## Archive for the ‘philosophy’ Category

### Theories of Probability — Perfectly Fair and Perfectly Awful

Tuesday, 11 April 2017

I've not heard nor read anyone remarking about a particular contrast between the classical approach to probability theory and the Bayesian subjectivist approach. The classical approach began with a presumption that the formal mathematical principles of probability could be discovered by considering situations that were impossibly good; the Bayesian subjectivist approach was founded on a presumption that those principles could be discovered by considered situations that were implausibly bad.

The classical development of probability theory began in 1654, when Fermat and Pascal took-up a problem of gambling on dice. At that time, the word probability and its cognates from the Latin probabilitas meant plausibility.

Fermat and Pascal developed a theory of the relative plausibility of various sequences of dice-throws. They worked from significant presumptions, including that the dice had a perfect symmetry (except in-so-far as one side could be distinguished from another), so that, with any given throw, it were no more plausible that one face should be upper-most than that any other face should be upper-most. A model of this sort could be be reworked for various other devices. Coins, wheels, and cards could be imagined as perfectly symmetrical. More generally, very similar outcomes could be imagined as each no more probable than any other. If one presumes that to be no more probable is to be equally probable, then a natural quantification arises.

Now, the preceptors did understand that most or all of the things that they were treating as perfectly symmetrical were no such thing. Even the most sincere efforts wouldn't produce a perfectly balanced die, coin, or roulette wheel, and so forth. But these theorists were very sure that consideration of these idealized cases had revealed the proper mathematics for use across all cases. Some were so sure of that mathematics that they inferred that it must be possible to describe the world in terms of cases that were somehow equally likely, without prior investigation positively revealing them as such. (The problem for this theory was that different descriptions divide the world into different cases; it would take some sort of investigation to reveal which of these descriptions, if any, results in division into cases of equal likelihood. Indeed, even with the notion of perfectly balanced dice, one is implicitly calling upon experience to understand what it means for a die to be more or less balanced; likewise for other devices.)

As subjectivists have it, to say that one thing is more probable than another is to say that that first thing is more believed than is the other. (GLS Shackle proposed that the probability of something might be measured by how surprised one would be if that something were discovered not to be true.)

But most subjectivists insist that there are rationality constraints that must be followed in forming these beliefs, so that for example if X is more probable than Y and Y more probable than Z, then X must be more probable than Z. And the Bayesian subjectivists make a particular demand for what they call coherence. These subjectivists imagine that one assigns quantifications of belief to outcomes; the quantifications are coherent if they could be used as gambling ratios without an opponent finding some combination of gambles with those ratios that would guarantee that one suffered a net loss. Such a combination is known as a Dutch book.

But, while quantifications can in theory be chosen that insulate one against the possibility of a Dutch book, it would only be under extraordinary circumstances that one could not avoid a Dutch book by some other means, such as simply rejecting complex contracts to gamble, and instead deciding on gambles one-at-a-time, without losing sight of the gambles to which one had already agreed. In the absence of complex contracts or something like them, it is not clear that one would need a preëstablished set of quantifications or even could justify committing to such a set. (It is also not clear why, if one's beliefs correspond to measures, one may not use different measures for gambling ratios.) Indeed, it is only under rather unusual circumstances that one is confronted by opponents who would attempt to get one to agree to a Dutch book. (I don't believe that anyone has ever tried to present me with such a combination, except hypothetically.) None-the-less, these theorists have been very sure that consideration of antagonistic cases of this class has revealed the proper mathematics for use across all cases.

The impossible goodness imagined by the classical theorists was of a different aspect than is the implausible badness of the Bayesian subjectivists. A fair coin is not a friendly coin. Still, one framework is that of the Ivory Tower, and the other is that of Murphy's Law.

### 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.

### The Hate Show

Friday, 24 February 2017

In George Orwell's novel 1984, people assembled each day for The Two Minute Hate. For two minutes, those gathered would feel and express their hatred of those whom they had been led to hate, by those whom they regarded as their guides. Orwell did not invent the idea of an interval or gathering for the purpose of hating. Such things are probably ancient, and were certainly called hates earlier in the 20th Century. Orwell hypothesized the formal institutionalization of scheduled rallies whose sole purpose was for hating.

