Archive for the ‘economics’ Category

On Deductibility of Local Taxes

Monday, 8 May 2017

In my field of awareness, there has recently been more discussion than usual about deductibility of constituent-state taxes and of municipal taxes from income computed for purposed of Federal taxation. I think that most of the discussion has been fundamentally wrong-headed.

In the textbooks of middle-schools, of high-schools, and of introductory courses in college on civics, on politics, or on economics, there are discussions of various proposed guidelines for taxation, based on ostensible or insinuated theories of justice. One commonly offered theory is that people should be compelled to pay based upon supposed ability; another is that they should be compelled to pay based upon the amount of services that they receive from the state.[1] I've yet to see such a discussion in such a textbook that could withstanding much critical examination.

In any case, these homilies don't serve to explain how-and-why taxation is effected in the real world, except in-so-far as some of their prescriptions are invoked to argue for a tax of one sort, even as conflicting rationalizations are offered (often by the very same people) to argue for taxes of other sorts. Historically and to the present day, taxation has been fundamentally opportunistic. That which has been taxed is whatever seemed to be most readily taxable. Targets of convenience have been wealth or income that has been thought to be easily tracked and measured, difficult to relocate outside of the jurisdiction, or for the taxation of which there is wide-spread acquiescence if not support within the community. (It is with respect to that last aspect that textbook theories have their real relevance.)

The state is not satiated by some steady extraction of wealth from the community. When extractions are greater than were expected, the state will not return the surplus to the taxpayer as such, except under extraordinary pressure; and, here-to-fore, states have always moved towards attempting to extract as much tax from their communities as the communities will suffer. This tendency is natural, as the people who make-up the state generally see their positions within society improve as they have increasing command over resources; mechanisms that exist in sectors whose rewards are determined by markets which cause participants to identify and pursue efficiencies simply have no correspondents within the state; the state is able to cultivate dependencies in the wider population; and many people imagine a very extensive rôle for the state within society (especially those people who lose sight of the distinction between the state and its subjects). The state grows ever larger and becomes ever worse at the allocation of resources, and so seeks ever greater extractions.

When, within the jurisdiction of a constituent state or within a municipality, there is greater community resistance than elsewhere to taxation, there is less taxation than there otherwise might be. That difference is a target of opportunity for a federal state, whose jurisdiction encompasses a wider community. There is a mechanism for obtaining the acquiescence of that wider community without typically triggering a significantly intensified resistance on the part of the communities subjected to a federal surtax in the face of lower taxes by other entities. That mechanism involves allowing taxpayers to deduct what taxes they pay to those other entities from the calculated worth of something that the federal state taxes; because, in the face of those deductions, parts of the wider community become less resistant to rate increases.

Let's say that people in jurisdictions A, B, and C, which are all of roughly the same size, face a federal tax of 30% on income, and that people in jurisdictions A and B face a more local 10% tax on pre-tax income, while people in jurisdiction C face a no such tax. If the federal tax is increased to 1/3 on taxable income, but local income taxes are made fully deductible, then the people of jurisdictions A and B face no net increase in income tax, and so may acquiesce; the people in jurisdiction C may thus find themselves out-voted and their taxes increased by about 3%.

A great many people imagine what thus happens is that, given deductibility of more local taxes, people in jurisdictions with lower local taxes are force to subsidize those in jurisdictions with higher local taxes; but that conclusion is spurious. It would in some sense follow if the quantity or quality of goods and services delivered by the state were well correlated with the amount of resources that it extracts from the community, but there is no such correlation, except in transitory cases in which the state deliberately impairs performance to provoke acquiescence to greater extractions. The people paying lower taxes than they otherwise might are not getting something from those paying higher taxes than would be tolerated without the mechanism of deductibility. They are simply less victimized. One would be no less mistaken in claiming that people who live in other nations with lower income taxes are ipso facto subsidized by American taxpayers.

(For purposes of economic analysis of some sorts, tax-cuts and subsidies are equivalent, but those in the jurisdictions that are less taxed by the federal state have not received a tax cut, they have instead not been subjected to tax increases imposed elsewhere. And the aforementioned equivalence holds only if either there is no prior property in resources, or the state has a prior claim on whatever resources are involved. If no one has a claim prior to taxation and subsidization, then no one is paying taxes; they are being extracted from resources that are un-owned. If the state has a prior claim, then there are again no tax-payers; there are people who are granted more or less wealth or income belonging to the state. And, if there are no tax-payers, then the tax-payers subsidize no one.)

