabilites for other outcomes would be 0.) For some alternative action b the expected utility would be p1(bu(o1) + p2(bu(o2) + … + pn(bu(on) and so forth. Expected-utility maximization is choosing that action with the highest expected utility.

Becker applied this model to dealing with crime. Becker argued that punishments could be escalated to reduce crime, until potential criminals implicitly regarded the expected utility of criminal action to be inferior to that of non-criminal action. If this is true, then when two otherwise similar crimes have different perceived rates of apprehension and conviction, the commission rate of the crime with the lower rate of apprehension and conviction can be lowered to that of the other crime by making its punishment worse. In other words, graver punishments can be substituted for higher perceived rates of apprehension and conviction, and for things that affect (or effect) the way in which people value successful commission of crime.

The simplest model of a utility function is one in which utility itself increases linearly with a quantitative description of the outcome. So, for example, a person with $2 million dollars might be said to experience twice the utility of a person with $1 million dollars. Possession of such a utility function is known as risk-neutrality. For purposes of exposition, Becker explains his theory with reference to risk-neutral people. That doesn't mean that he believed that people truly are risk neutral. Tabarrok quotes a passage in which Becker explains himself by explicit reference to risk-neutrality, but Tabarrok misses the significance — because Tabarrok does not really understand the model, and confuses risk-neutrality with rationality — and proceeds as if Becker's claim hangs on a proposition that people are risk-neutral. It doesn't.

Becker's real thought doesn't even depend upon all those mathematical assumptions that allow the application of arithmetic to the issue. The real thought is simply that, for any contemplated rates of crime, we can escalate punishments to some point at which, even with very low rates of apprehension and conviction, commission will be driven below the contemplated rate. The model of people as maximizers of expected utility is here essentially a heuristic, to help us understand the active absurdity of the once fashionable claim that potential criminals are indifferent to incentives.

However, as a community shifts to relying upon punishment from relying upon other things (better policing, aid to children in developing enlightened self-interest, efforts at rehabilitation of criminals), the punishments must become increasingly … awful. And that is the moral reason that we are damned if we simply proceed as Becker said that we hypothetically could. A society of monsters licenses itself to do horrific things to people by lowering its commitment to other means of reducing crime.


[1] Another way of writing pi(a) would be prob(oi|a). We could write ui for u(oi) to and express the expected utility as p1(au1 + p2(au2 + … + pn(aun but it's important here to be aware of the utility function as such.

What Does the Goldsmith Use for Money?

Thursday, 10 December 2015

Irked by an up-tick in nonsense about money, I decided to haul-out a piece that I'd written years ago on some of the basics of monetary theory — Money 101 as it were — rework some of the old sections, and add some material motivated by new annoyances. I would then post it here.

But, in the course of working on that entry, I was confronted by a problem of that theory. I didn't and don't want just to ignore it, but the Money 101 entry is already rather long. So I decided that I should write a separate entry on the problem.

Part of the difficulty in writing this separate entry is that the problem vanishes if one makes some of the ordinary presumptions of neo-classical economics. I feel that I need to explain why those presumptions should not be made. But, given my audience, I feel that I need to explain the presumptions themselves. This entry may seem still more awkward than usual, as I try not to make it too abstruse.

You'd be quite correct in thinking that this entry could be much better written than it is — if I'd put more time and effort into its composition. But I want to do other things, and don't want this entry to be yet another piece on a back-burner.


Money is a medium of exchange. That is to say that people obtain some amount of it by exchange for the purpose of yet further exchange. It contrasts with things manufactured by them for exchange, and with things obtained for use other than in further exchange. Money arises whenever someone is clever enough to accept more of a commodity than he or she would otherwise want (at the given rate of exchange), and uses it in a further trade. What we ordinarily recognize as money is whatever money has become standard in the exchanges that we observe, but any commodity obtained in one exchange, with the intention of being exchanged yet again, and then indeed thus traded, was money.

Historically, commodity money is routinely followed by commodity-based money, with promissory notes circulating as money. There may at first seem to be no real difference between commodity money and commodity-based money, but fractional-reserve banking actually makes that difference very real, with the promises exceeding the stock of the commodity held to meet those promises, so that the amount of money exceeds the stock of the commodity. And, following upon the introduction of commodity-based money, we observe the introduction of fiat money, where notes that make no promises somehow circulate as money.[1]

Economists — not merely advocates of commodity money or of commodity-based money, but economists more widely — have a great difficulty in explaining why fiat money should have any value in a market economy. We can say a great deal about what prices must obtain if people use some given stock of notes as money for exchanges of some given set of stocks or flows of commodities, and have some given available technologies for transferring these notes, but it seems that we cannot fully explain why people agree to make these exchanges using this money, and hence we cannot explain the value of this money.