Such gatherings are now routine, normalized. Some take place on a national or international level, on weekly or even daily bases. Others are smaller or less frequent. People collect in theaters or around television sets, and they hate. But few observers or participants see these gatherings for what they are, because the hatred is packaged as comedy. During these gatherings, there is very little in the way of clever violation of expectation, which is essential to intelligent comedy. Instead, there is ventilation — of disdain, of anger, of hatred, sometimes of fury — at those outside that group with whom the performers and audience identify. Treatment of hatred as comedy is not something new, but the acceptance of unacknowledged hatred as comedy has become commonplace. Gatherings for what most of us once would have called comedy have been increasingly displaced; our comedy shows have been replaced by Hates. We have Thirty Minute Hates, Sixty Minute Hates, Ninety Minute Hates.

The institutionalization has largely been private, but it has had something degree of state sponsorship, as when President Obama grinned broadly in response to Wanda Sykes' expressed wish that the kidneys of Rush Limbaugh should fail, during the 2009 White House Correspondents Association Dinner.

When I last visited my parents, who willfully live in an ideological echo chamber, they made a point each week of sitting together and watching Full Frontal with Samantha Bee. They laughed at nothing; they smiled at nothing; because nothing on it was funny. Nor did it deliver any fresh insights. What it delivered was hatred. But that was apparently what my parents wanted — a Twenty One Minute Hate.

### No Need for Doors

Thursday, 9 February 2017

84 Lumber bought airtime within the broadcast of the 2017 Superbowl, and presented a video of a Latina mother and daughter travelling through what seems to be Mexico, plainly in hopes of entering America. Inter-spliced with the scenes of their travel are scenes of Americans, clearly constructing something. When the mother and daughter reach the border, they are confronted by a grey and terrible wall. But, as they seek for some hope, they find it — sunlight somehow shining through a section of that wall. Running to it, they find a door. In the awful wall, it was a great door that the Americans in the other scenes were building.

84 Lumber is being attacked for their video, on a theory that its purpose were to defend illegal immigration. Naturally, 84 Lumber denies that their message were any such defense; they now claim that the door were a metaphor for the institutions of legal entry.

I don't encounter a lot of people who will honestly speak in favor of illegal immigration. They ought to do so. There is nothing wrong with illegal immigration. Nothing.

The vast majority of people who oppose illegal immigration or want greater legal restriction on immigration do not do so from racism, and I am very sorry that they have been slandered and libelled; but recognizing the inappropriateness of that accusation doesn't serve to support a case for denying people entry.

Indeed, immigrants might come to our nation and do a variety of things that are violations of the rights of the people who are here now, or that are otherwise undesirable; but every genuine right that might violated by an immigrant could also be violated by someone born and raised here; more generally, every socially corrosive act that might be perpetrated by an immigrant could also be perpetrated by a native. A man or woman who was born here can violate the property and person of someone else; a man or woman who was born here can demand that his or her religion or language be give a privileged legal status; a man or woman who was born here can live at the expense of the taxpayers. None of these behaviors is made better or worse by virtue of where the person were born, nor by whether he or she were allowed to immigrate by the law. I will grant that groups coming from some foreign cultures have a greater share of members likely to do undesirable things of some sorts; but some groups native to America have a greater share of members likely to do undesirable things of some sorts.

There is a dire confusion of the legal with the moral, both on the part of those who insist that illegal immigrants are already in the wrong by virtue of having broken laws that are ostensibly ours in coming here, and by those who insist that there is no such thing as an illegal immigrant. Law can be wrong, and when it is wrong then it may be ignored without doing wrong. Those immigrants here in violation of law are neither wrong simply for being illegal, nor legal because they are not wrong to be here.

America is not a club nor a corporation. The persons and properties within the area occupied by America are not ipso facto in any way the property of all Americans. The right to trade, the right to give without condition, and the right to take that which is freely offered are not rights that in any way reflect nationality. Those who would do business with newcomers are within their rights; newcomers who would do business with those Americans are within their rights.

It's offensively absurd to claim an entitlement to exclude people by pointing to state-managed infrastructure and programmes. They weren't brought into existence through some sort of social contract; ultimately, they were effected through threats of violence; and generally they crowded-out alternative institutions that would have been created by free people. Of course, the welfare state cannot survive in a world of such freedom; it could not survive even if the progressives were allowed to pursue their wildest dreams of taxation, nationally or globally. But so much the worse for the false generosity and false security of the welfare state, which cannot avoid bankruptcy in this century, regardless of whether it keeps all of us trapped on one side or another of its jurisdictional boundaries.