Eliminating the deductibility of other taxes would create greater resistance to federal taxes, as some who had previously not been subjected to higher levels then would be. But not everyone thus penalized would previously have been a supporter of imposing those levels on others. Innocent by-standers would be dragged into a fight; there could not be justice in that.


[1] When I say state, I don't necessarily mean one of the constituent states of a federation such as the United States. I certainly don't mean the jurisdicational area of one of those states, nor the inhabitants of such an area. A state is an organization that successfully claims an effective monopoly of some sort in the control of violence.

Spurious Invocations and Socialized Medicine

Sunday, 19 March 2017

Advocates for funding or for in-kind provision of medical services through the state — some degree of socialization of medicine — frequently assert that there is a basic human right to health or to medical services. But there is invariably a bait-and-switch, because health cannot be provided as a right, basic or otherwise, universal to human beings or even held by all members of a large, naturally formed community such as a nation; and a right to medical services gauged in terms other than consequences for health would be grossly implausible and otherwise unappealing.

It should be immediately obvious that there cannot be a basic right to medical services, because a basic right exists in any context in which there is a person, even when that person is in isolation. One cannot make a claim to the services of others if there are no others, nor can one make a claim to the use of technologies that simply don't exist. That's why genuine liberalism understands that basic rights aren't claims to the services of others, but instead are claims to be free from various sorts of interference by others. Robinson Crusoe cannot see a doctor when he is alone on the island, yet can speak his mind whether he is alone or has neighbors.

Derived rights are another matter. Derived rights are founded upon basic rights, but may emerge in a social context and be informed by the available resources, including technology. And there might even be a derived right that, though only emerging in some context, were universal to some population and involved positive claims to goods or to services. To provide an argument that health or medical care were just such a right, advocates of socialized medicine would have to identify and explain a process of derivation. While some persons making the assertion that there were instead a basic right to health or to medical care are simply swept-up by emotion, doing so also short-circuits a recognition of responsibility for that identification and for its explanation.

There are advocates who speak and write of the social contract and propose to find support thereïn for socialized medicine at present levels, and perhaps at still greater levels. But what is here called the social contract is not the contract that Hobbesians or liberals once imagined to be adopted at the beginnings of civil society; rather, a set of expectations held by some members of a society is being called a contract, as if such expectations alone could somehow contractually bind everyone within that society. The need to identify and explain the derivation of an ostensible right to medical care remains unmet by the use of the misleading metaphor of a contract. (Perhaps Mr Crusoe expects Friday to begin studying medicine upon arrival, but what of it?) It might also be noted that reference of this sort to a social contract is profoundly conservative — in the original sense of conservative — because the principal informant of expectations about social outcomes is tradition. And, if such expectations did have the sort of moral force that is imputed to them by the invocation of the social contract, then practices such as the subordination of women in various societies could be defended by reference to the social contracts of those societies. Even if such defense is somehow progressive, it is utterly illiberal.

In any case, health itself cannot be delivered as a right universal to human beings nor within some smaller but still large and naturally formed community. Some people have dire medical conditions for which there is no effective treatment, so there is no right to health itself. One might acknowledge that indeed there is no right to health yet assert that there were still a right to medical care; but others have conditions that could be corrected only by diverting resources that would otherwise be used to provide medical treatment to different people; and it is incoherent to speak of rights as things that may be in conflict — indeed, the point of insisting that health or medical care were a right (as opposed to a lesser desideratum) is to make an over-riding claim. One might finally punt to an assertion that everyone simply had a right to medical care regardless of need; but, thus unlinked, there is no more reason to suppose an entitlement to some allotment of adhesive bandages and of aspirin tablets than to suppose an entitlement to an allotment of bubble gum.

The actual provision of medical goods and services under socialized medicine cannot be about rights, and so it isn't about rights; it is instead a matter of politicized collectivist calculations. Essentially, popular opinion is motivated by a naïve and incoherent utilitarianism — trying somehow to maximize an implicitly quantified sum of human well-being (with perhaps odd lexicographical properties), but making exceptions here and there driven by pity or by respect for some people and enabled by blindness to the costs to others; and officials of various sorts try to keep some share of the public happy but more generally pursue their own interests. Those who are not served under the programme or who find their access to medical care reduced or even effectively ended by socialism are waved-away as unfortunate victims of practical limitations, previous talk of rights not-withstanding.

