Those who used to follow my LJ (long since deleted and purged) might recall that I find Rush Limbaugh deeply offensive, and began actively avoiding listening to him after he blamed the 1992 Los Angeles riots on Rodney King.

But is it funny to accuse Limbaugh of treason for expressing a hope that the Administration fails in its programmes of state expansion? Is it funny to suggest that Limbaugh is a henchman of Osama bin Laden? Is it funny to express a hope that Limbaugh suffer from kidney failure?

Apparently our current President thinks that it is.

There should never have been any acceptance of the entwined notions that bald hatred, utterly lacking cleverness, counts as comedy, and that so long as it's labelled as comedy it somehow doesn't count as hatred.

Some people try to light a candle. Some people curse the darkness. Me? Part of me wants to model the darkness.

I was led to this reälization upon reading the latest entry from zenicurean. In response to news reports about the latest swine-flu concerns, he writes

Plenty of first reactions appear to heavily involve doing things actual health care experts are not chiefly concerned about getting done, but that's how it always works, isn't it?

And I almost immediately thought about why those first reäctions are what they are. For example

• Officials want to be seen as doing something.
• People, including officials, often greatly over-estimate their understanding of issues that have (or seem to have) a significant bearing on general welfare.
• Officials with axes to grind are quick to find excuses for the grinding.
• Politicians can exploit the prejudices and desires of voters who are predisposed to support various measures (such as blocking foreign trade or travel, or subsidizing some profession).

So, could we pull this altogether, and surely other things that don't come so quickly to-mind, perhaps into a mathematical model, or perhaps into something less formal, that would have some predictive efficacy, or at least some distinctive explanatory efficacy?

I have posted one entry to this 'blog that made reference to Cournot-Nash equilibria, and I expect to write another soon. I'm going to use this entry to explain the concept of a Cournot-Nash equilibrium, without resorting to mathematical formulæ.

First, let me give my favorite example of the idea, the behavior of prairie dog mothers in at least some towns. Prairie dogs are omnivores; they are primarily herbivorous, but will also consume small animals such as insects. If a prairie dog mother stays away from her litter of pups, they are liable to be eaten by something, so she will prefer food that is close at-hand — such as the pups of another mother who is away from her burrow. In fact, in some towns, when pups are eaten, it is usually by mothers trying to get home before their own pups are eaten. If any one prairie dog were to stop eating pups while the others continued, then her own pups would more likely be eaten because she'd be away from home for longer or more frequent periods. They eat each other's babies because they eat each other's babies.

Some of you may be thinking of the Prisoners' Dilemma, which, under classic assumptions, results in a similar mess. It too is an example of a Cournot-Nash equilibrium.

The essence of a Cournot-Nash equilibrium is that each participant has no incentive to change behavior unless other players change behavior, so each — and thus every — participant sticks with his or her established behavior. Although the prairie dog example and the classic telling of the Prisoners' Dilemma are sub-optimal equilibria, it could be the case that an equilibrium were the best-possible equilibrium, and no one had an incentive to change his or her behavior so long as no one else changed his or her behavior; so it's important to distinguish optimal Cournot-Nash equilibria from sub-optimal Cournot-Nash equlibria.

The Nash to whom the name refers is John Forbes Nash jr, whose life and work were grossly misrepresented in the movie A Beautiful Mind (2001). Nash's most famous accomplishment was explicitly generalizing and formalizing the idea of a Cournot-Nash equilibrium, which some simply call a Nash equilibrium. But there were famous antecedent uses of the idea, the best-known of which was by Antoine Augustin Cournot, in an 1838 model of oligopolistic competition.[1]

A less-often recognized antecedent use was by Thomas Hobbes in Leviathan (1651). Hobbes famously proposes that, in the absence of a State, life will be nasty, brutish, and short. More specifically, he said

Hereby it is manifest that during the time men live without a common power to keep them all in awe, they are in that condition which is called war; and such a war as is of every man against every man. For war consisteth not in battle only, or the act of fighting, but in a tract of time, wherein the will to contend by battle is sufficiently known: and therefore the notion of time is to be considered in the nature of war, as it is in the nature of weather. For as the nature of foul weather lieth not in a shower or two of rain, but in an inclination thereto of many days together: so the nature of war consisteth not in actual fighting, but in the known disposition thereto during all the time there is no assurance to the contrary. All other time is peace.

Whatsoever therefore is consequent to a time of war, where every man is enemy to every man, the same consequent to the time wherein men live without other security than what their own strength and their own invention shall furnish them withal. In such condition there is no place for industry, because the fruit thereof is uncertain: and consequently no culture of the earth; no navigation, nor use of the commodities that may be imported by sea; no commodious building; no instruments of moving and removing such things as require much force; no knowledge of the face of the earth; no account of time; no arts; no letters; no society; and which is worst of all, continual fear, and danger of violent death; and the life of man, solitary, poor, nasty, brutish, and short.[2]

According to Hobbes, without the State, production is subject to predation, so potential producers have less incentive to produce and everyone has incentive to prey upon everyone else.

But Hobbes has also identified a special case of one solution to what would otherwise be a sub-optimal Cournot-Nash equilibrium. In Leviathan, men end the war amongst them by explicitly agreeing to the creätion of an institution (the State) which will change the equilibrium. More generally, agreements need not be explicit or conscious, and the transforming institution could be a code of conduct. For example, the classic statement of the Prisoners' Dilemma treats the game as played in a social vacuum of a sort. In real life, people build reputations, reward desired behaviors, and punish the behaviors to which they object. Commitment mechanisms don't necessarily free us from every possible sub-optimal Cournot-Nash equlibrium, but naïve game theory too often fails to consider their possibility. (There was some perverse gloating in A Beautiful Mind about how Nash had somehow refuted Adam Smith, but the liberal order of which Smith wrote is filled with commitment mechanisms. Private property itself is an example of such a mechanism.)