Many people who are going or went through the process of legal immigration may feel that it is unfair for others now to jump the queue; but the queue should never have existed in the first place, and one only compounds the injustice by imposing it upon others.

There should be no queue, no wall, no need for doors.

### λέγει αὐτῷ ὁ Πιλᾶτος τί ἐστιν ἀλήθεια;

Wednesday, 25 January 2017

Years ago, National Lampoon had a monthly column that they entitled True Facts. The title was a joke, not because the contents weren't true (they were an assembly of extraödinary news reports), but because facts cannot be untrue; something untrue is not a fact. Yet many people in various contexts were using terms such as actual fact, real fact, and true fact, almost as if it were possible for some facts to be false, imaginary, unreal. People still do, perhaps even more often. One can find lots of instances of people using imaginary fact; sometimes they do so ironically, but more often they are quite serious. By imaginary fact they mean a proposition that may be untrue, is likely to be untrue, or simply is untrue. In this retasking of the word fact, they've lost the use of the word to talk about facts, unless they add a word such as true. But, with that change in meaning, it not only becomes possible to use a term such as alternative fact to refer to a rival claim, but it becomes harder to see that untrue rival claims don't have equal standing with true rival claims, as they are all supposedly facts.

We aren't at all helped here that a great many people don't understand the words true and truth. That's not simply a problem of vocabulary. Truth is a hard concept, because it entails a meta-propositional act of mapping from a proposition back to itself. That is to say that, in most cases when we apply the word true or equivalent and certainly in the case of true facts, we are explicitly or implicitly making a proposition about a proposition. When we say It's true that I went to the store, that actual referent of the grammatic subject is not I, but the proposition that I went to the store, yet the upshot of this sentence is merely what would be conveyed in saying I went to the store. We perhaps don't need this device of recasting a proposition (I went to the store) as a meta-proposition (It is true that I went to the store), but it is useful because we are not omniscient, and must entertain propositions that are uncertain or discovered to be false; the concept of truth complements the conditions of falsehood and of uncertainty. Yet it is very hard to see that function, exactly because we use the concept to discuss itself. Truth is more easily named than described, if indeed a description is possible.

The difficulty in understanding the nature of truth makes it psychologically easier to embrace such notions as that all aspects of of past, present, and future are simply artefacts of individual belief or of group belief (expressed with formulæ such as truth is a social construct) or that what one wants or ought to want is to be treated a true. The word fact may then be used for components of narratives; embracing one narrative is seen as licensing one to accept propositions as fact that are alternative to components of rival narratives, and to reject propositions for no better reason than that they participate in rival narratives. Evolution of narratives is seen as licensing one to change the status of a proposition from fact to falsehood, or vice versa, even when discussing history. And we may even observe those socially identified as fact-checkers testing claims against narratives which are themselves never fact-checked, because the checkers implictly treat their favored narratives as the ultimate determinant of fact.

When Pilate asked What is truth?, perhaps he was truly curious as to the nature of truth, but he may merely have been asking why he should give a damn about it. Our political leaders have become ever more disdainful of truth. They have long offered us alternative facts, and their followers in each of our major political tribes and in most of the smaller groups as well have decided that, for them, these are the facts. Now we have an Administration that does so more baldly and less artfully. One might hope that this practice will explode on them; but, even if that explosion should happen, their opponents are likely to see an expansion of the envelope within which they may disregard the facts.

Sunday, 22 January 2017

Thinking about there already being an effort to persuade voters that they must support whomever the Democratic Party nominates in 2018 and in 2020, I was naturally led to wonder what sort of candidates those would be; and thence, more generally, what politics would be like in about three years.

What politics will be is something within the context of what they can be, so I try to imagine the plausible scenarii. To me, these look very grim.

I expect the Republican Party to continue to reshape itself around Donald Joseph Trump, to be more informed by his poison. I don't expect the dissenters within the Republican Party to enjoy much success, especially as I don't expect them to find any help either from main-stream of the media or from the alternative led by Fox. Some of the better people in that tribe whom we call the political right will leave it, and even some people who were enthusiastic about Trump will see or sense where things are leading, and turn away; however, it will continue to recruit people who were not previously its members but are attracted to Trump or to Trumpism. And a very large share of those who were already members of that tribe will reshape their ostensible beliefs to fit the pronouncements and actions of Donald Trump.