I'm not at all a fan of collectivist calculations; typically they assume quantifications that don't hold, and otherwise they seem arbitrary in what they seek to maximize. But, if those calculations truly made sense, then one would want to consider the long run, to include the well-being of people in the future in one's aggregation; and thereïn lies the rub. Unless one assumes that humankind is fairly soon to come to an end, there are more people yet to be born than are alive to-day. If there truly were a collective aggregate to maximize, then anything done to-day that impaired economic development in the future would be counter-indicated. If people in the future were generally wealthier, then they would enjoy better medical care and almost surely better health. If we allow for considerations beyond the medical, the case for economic development is greater still. And, because it cannot allocate resources with economic efficiency, socialized medicine is ultimately a drag on economic development and thus on medical progress.

Socialized medicine doesn't deliver a basic right; it doesn't deliver a derived right; in the long run, it means that more people suffer (though suffering itself has no aggregate across persons) and that at any given age a greater share of people die. Refusing to face these points doesn't make one a nicer person; accepting the truth doesn't make one uncaring. Forcing the innocent to swallow bad medicine is not kindness.

Lotteries as Cost-Saving Mechanisms

Thursday, 23 February 2017

In decision theory, it's useful to conceptualize all choices as amongst lotteries. Even a choice that has an absolutely certain outcome may be imagined as a sort of trivial lottery, where one outcome had the equivalent of a 100% probability and all other outcomes had the equivalent of a 0% probability. But most of the choices that people typically imagine may be made with certainty cannot, and things that actually can be chosen with certainty are not things to which people give much conscious thought. For example, in a restaurant. one cannot choose tea with certainty; one cannot even choose to order tea with certainty. One can chose to try to order tea; however, whether one's language-processing centers and apparatus of speech will do what one wants is somewhat in doubt. But most people don't recognize the vast majority of their choices as amongst lotteries because it isn't particularly useful for them to make the recognition.

That said, it's still interesting (to me at least!) to note how people respond to the things that nearly everyone does recognize as lotteries. If Group A wants the m members of Group B to do something for them, they can pay D to them each, for a total cost of m · D, or they can offer a prize P; and if m is a moderate-to-large number then almost always the least value of P that will motivate the group is rather less than the the value of m · D, even when there is no sense of supporting a worthy cause. In the clearest illustration, what Group A want of Group B is just money. Most people will give you a five-dollar bill for five one-dollar bills, but few will ordinarily give you that five-dollar bill for four one-dollar bills. However, perhaps a million people will give you five dollars for a one-in-a-million chance at four million dollars.

In the context of various social confusions, there are restrictions on selling chances at money in exchange for money.[1] But chances at money or at other prizes are fairly freely traded for information that is worth money. Think of how many times you are offered a chance at a large sum of money or at a valuable commodity (such as a vehicle) in exchange for taking a consumer survey or for providing contact information. You might refuse — I do — but a lottery is offered because information is provided by more people than could be motivated to do so for the same sum divided into simple payments.

It's often claimed that people are irrational to make bets in which the price of participation exceeds the probability of the payoff times the size of the payoff. I don't want to claim that; the issue is actually very nuanced. (There have been studies that attempt to estimate the extent to which a systemic misappraisal of probabilities affect behavior, but most or all of these studies are hopelessly tainted by the active desire to find irrational behavior and by some questionable presumptions concerning how uncertainty ought to be handled.) But, in any case, it's interesting that a group can conserve its resources by using a lottery to motivate behavior. And, returning to the point that in reality almost everything is a lottery, one has to wonder to what extent the world more generally is getting us to do things on the cheap.


[1] The inescapability of lotteries is fatal to ordinary attempts to condemn gambling as immoral. That something were immoral or unwise would not ipso facto be sufficient to justify outlawing it. And outlawing payment in money while allowing payment in commodities is absurd.

Deal-Breakers

Saturday, 7 January 2017

Elsewhere, Pierre Lemieux asked In two sentences, what do you think of the Monty Hall paradox? Unless I construct sentences loaded with conjunctions (which would seem to violate the spirit of the request), an answer in just two sentences will be unsatisfactory (though I provided one). Here in my 'blog, I'll write at greater length.


