In the course of a present investigation of how the main-stream of economics lost sight of the general concept of utility, I looked again at the celebrated article Specimen Theoriæ Novæ de Mensura Sortis by Daniel Bernoulli, in which he proposed to resolve the Saint Petersburg Paradox[1] by revaluing the pay-off in terms of something other than the quantity of money.

The standard translation of his article into English[2] replaces Latin emolument- everywhere with utility, but emolumentum actually meant benefit.[3] Bernoulli's own words in his original paper show no more than that he thought that the actual marginal benefit of money were for some reason diminishing as the quantity of money were increased. However. before Bernoulli arrived at his resolution, Gabriel Cramer arrived at a resolution that had similar characteristics; and, when Bernoulli later learned of this resolution, he quoted Cramer. Cramer declared that money was properly valued à proportion de l' uſage [in proportion to the usage]. The term uſage itself carries exactly the original sense of utility. (Cramer goes on to associate the usefulness of money with plaiſir, but does not make it clear whether he has a purely hedonic notion of usefulness.) Bernoulli did not distinguish his position from that of Cramer on this point, so it is perfectly reasonable to read Bernoulli as having regarded the actual gain from money as measured by its usefulness.

Of course, both Cramer and Bernoulli were presuming that usefulness were a measure, rather than a preördering of some other sort.

[1] The classic version of the Saint Petersburg Paradox imagines a gamble. A coin whose probability of heads is that of tails is to be flipped until it comes-up tails; thus, the chance of the gamble ending on the n-th toss is ¹/2ⁿ. Initially, the payoff is 2 ducats, but this is doubled after each time that the coin comes-up heads; if the coin first comes up tails on the n-th flip, then the pay-off of the gamble will be 2ⁿ ducats. So the expected pay-off of the gamble is ∑[(¹/2ⁿ)·(2ⁿ ducats)] = 1 ducat + 1 ducat + … = ∞ ducats Yet one never sees people buying such contracts for very much; and most people, asked to imagine how much they would pay, say that they wouldn't offer very much.

Cramer's resolution did not account for the preëxisting wealth of an individual offered a gamble, and he suggested that the measure of usefulness of money might be measured as a square root of the quantity of money. Bernoulli's resolution did account for preëxisting wealth, and suggested that the actual benefit of money were measurable as a natural logarithm.

I'm amongst those who note that one cannot buy that which is not sold, and who believe that people asked to imagine what they would pay for such a contract instead imagine what they would pay for what were represented as such a contract, which could not possibly deliver astonishingly large amounts of purchasing power.

[2] Exposition of a New Theory on the Measurement of Risk in Econometrica v22 (1954) #1 (January) pp 22–36.

[3] In a footnote, translator Louise Sommer claims that mean utility is a free translation of emolumentum medium and then that the literal translation would be mean utility; I believe that she had meant to offer something else as the literal translation, but lost her train of thought.

As occasionally noted in publicly accessible entries to this 'blog, I have been working on a paper on qualitative probability. A day or so before Christmas, I had a draft that I was willing to promote beyond a circle of friends.

I sent links to a few researchers, some of them quite prominent in the field. One of them responded very quickly in a way that I found very encouraging; and his remarks motivated me to make some improvements in the verbal exposition.

I hoped and still hope to receive responses from others, but as of to-day have not. I'd set to-day as my dead-line to begin the process of submitting the paper to academic journals, and therefore have done so.

The process of submission is emotionally difficult for many authors, and my past experiences have been especially bad, including having a journal fail to reach a decision for more than a year-and-a-half, so that I ultimate withdrew the paper from their consideration. I even abandoned one short paper because the psychological cost of trying to get it accepted in some journal was significantly impeding my development of other work. While there is some possibility that finding acceptance for this latest paper will be less painful, I am likely to be in for a very trying time.

It is to be hoped that, none-the-less, I will be able to make some progress on the next paper in the programme of which my paper on indecision and now this paper on probability are the first two installments. In the presumably forth-coming paper, I will integrate incomplete preferences with incompletely ordered probabilities to arrive at a theory of rational decision-making more generalized and more reälistic than that of expected-utility maximization. A fourth and fifth installment are to follow that.

But the probability paper may be the most important thing that I will ever have written.

It has famously been argued that the word game cannot be defined in a way that adequately captures the various senses in which it is used. I believe that, in everyday use, the term game most often means a system of contrived challenges properly imposed or undertaken for purposes of amusement. Hence, someone might assert something such as Love is not a game! But, even in lay-use, game can have other meanings. For example, when a person proceeds deceitfully or insincerely, he or she may be said to be making a game of things, without necessarily seeking amusement in proceeding in this way.