(If Trump should leave office early, then the Party will presumably work to reshape itself around Michael Richard Pence, who will attempt to segue from whatever Trumpism then is, to a frightening social conservatism. But I don't expect Trump to be removed.)

Meanwhile, the aforementioned Democrats are in a dark political death-pit. Their most recent nomination was decided as a struggle between what progressivism has become (and was always destined to be) and crony capitalism posturing opportunistically as that progressivism. The leadership ensured that the crony capitalist got the nomination, but the subsequent result was, if anything, to intensify the need of the leadership to pander to the progressive urges of the Party's base. And the response of the base to Trump's election has been to move still further left and to become more overtly violent.

That base is about 25% of the nation and of the voters. It likes to imagine itself as a plurality, as a majority, or sometimes even as the other 98% or as the 99%. But the political left has inflated its apparent size by taking disproportionate control of the commanding heights of our social institutions, and by implicitly coöperating with the political right (also only about a quarter of the population) to marginalize those with views that do not conform to the left-right framework; remarkably, the political right has kept the political left viable, and vice versa. (These days, about a third of the American population wants the state to be less involved both in matters of sex and of religion and in matters ordinarily classified as economic. That makes them a larger group than either the left or the right, but not larger than the two combined.) Given how small they actually are, the left (like the right) cannot take political power without getting votes from those outside their tribe. If the Democratic Party cannot free itself from the influence of those who continue down the path of progressivism, then it cannot return to power based upon a positive appeal; its hopes would lie only in Republican over-reach.

Which over-reach would certainly have recent precedence. In 2006 and 2008, the Republican Party was in its own death-pit. They'd stumbled into it under the influence of neo-conservatism. The neo-conservatives pursued two wars, guided by a theory that the people in Afghanistan and in Iraq were aching for liberal democracy and prepared to fight for it. And they pursued fiscal and regulatory policies that triggered a major financial crisis. The Republicans lost control of both chambers of Congress, and then of the White House.

What pulled them from that death-pit was the Tea Party, which began coälescing with rallies, and then organized itself well enough to displace candidates of the Republican establishment in primary races. Those in the Republican establishment who held onto their positions fought vigorously with the Tea Party, which served to burnish the credentials of the Tea Party candidates and office-holders. Attempts by the left to treat the Tea Party Republicans as responsible for the prior actions of the neo-conservative Republicans were unsuccessful in persuading those outside the Democratic base. Ultimately, it seems that the Tea Party failed in its objectives; they did not succeed in capturing the leadership of the Republican Party, and some office-holders who had cultivated the support of the Tea Party betrayed their trust. The Tea Party appears now itself displaced by an uglier and angrier populism. But the Tea Party had the effect of allowing the Republican Party largely to free itself from association with the awful policies of the Administration of George Walker Bush.

That brings me to the Women's March on Washington, and to its sister Marches in other cities. It is not impossible that these rallies could be the beginning of a process that could reälign the Democratic Party, pulling it from its death-pit as the Tea Party pulled the Republican Party from its own. The odds, however, are very much against that reälignment.

First, though a great many of the women who participated wanted to be heard, rather that to be told what to say by celebrities and by iconsdefinitely shouting No! to goddamn'd Donald Joseph Trump, but not all saying Yes! to what the Democratic Party or its progressive base have been offering — the objective of most of those who called and led these marches in the first place was not to reälign the Party, but to reälign women. A new leadership of reformers would have to be found.

Second, while the Tea Party did not much have to fight the Republican base, that is exactly what anyone seeking fundamentally to reälign the Democratic Party would have to do.

Those without much hope for the Republican or Democratic Parties as instruments of positive change sometimes turn to third parties. Some exist, others could be creäted. We've already seen a collapse of the institutionalized myth that third parties must always be formed either around one issue or around one candidate. The left and the right will join together, through the media that they control and through bi-partisan commissions, to fight the emergence of a real alternative; but, if the left continues to get ever more repulsive to those voters outside of the left and right, then the right will have a greatly weakened partner in their unholy alliance to exclude rival views. I don't imagine that I myself will find a party or Presidential candidate whom I can, in good conscience, support; but perhaps 2020 will be made less awful by the emergence of a better major party.

### A Blame Game

Sunday, 22 January 2017

I have previously explored the logical absurdity of insisting that those who don't vote for one of the two foremost candidates in an election are effectively voting for the other of these two candidates. That analysis could easily be generalized to include ballot measures; where abstaining from voting has sometimes been claimed to be the same as opposing a measure, and sometimes been claimed to be the same as supporting the measure.