The first appearance in print of what's called the Monty Hall Problem seems to have been in a letter by Steve Selvin to The American Statistician v29 (1975) #1. The problem resembles those with which Monty Hall used to present contestants on Let's Make a Deal, though Hall has asserted that no problem quite like it were presented on that show. The most popular statement of the Monty Hall Problem came in a letter by Craig Whitaker to the Ask Marilyn column of Parade:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, Do you want to pick door No. 2? Is it to your advantage to switch your choice?

(Before we continue, take car and goat to stand, respectively, for something that you want and something that you don't want, regardless of your actual feelings about cars and about goats.)

There has been considerable controversy about the proper answer, but the text-book answer is that, indeed, one should switch choices. The argument is that, initially, one has a 1/3 probability that the chosen Door has the car, and a 2/3 probability that the car is behind one of the other two Doors. When the host opens one of the other two Doors, the probability remains that the car is behind one of the unchosen Doors, but has gone to 0 for the opened Door, which is to say that the probability is now 2/3 that the car is behind the unchosen, unopened Door.


My first issue with the text-book answer is with its assignment of initial, quantified probabilities. I cannot even see a basis for qualitative probabilities here; which is to say that I don't see a proper reason for thinking either that the probability of the car being behind a given Door is equal to that for any other Door or that the probability of the car being behind some one Door is greater than that of any other Door. As far as I'm concerned, there is no ordering at all.

The belief that there must be an ordering usually follows upon the even bolder presumption that there must be a quantification. Because quantification has proven to be extremely successful in a great many applications, some people make the inference that it can be successfully applied to any and every question. Others, a bit less rash, take the position that it can be applied everywhere except where it is clearly shown not to be applicable. But even the less rash dogma violates Ockham's razor. Some believe that they have a direct apprehension of such quantification. However, for most of human history, if people thought that they had such literal intuitions then they were silent about it; a quantified notion of probability did not begin to take hold until the second half of the Seventeenth Century. And appeals to the authority of one's intuition should carry little if any weight.

Various thinkers have adopted what is sometimes called the principle of indifference or the principle of insufficient reason to argue that, in the absence of any evidence to the contrary, each of n collectively exhaustive and mutually exclusive possibilities must be assigned equal likelihood. But our division of possibilities into n cases, rather than some other number of cases, is an artefact of taxonomy. Perhaps one or more of the Doors is red and the remainder blue; our first division could then be between two possibilities, so that (under the principle of indifference) one Door would have an initial probability of 1/2 and each of the other two would have a probability of 1/4.

Other persons will propose that we have watched the game played many times, and observed that a car has with very nearly equal frequency appeared behind each of the three Doors. But, while that information might be helpful were we to play many times, I'm not aware of any real justification for treating frequencies as decision-theoretic weights in application to isolated events. You won't be on Monty's show to-morrow.

Indeed, if a guest player truly thought that the Doors initially represented equal expectations, then that player would be unable to choose amongst them, or even to delegate the choice (as the delegation has an expectation equal to that of each Door); indifference is a strange, limiting case. However, indecision — the aforementioned lack of ordering — allows the guest player to delegate the decision. So, either the Door was picked for the guest player (rather than by the guest player), or the guest player associated the chosen Door with a greater probability than either unchosen Door. That point might seem a mere quibble, but declaring that the guest player picked the Door is part of a rhetorical structure that surreptitiously and fallaciously commits the guest player to a positive judgment of prior probability. If there is no case for such commitment, then the paradox collapses.


Well, okay now, let's just beg the question, and say not only that you were assigned Door Number 1, but that for some mysterious reason you know that there is an equal probability of the car being behind each of the Doors. The host then opens Door Number 3, and there's a goat. The problem as stated does not explain why the host opened Door Number 3. The classical statement of the problem does not tell the reader what rule is being used by the host; the presentation tells us that the host knows what's behind the doors, but says nothing about whether or how he uses that knowledge. Hypothetically, he might always open a Door with a goat, or he might use some other rule, so that there were a possibility that he would open the Door with a car, leaving the guest player to select between two concealed goats.