On the other hand, most economists seem to be comfortable in the explanation of commodity money and of commodity-based money. It is claimed to be the value of the commodity in non-monetary use. That is to say that to explain the value, for example, of an American silver dollar, one would find the persons who wanted to smith the silver or use it for wiring or somesuch, and see what commodities they would and could offer for that amount of silver. (To express the value in other commodities, one would have to follow a chain of offered exchanges.)

However, this explanation of the value of commodity money and of commodity-based money cannot account for the full value of an indefinitely circulating money.


Before continuing the principal discussion, I want to critique some features of neo-classical economics — the mainstream of micrœconomic theory.[2]

Neo-classical economics proceeds almost entirely within a framework of limiting cases; even when a neo-classical theorist makes a move towards greater reälism with respect to some aspect of the framework, most of the rest of the theorizing retains the familiar limiting-case features. The use of these limiting cases often produces models that are defensible on instrumentalist grounds, but certainly not when they cause whatever is the problem principally under consideration simply to leave sight.

In the case of the problem here to be raised, three of the standard presumptions of neo-classical economics that are objectionable are:

  • that preferences are complete
  • that goods and services are continuously divisible
  • that small costs may simply be ignored

The idea that preferences are complete is that, for absolutely every two potential choices, either a person thinks that one is better than the other, or the person thinks that they are, effectively, equally good. Cases in which people instead behave in some meaningfully different way both from treating the one as better than the other and from treating the two as equally good (or equally bad) are disallowed. I've attacked the literal truth of completeness elsewhere.

The idea that goods and services are continuously divisible might be attacked on the basis of physical theory — what we know of the properties of matter. But, before we pick such nits, I think that we ought to concern ourselves with how finely the human mind actually divides things. Even the folk who carefully eye bottles of water, seeking to determine which is most full, don't get below a particular resolution. And if perfectly accurate and precise measures were always available, then we'd be lost beyond some number of digits to the right of the decimal point.[3] (Our limitations in this regard are entangled with the costs of resolution, which might bring us to the issue of small costs being ignored, except that the costs of ever finer resolution can sky-rocket!)

I don't think that the presumption that small costs may simply be ignored needs much explanation. But note that it can sometimes directly contradict the presumption of completeness of preferences! A cost corresponds to forgone goods or services, and small costs are small variations in the goods or services that one might have had.

I believe that in many other cases, these three presumptions are not a matter of great concern, though they are objectionable in explanation of the value of a money that is a commodity or is based upon a commodity. But there's a fourth presumption that is relevant and that I do not think is ever justified. Specifically

  • that, when an agent is otherwise indifferent amongst choices, he or she makes that choice which would be required for the theory to work

That is to say that not only does Buridan's ass choose one of the bails of hay but, if theory won't work unless he chooses the left bail in particular, then he just does. The weaker presumption, that an indifferent agent (person or donkey) will choose, is usually based on a theory that the agent can and will flip a coin, but the idea that the agent will flip a coin contradicts expected utility theory, the mainstream of the theory of choice under risk. The stronger presumption that the agent will necessarily just happen to choose whatever is needed for the rest of the theory to work is incoherent.


In some contexts, most people understand that, for any person to agree to an exchange, he or she must expect to be better-off if the exchange takes place than if it does not. Most people lose sight of that point in a variety of contexts; some screw their eyes shut so as not to see it. Under the presumptions of neo-classical economics, it can be made to disappear.