Economists and mathematicians applying themselves to problems of economics or proximate to those of economics can use the term so very broadly as to refer to any problem of optimization. But, most often, they mean a system in which multiple parties interact with the potential for one or more parties to advance an interest or something that is treated as an interest (such as reproduction). It is in this sense that I here use the term game.

The rules of games are often subject to to change, and those changes may be affected or effected by players of the governed game. There is thus a meta-game — a system in which multiple parties interact with the potential for one or more of them to advance an interest by changing the rules of the game; or, in the context of others trying to changing the rules, by preserving the rules. The concept of meta-games is hugely important for understanding social processes.

Of course, a meta-game might have its own meta-game — a meta-meta-game. For example, the determination of a legal frame-work might be the meta-game of the social processes that the frame-work governs, and a struggle over social values might be the meta-game of the determination of the frame-work and thus the meta-meta-game of those social processes. But it can be difficult — without necessarily being useful — to work-out an actual hierarchy.

Sometimes, all that we really need to recognize is that some activity is a meta-game of some other game, without concerning ourselves as to whether the other game is itself a meta-game. People might readily recognize meta-gaming in activities such as political lobbying, but they generally don't recognize it when it's effected by psychologists, by teachers, or by screen-writers.

I want to draw upon this notion of meta-games for at least one 'blog entry, but I will probably want to draw upon it for multiple entries, so I will leave this entry as infrastructure. And I may later and without notice rework it, in an attempt to improve it as infrastructure.

It was once socially accepted that people were not responsible for acts of a wide variety if the persons engaged in them while intoxicated, even if the intoxication were quite voluntary and the engagement active. Over time that attitude has eroded. After all, a person who chooses to be intoxicated chooses to engage in increased probability that he or she will effect those acts. If a person who chose to drink passes-out on the front lawn, drives his vehicle into a pedestrian, or beats his domestic partner, few people would insist that he didn't choose to do such a thing. And, should we meet one of those few people, we rightly suspect that they cannot be trusted to use intoxicants responsibly.

In response to the campaign of Bernard (Bernie) Sanders, a great many people embraced things that they called democratic socialism. They didn't actually agree amongst themselves as to what this term meant. Many of them insisted that democratic socialism weren't socialism, which insistence did not provoke as often as it should a question as to why then its name should contain socialism. The answer simply was that Sanders had long referred to what he advocated with this term; they were stuck with socialism if they held onto Sanders. Whether they admitted that democratic socialism referred to socialism or not, all of the folk calling for something by that name sought to neutralize the dire associations of socialism with various outcomes that had been observed when regimes had been identified by that label. And all of these folk, whether or not they acknowledged that they were referring to socialism, agreed that what they called democratic socialism would indeed be democratic.

That insistence has afforded them a rhetorical ploy for dealing not only with socialistic regimes that were never democratic, but with socialistic regimes that have lost popular support, such as that in Venezuela. Absenting that support, these regimes are said not to be democratic, and hence plainly not to represent whatever might properly be called democratic socialism. But when a socialistic regime is brought to power by democratic means, in a framework of law that was effected by democratic means, and then uses that law to take unpopular actions, to insist that the regime is undemocratic begins to resemble claiming that the neighbors passed-out on the lawn, driving their cars into pedestrians, or beating their domestic partners did not choose to do such things. Oh yes they did. And anyone who insists otherwise is to be regarded as dangerous with the relevant intoxicants, including ballots.

Indeed, for most of recent history, popular opinion was not treated as particularly important in application to America by most Americans who came to call for democratic socialism. They had earlier thought it perfectly democratic when the Democratic Party, democratically elected to majority control of both Chambers of Congress and to the Presidency, effected various measures that were in fact widely unpopular with the more general population. President Obama advised the Republicans to win some elections. When they did, so that the Democrats lost first the House of Representatives and then the Senate, he and most of these folk for democratic socialism held to the idea that his democratic election to the Presidency legitimized his actions in defiance both of the votes of the Congress and of popular opinion amongst the wider population. Popular opinion in Venezuela and elsewhere has emerged as ostensibly relevant to democratic socialism exactly and only because, once again, socialism — even socialism within a framework democratically effected — has devolved as it always will if allowed to persist. There is no magic in democracy.

The state is a terrible institution, to be checked by an institutional framework that resists its growth, instead of enabled to grow by fantasies that amateurs or experts can use it expansively to bring about a more humane world.

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.

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.

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.

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 symmetric, 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.]

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.

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.