Nowhere in the statement of the problem are we told that you are the sole guest player. Something seems to go very wrong with the text-book answer if you are not. Imagine that there are many guest players, and that outcomes are duplicated in cases in which more than one guest player selects or is otherwise assigned the same Door. The host opens Door Number 3, and each of the guest players who were assigned that Door trudges away with a goat. As with the scenario in which only one guest player is imagined, more than one rule may govern this choice made by the host. Now, each guest player who was assigned Door Number 1 is permitted to change his or her assignment to Door Number 2, and each guest player who was assigned Door Number 2 is allowed to change his or her assignment to Door Number 1. (Some of you might recall that I proposed a scenario essentially of this sort in a 'blog entry for 1 April 2009.) Their situations appear to be symmetrical, such that if one set of guest players should switch then so should the other; yet if one Door is the better choice for one group then it seems that it ought also to be the better for the other group.

The resolution is in understanding that the text-book solution silently assumed that the host were following a particular rule of selection, and that this rule were known to the guest player, whose up-dating of probabilities thus could be informed by that knowledge. But, in order for the text-book solution to be correct, all players must be targeted in the same manner by the response of the host. When there is only one guest player, it is possible for the host to observe rules that respond to all guest players in ways that are not not possible when there are multiple guest players, unless they are somehow all assigned the same Door. It isn't even possible to do this for two sets of players each assigned different Doors.


Given the typical presentation of the problem, the typical statement of ostensible solution is wrong; it doesn't solve the problem that was given, and doesn't identify the problem that was actually solved.


[No goats were harmed in the writing of this entry.]

Headway

Saturday, 7 January 2017

My paper on indecision is part of a much larger project. The next step in that project is to provide a formal theory of probability in which it is not always possible to say of outcomes either that one is more probable than another or that they are equality likely. That theory needs to be sufficient to explain the behavior of rational economic agents.

I began struggling actively with this problem before the paper on indecision was published. What I've had is an evolving set of axiomata that resembles the nest of a rat. I've thought that the set has been sufficient; but the axiomata have made over-lapping assertions, there have been rather a lot of them, and one of them has been complex to a degree that made me uncomfortable. Were I better at mathematics, then things might have been put in good order long ago. (I am more able at mathematics than is the typical economist, but I wish that I were considerably still better.) On the other hand, while there are certainly people better at mathematics than am I, no one seems to have accomplished what I seek to do. Economics is, after all, more than its mathematics.

What has most bothered me has been that complex axiom. There hasn't seemed much hope of resolving the general over-lap and of reducing the number of axiomata without first reducing that particular axiom. On 2 January, I was able to do just that, dissolving that axiom into two axiomata, each of which is acceptably simple. Granted that the number of axiomata increased by one, but now that the parts are each simple, I can begin to see how to reduce their overlap. Eliminating that overlap should either pare or vindicate the number of axiomata.

I don't know whether, upon getting results completed and a paper written around them, I would be able to get my work published in a respectable journal. I don't know whether, upon my work's getting published, it would find a significant readership. But the work is deeply important.

On the Economists' use of Rent*

Wednesday, 21 December 2016

Ordinary language typically uses rent to mean a recurring payment for the use of some good or service, especially for the use of land. The word has various other meanings in ordinary language; but, in economics, rent is used to mean something given in exchange, above and beyond what would have been the minimum necessary to effect the exchange in the absence of some restraint of trade. Usually, this concept is applied to pecuniary payment for a good or service above and beyond the minimum necessary to get that good or service, but one should see that exchanges without money might still involve such increased payment of one good or service for another, and that the same basic idea could be applied to cases in which someone were compelled to deliver more of a good or service than the minimum otherwise necessary to secure some amount of money.


It's mostly because of David Ricardo (18 April 1772 – 11 September 1823), an influential economist, that rent has this meaning. Ricardo used the word rent to refer to payment for the indestructible powers of land. That is to say that rent meant payment for the use of those properties of land that were not diminished by use; payment for harvesting things such as preëxisting plants and minerals would not, strictly speaking, be rent. Perhaps the only thing that could literally meet this criterion would be specific area, but Ricardo favored simplified models, so one might consider highly durable or naturally renewed properties as indestructible.

In Ricardo's mind, if someone renting land were given a right to cut down trees already on the land, or to quarry marble from it, then this right were essentially of the same sort as the right of someone buying lumber or stone at a mill; we certainly don't label the prices of such commodities as rent. Ricardo wanted to identify what were distinctive and essential in what we called rent, and to reserve the word rent just for those components of payments.