The primary purpose of claims of these forms is to pressure someone into voting for a candidate whom — or measure which — the potential voter finds unappealing. We especially see these claims when there are actual candidates, or formulated ballot measures. But we also see that purpose at play when an election has been held and candidates and proposal for the next election are not yet identified. Some of those declaring You are now to blame for X because you did not vote for Y! are hoping to motivate the audience to tolerate whatever is demanded by the claimant's faction in that next election. An alternative would be to promise to offer something better than Y in that next election; but they are engaged in brinksmanship, threatening to take the community off a cliff if a plurality don't agree to their demands.

Other motivations for such claims in the wake of an election are simple ventilation and blame-shifting. It is frustrating to lose an election, and a blow to the ego to acknowledge that one's own faction may be largely responsible for that loss.[1]

There's another, unrecognized motivation for these claims. Although there is a very great logical distance between refusing to support one of the two major political tribes and thinking as do members of the other major tribe, it is easy enough for tribal members to disregard that distinction almost perfectly. Thus, these absurd claims that refusal to support Y is operationally the same thing as supporting X implicitly become part of a more general psychological device of treating politics as all falling along a left-right spectrum, and thereby avoiding any challenge to one's thought or behavior that cannot be dismissed from the left by pointing to the right or from the right by pointing to the left, and saying You guys are worse!, even if the challenger is not one of those guys. The challenge may even be spuriously taken as proof that, after all, the challenger were really a member of the other tribe, as he or she is not challenging them, and them alone.

[1] For example, James Henry (Jim) Webb could have beaten any of the Republican candidates for President in 2016, and it is at least plausible that Bernard (Bernie) Sanders could have beaten Donald J[oseph] Trump; but the Democratic Party chose its weakest or second-weakest candidate. (Martin Joseph O'Malley might have been a still worse choice, as his mythology of Baltimore collapsed in the face of the police murder of Freddie Carlos Gray jr.)

### 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.]

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.

### Dead Celebrities and the Constitution

Monday, 2 January 2017

The law has long treated the images of living persons as something like trademarks, so that the use of such images without the consent of those persons is restricted in various ways. Over the last few decades, there have been efforts — some successful — to turn these images into property of a sort that may legally be bequeathed upon death, as opposed to such images lapsing into the public domain.

The potential monetary rewards increased simply as celebrity became more culturally important. And the evolution of CGI has made it possible to fabricate the appearance of persons in video, not only increasing opportunities to make money from such images but to use those images in ways that many of us would see as grossly abusive (for example, in pornography).

Reflexively, quite a few people want law at a Federal level to protect the images of the dead. But there is some reasonable question as to whether the US Constitution empowers the Federal government to act.

The rub comes by way of Article I §8, which enumerates the powers of Congress. It specifically empowers Congress

To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;

As I've explained, this enumeration did not creäte copyrights; it instead gave Congress limited power to protect them; without that empowerment, the matter would simply have been left in the hands of common law and of the legislation of the constituent states. But neither §8 nor any other part of the unamended Constitution makes explicit mention of intellectual property of any other sort, and it is an unreasonable stretch to suggest that there is implicit reference to similar such property, exactly because there had been a felt need for explicit mention of the rights of authors and of inventors. Any prerogative to protect the images of the dead was left in the hands of the constituent states.

I used the word unamended advisedly, because one might try to make a case that the Fourteenth Amendment empowers the Congress to treat personal images as continuing to be property beyond personal death. But one can legitimately make that claim only if somehow the associated rights are basic rights of persons (or of US citizens as such) or can be shown to derive from basic rights; the Fourteenth Amendment doesn't empower Congress to reconfigure legal rights ad libitum.

There's a wide-spread propensity to confuse great desirability with moral necessity. But the penalties of law are always ultimately acts of violence, and there's a need for more than emotional appeal when the law forbids something. So, while it would be greatly desirable for the images of the celebrated dead to be treated with something like the respect that they would have received when alive, a solid case should be made for regarding them as property, or indeed they should be regarded as not property.

Some efforts to make personal images into property that remains such beyond the death of the persons have focussed on getting constituent states to have it treated as such in law. It's perhaps worth noting that the Fourteenth Amendment might be read to block the constituent states from converting these images to property (though I am sure that no court to-day would accept that reading).