Imagine that Ann has some quantity of blackberries, and Bob has some quantity of strawberries, and that Ann would rather have the strawberries that Bob has, and that Bob would rather have the blackberries that Ann has, and that they each feel this way even accounting for the costs of arranging and effecting a trade. In the real world, the trade will take place; and in the neo-classical world the trade will take place. Chances are, the trade would take place even if Ann were offering a slightly smaller quantity of blackberries while Bob offered the same amount of strawberries. In the real world, if we decrease the quantity of blackberries below some point, Bob may still think that the blackberries would have been worth it, except for the hassle of negotiation and transfer; in the neo-classical world, that hassle is usually considered small enough to ignore. So we leave reality behind, and can keep paring-back the offered amount of blackberries. We can do so with infinite precision, because blackberries are imagined to be continuously divisible, and because Bob is imagined to have complete preferences. Eventually, we reach the point at which the offered amount of blackberries is worth exactly as much to Bob as the strawberries that he has. But, at every place up to that point, he would agree to a trade; to put that in mathematical jargon, so long as there is any ε (no matter how tiny) of blackberries greater than the amount at which he is indifferent, neo-classical Bob will make the trade. So the claim is that, at the limit, he will still make the trade, even though he has nothing to gain. Mind you that this is a limit approached from one side. If the epsilons were all short-falls, rather that surpluses, then Bob would have been refusing right up to the limit. Still, neo-classical Bob might work well enough as a model for real-world Bob if short-falls just never occur for him. If they do, it would be quite terrible to claim that the behavior to one side of the limit (by even an ε) is the behavior when approached from the other side, and that Bob both trades and refuses to trade at the limit, or trades both ways (strawberries for blackberries or blackberries for strawberries) at the limit.[4]

The value of an additional amount, more or less, of strawberries or of blackberries relative to other possible changes, doesn't typically stay the same. In particular, as one has ever more of something, one would increasingly find more of something else relatively more useful; and as one has ever less of something, one would increasingly find more of something else less useful.[5] As a result, under the presumptions of neo-classical economics, one could expect that, by playing with the amounts of blackberries that Ann has, and the amount of strawberries that Bob has, one could produce a situation in which each valued what they had equal to what the other had. Given these presumptions, as soon as Ann and Bob have made a trade, they might be willing to make the inverting trade, so that they end-up where they were! And I've seen models in which it is implicit that just this sort of thing happens!


So long as we understand these assumptions as producing imperfect instruments, they may have great value. Newtonian physics has been empirically falsified, and never really held together, but it works fine not merely for much technology, but for investigating the basic answer to various scientific questions. Likewise for some applications of neo-classical economics. But one must not confuse artefacts of counter-factual assumptions with actual answers to whatever questions are at hand.


Imagine three people, Aya, Gus, and Tor. Aya has a pepper but wants strawberries; Gus has strawberries but wants okra; Tor has okra but wants a pepper.

Agenthaswants
Ayapepperstrawberries
Gusstrawberriesokra
Torokrapepper

Aya can get what she really wants by using okra as a medium of exchange (trading the pepper for okra and then the okra for strawberries); or Gus can get what he wants by using the pepper as a medium of exchange (trading the strawberries for the pepper and then the pepper for okra); or Tor can get what he wants by using the strawberries as a medium of exchange (trading the okra for the strawberries and then the strawberries for the pepper).

But if the only potential use that Aya has for the okra is as a medium of exchange, and likewise for Gus with the pepper and for Tor with the strawberries, then it will not make sense for Aya to use the strawberries as a medium of exchange, for Gus to use okra as a medium of exchange, nor for Tor to use the pepper as a medium of exchange. No matter what is used as money, the person responsible for it having value in exchange is also a sink for the money; once it is in his or her hands, it will cease to circulate as money.

One might imagine a larger community, in which the money had to pass through more hands to reach a sink. But the reasoning that launched the money was based upon its value to a person who would be a sink. If the money could not be expected to reach a sink, it could not be expected to reach the person who gave it value. It seems that it must go to a sink to be money.

My model of Aya, Gus, and Tor has only persons each of whom places no value on the item for which he or she could initially trade, except as a medium of exchange; and the trades considered are those in which each person gives all of his or her stock. We can imagine an economy with a large number of people, many or all of whom place some value on various or all of the sorts of commodities that might be used as money. We may presume that some goods and services are possessed by more than one person and that some goods and services are sought by more than one person. For various potential transactions, we might suppose competition both amongst those seeking the monetary commodity (for use as money or for non-monetary use) and amongst those offering the monetary commodity to them. We may conceive that many stocks of goods and of services are divisible.