Ricardo imagined land as of different qualities, even when viewed only in terms of indestructible properties, but imagined the existing quantities of lands of each quality as not something ever increased by human action. And, in the context of his models, he concluded that rent were not determined by its cost of manufacture nor otherwise by some minimum below which the land-owner could not afford to produce it; rent, according to Ricardo, were purely an artefact of monopoly in the provision of land.

So long as this belief prevailed, it was natural for economists to extend the use of the word rent to other payments which they regarded as perfectly analogous. The word rent came to stand for any payment above and beyond the minimum necessary to effect an exchange were there a non-monopolistic market. And, even when most economists moved away from Ricardo's theory, as classical economics yielded to more thorough-going marginalism, they held onto this extended use of the term rent.


Because this use of rent can certainly be confusing, both when economists are interacting with lay-persons and when economists are attempting to discuss markets in which commodities are leased, sometimes instead of the bald word rent, they use the term economic rent. (This solution is imperfect, as that term can in ordinary language refer to a leasing payment which is in some sense reasonable for a lessee or potential lessee to bear.)


Economic rent, and the pursuit of rent — called rent-seeking — are considered quite important by most economists.

Rent-seeking, perhaps often unconscious but certainly almost never acknowledged, is wide-spread, and explains a very great deal of the political process.

Rents cannot be paid unless they are paid by someone; often, those paying them do not even realize that they are bearing these costs, or mistake their sources. Worse, rents typically transfer wealth inefficiently, with more lost by whoever is made to pay the rent than would be lost by some other transfer mechanism. Still worse, rent-seeking imposes costs even when it is unsuccessful.


Within a neo-classical framework, rent (or economic rent) might be alternately be defined as something given in exchange, above and beyond the opportunity cost of producing that for which it is exchanged. When the frequent assumptions of complete preferences, continuous divisibility of goods and of services, and ignorability of small costs hold, this new definition is equivalent to the original definition. But, exactly because one ought not to over-commit to those assumptions, it is best not to adopt the alternate definition as such.

I have encountered professors of economics asserting things to be rents that certainly were not. For example, one simply declared that the salary of a specific basketball player were a rent, but the professor had lost himself in a taxonomy which imagined the player simply as playing basketball or as idling. In fact, the player could have played for teams other than the one that hired him, and could have applied his abilities to something other than playing in professional basketball. If there were a rent in his salary, it may not even have been the major portion.


* This entry is primarily infrastructural. I want to be able to refer to rent and to rent-seeking in later entries, without there defining the associated terms.

A Matter of Interest

Sunday, 23 October 2016

Eugen Ritter von Böhm-Bawerk, an important economist of the second generation of the Austrian School, produced a theory of interest rates based upon the interplay of time-preference with the significance of time in production. (Previous theories had either looked towards just the one or towards just the other, or sought explanation in terms of social power.) This theory was adopted by Knut Wicksell and by Irving Fisher. Fisher translated most of the theory into neo-classical, mathematical terms. Hans Mayer provided one important element that Fisher had missed. I was exposed to this neo-classical translation by J[ames] Huston McCulloch in an undergraduate course on money and banking.

Years later, towards creäting a fuller explanation, I played with relaxing some of the assumptions. And some time after that, I wrote a paper for a graduate class in which I extended Fisher's two-period model to handle continuous time (by way of a space of ℵ1 dimensions). I've occasionally thought to write-up that aforementioned fuller explanation, but mostly been put-off by the task of generating the involved graphs to my satisfaction.

Recently, I was sufficiently moved to begin that project. I wasn't imagining doing anything much other than fleshing-out a translation previously effected by others, so I was considering publishing the exposition as a webpage, or as a .pdf.

But, as I've labored it, trying to be clear and correct and reasonably complete, I've seen how to talk about some old disagreements amongst economists that I don't know were ever properly settled — perhaps these quarrels were not even properly understood by any of the major disputants, who each may have been talking past the others. So I may steer towards producing something that I can submit to an academic journal. (The unhappy part of doing that would be identifying and reviewing the literature of the conflict, with which I currently have only second-hand familiarity.)

Perhaps I'll produce both something along the lines that I'd originally intended, and a paper for a journal.

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.