When stocks of a commodity are divisible it becomes possible (and sometimes necessary) to put some portion to one use and the remainder into another use or into other uses. Various portions may be traded with various persons, and some may be put to use other than in exchange; and these different sorts of allocation of different portions may make sense because (as said earlier) as one has ever more of something, one would increasingly find more of something else relatively more useful; and as one has ever less of something, one would increasingly find more of something else less useful. It certainly becomes conceivable for some people to acquire both stocks of the monetary commodity for use as money and stocks for non-monetary use.

But, even with these added complications, it seems that the persons responsible for the monetary commodity having value in exchange are also sinks for the money; once it is in their hands, it will cease to circulate as money.

Whatever may be their priorities, rational people make only trades that they regard as improving expectations, and do not forgo greater such improvements for lesser improvements. In a neo-classical framework, that improvement might be imagined to be 0, the ghost of a departed ε, but in the real world it must be more than that. Trading with the monetary commodity is no exception to the rule that rational people do not trade unless they expect their priorities to be best served by the trade.

If a person wants a positive amount of the monetary commodity for use in trade, that means that (given his or her priorities) the anticipated value of the use of that portion as money exceeds the anticipated value of that portion in other use; it must be expected that someone will give give something worth more than that other use. We may then consider that next person. Either he or she will put the whole to non-monetary use, removing it from circulation as money, or will reserve some for monetary use. But we cannot indefinitely pass the buck if we are explaining the value of the monetary commodity by its non-monetary use. Eventually, either all of the commodity will have been removed from monetary use, or we will be back to someone whose position has already been considered. If money circulates indefinitely then it must for all participants have a greater value than they place on its non-monetary use!

My understanding of the relevant history is more limited than that of some people, but I think that some commodity money and commodity-based money has enjoyed enough circulation to indicate or at least to suggest that it might well circulate forever, that its value as money is not fully explained by its value in non-monetary use. [Addendum (2015:12/13): The recurring practice of fractional-reserve banking is only sustainable if money circulates indefinitely. Some opponents of the practice may insist that it is unsustainable; but, in any case, the monetary commodity must be fairly far removed from a sink for fractional-reserve banking to work at all, and frequent observation of fractional-reserve banking suggests that money indeed circulates indefinitely.]

If that is correct, then we want to explain the additional value. And, quite possibly, we might find in such an explanation something that will help us to explain the value of fiat money.


[1] At least passing mention should be made of the point that, if what appears to be fiat money is legal tender and there are price controls, then the money may be considered to be backed by the price-controlled commodites, or perhaps by the punishment delivered to those who fail to produce the commodities at those prices when the money is presented.

[2] There is no objection to marginalism here. Although both neo-classical economists and opponents of marginalism often treat them as if conterminous, they are not.

[3] With limited bearing on the problem of money, but of potential interest in other contexts, there is an additional issue of divisibility for commodities that are not simply measures of a substance, of space, or of time. Dividing something such as a car in two is not like dividing water into two containers. If for every proposed fractionalization (a half, a third, a fourth, &c) we could somehow find or construct some car which under natural descriptions had that fraction of each feature of another car (half as much leg-room, half as much cargo space, &c) and such that all persons regarded the corresponding multiplicity of these lesser cars as equivalent to one of the larger cars, then we might have a case for a sort of divisibility. But those conditions cannot be met.

[4] It would be then as if one claimed that, within a range from 0 to π, tan(π/2) were variously positive and negative simply whenever that makes a theory work.

[5] This is the actual law of diminishing marginal utility, though neo-classical economics gets lost in a special case of the principle.

Slavery, Slavery, and the Political Left

Monday, 2 November 2015

While the word slavery gets used in many ways, its core meaning is that of a personal condition of being property of another person or of a group of persons

However, there are recurring attempts to redefine slavery, insisting that a person who reaped only subsistence from his or her labor were by definition a slave. Now, this proposed definition is really orthogonal to any proper definition.

  • On the one hand, a person only reaps subsistence when living with a minimal technological infrastructure in a world of markèd scarcity. Much of humankind for most of history lived with little or no production above surplus, regardless of whether someone else were making ownership claims against them.
  • In some cases, people have had lives of relative material comfort, and yet would have been tortured or killed by their masters had they sought different employment.

(Compounding the problem with the redefinition, people who are consuming commodities far in excess of their needs for survival like to redefine subsist to include various comforts, such as electronic entertainment.)

Perhaps most of the people who abuse the world slave in this manner do so thoughtlessly; but it ties-together with an aspect of left-wing thought to afford them a significant evasion, deceiving others and deceiving themselves. That aspect is a resistence to acknowledging a relationship between wage-rates and the amount of labor employed in an economy.

One sees this failure in present support for an increase in statutory minimum wages. What these laws really say, to put things quite simply — yet perfectly truthfully — is that if an employer or would-be employer is unwilling or unable to employ a worker at or above the statutory minimum, then the employer must fire the worker, or not hire the worker in the first place. Most advocates presume that the employer will neither fire nor refrain from hiring, as if demand for labor were perfectly inflexible.

A rather pure expression of this dissociation of wage-rates from labor employment is found in the economic model of Piero Sraffa.[1] Sraffa's work is utterly unknown to most lay-people, and unfamiliar to most economists, but to economists on the far left it is an important benchmark, exactly because it claims so much of what they want to claim. However, its persuasive success is largely a matter of subscribers failing to note or to acknowledge a great deal implicit in the model. Perhaps most remarkably, in his model, the very same amount of labor is produced and consumed with absolute disregard for the wage-rate. That is to say that workers deliver the same labor (imagined as a scalar quantity) whether they are offered literally nothing in return (not even subsistence), or all of production is given to them as wages (with the same wage-rate for each worker).

When I look at the Sraffan model, I see workers behaving as if they are slaves. When their wages provide them no more than sustenance, they are as miserable slaves; when their wages provide them less than sustenance, they are as dying slaves; when their wages provide them far more than sustenance, they are as materially comfortable slaves. What makes them seem to be slaves is that they never exercise, and thus appear not to have, any freedom of choice in where they work nor in how hard they work.

(In those states of the United States that allowed private ownership of slaves, slaves were expected to deliver some fixed quota to their owners. They were not typically offered rewards for exceeding these quotas; they were punished, sometimes horrifically, for failing to meet them. I know of no other way, in the real word, to get the sort of labor production that Sraffa describes.)

In Sraffa's model, whatever production does not go to workers, goes to the owners of the other productive resources — essentially to the capitalists.[2] If one embraces Sraffa's model or something very much like it, and if one waves-away the proper meaning of slavery and instead uses it to mean one who is paid no more than sustenance, then it is easy to insist that, in a system that most favors a distinct class of capitalists, workers would be slaves, whereäs alternatives decreasingly favorable to such capitalists move workers ever further away from slavery. And if one imagines the workers getting an ever greater share exactly as production is administrated on behalf of the worker, then the movement away from slavery is a movement towards socialism.

However, if one continues to accept a model along the lines of Sraffa, yet restores the proper meaning of slavery, then one begins to see one why it had been doubly convenient to redefine the term. Because, in imagining a world in which workers never, one way or another, exercise freedom of choice in labor regardless of how production is distributed, the left has come perilously close to suggesting that workers, under socialism, would be slaves.

The underlying truth is that labor is one of the means of production. If an economy is fully socialized, then the potential worker must be employed however and wherever the best interests of the community as a whole are served, and his or her interests count no more in this decision than do those of anyone else.

This grim principle has repeatedly been illustrated in communities that have attempted a very high degree of socialism. Sometimes the attempt has been hijacked by leaders with less that sincere interest in communal well-being, but these leaders were able to make the populace their slaves because socialism required slavery of the populace. Trotsky's observation that

The old principle: who does not work shall not eat, has been replaced with a new one: who does not obey shall not eat.[3]

was true under Stalin because it or something like it would, as a practical matter, have been true under any fully realized socialism.

Meanwhile, as much as many people living in more market-oriented economies like to imagine themselves as slaves to their employers, they're fully aware that these employers cannot send agents to recapture them should they quit their jobs. To the extent that any group of persons other than ourselves exercises such ownership over us, that group is the state — the very institution usually entrusted to effect socialistic measures.

A movement towards socialism is a movement towards slavery, rather than away from it, and if one is going to bring the subject of slavery into an honest defense of socialism against all alternatives, then it is necessary somehow to make a case for slavery.


[1] The Production of Commodities by Commodities; Prelude to a Critique of Economic Theory (1960).

[2] Note how advocates of higher statutory minimum wages point with outrage at those who amass great wealth while paying workers less that some proposed statutory minimum wage, as if there were a zero-sum game being played between employer and employee.

[3] The Revolution Betrayed, ch 11 Whither the Soviet Union? § 2 The Struggle of the Bureaucracy with the Class Enemy.