Perhaps, in time, even the prairie dogs will evolve a mechanism such that eating each other's pups is no longer an equilibrium.

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[1] Recherches sur les principes mathématiques de la théorie des richesses, Ch 7.

[2] Chapter XIII ¶ 8-9.

As noted earlier, I've been reading Subjective Probability: The Real Thing by Richard C. Jeffrey. It's a short book, but I've been distracted by other things, and I've also been slowed by the condition of the book; it's full of errors. For example,

It seems evident that black ravens confirm (H) All ravens are black and that nonblack nonravens do not. Yet H is equivalent to All nonravens are nonblack.

Uhm, no: (X ⇒ Y) ≡ (¬X ∨ Y) = (Y ∨ ¬X) = (¬¬Y ∨ ¬X) = [¬(¬Y) ∨ ¬X] ≡ (¬Y ⇒ ¬X) In words, that all ravens are black is equivalent to that all non-black things are non-ravens.[1]

The bobbled expressions and at least one expositional omission sometimes had me wondering if he and his felllows were barking mad. Some of the notational errors have really thrown me, as my first reäction was to wonder if I'd missed something.

Authors make mistakes. That's principally why there are editors. But it appears that Cambridge University Press did little or no real editting of this book. (A link to a PDF file of the manuscript may be found at Jeffrey's website, and used for comparison.) Granted that the book is posthumous, and that Jeffrey was dead more than a year before publication, so they couldn't ask him about various things. But someone should have read this thing carefully enough to spot all these errors. In most of the cases that I've seen, I can identify the appropriate correction. Perhaps in some cases the best that could be done would be to alert the reader that there was a problem. In any case, it seems that Cambridge University Press wouldn't be bothered.

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[1]The question, then, is of why, say, a red flower (a non-black non-raven) isn't taken as confirmation that all ravens are black. The answer, of course, lies principally in the difference between reasoning from plausibility versus reasoning from certainty.

Yester-day, I again encountered the slogan No Blood for Oil!, made popular in the run-up to the invasion of Iraq.

I greatly doubt that the people who embrace this slogan have much thought about what it would really mean to forswear the use of violence over economic resources. Only a tiny minority are truly prepared to do that.

This proposition should be obvious in the case of those who want the State to actively participate in decisions about the allocation of resources. The point in having the State determine what quantities will be produced or to whom or to what production will go, or at what prices goods or services will be sold is to use violence or a threat of violence, effected by police and by prison guards. Were the economic administration to be by friendly persuasion, it could be done without the State.

Removing the State as an active participant doesn't utterly remove violence from the equation. If one believes that individuals or communities may forceably defend acquisition, retention, or distribution of goods or of services, then one accepts the use of violence over economic resources. It doesn't matter whether the forceable defense is provided by the State, by private protection agencies, by mobs, or by rugged individualists.

So if one believes that the state should provide the poor with home heating oil, or control gasoline prices, or if one believes in forceably defendable private property in petroleum or in forceably defendable anarcho-socialistic management of petroleum, then one believes in trading blood for oil.

In order to genuinely reject such an exchange, one would have to be truly and utterly pacifistic about petroleum, as are the Amish (albeït that a petroleum pacifist might be violent about other things).

Now, I surely don't claim that the United States should ever use its military in an attempt to secure foreign sources of goods or of services. (We can set aside debate over what the actual relationship were of the invasion of Iraq to American dependence upon Middle Eastern petroleum.) But simple-minded slogans and ad hoc moralizations don't typically propel discourse or move convictions in a humane direction.

Years ago, a friend of mine used to regularly listen to right-wing talk radio. (I imagine that he still does.) I was often a passenger in his car, and there usually had to listen to this programming as well. What I heard drove me up a wall. These commentators didn't usually target people with whose views I agreed, but they routinely misrepresented the arguments that were used by their opponents, made ridiculous universalizations or near-universalizations about the motivations of these opponents, and pretended that the only alternatives to the views of the political left were those of the political right. And the abiding emotion was hate.

For the past few days, I have been visiting my parents. Nearly every evening, they watch MSNBC, and I catch some of it whenever I visit them. What I hear drives me up a wall. The commentators of MSNBC don't usually target people with whose views I agree, but they routinely misrepresent the arguments that have been used by their opponents, make ridiculous universalizations or near-universalizations about the motivations of these opponents, and pretend that the only alternative to the views of the political right are those of the political left. And the abiding emotion is hate.

For example, during this latest visit, I heard Rachel Maddow mocking William Kristol as ostensibly claiming a few weeks into the invasion of Iraq that the war was won, when what Kristol had actually said was that every battle had been decisively won. Were I now to claim that, a few weeks into the American Civil War, every battle had been decisively won by the Confederacy, I would plainly not be claiming that the Confederacy had won the war.

(Maddow was more generally concerned to pretend that the neoconservatives were trying to reposition and to repackage themselves as supporters of the war policy of the Obama Administration. The truth is that, in actual practice, this policy far more closely resembles that of the later Bush Administration than it does the policy described during the Obama candidacy. The neoconservatives, then, don't have to reposition much, though they plainly need to repackage if they are to regain active influence, since their persons and past organizations are anathematized.)

On top of being bothered by all this hate and misrepresentation in-and-of-itself, I am bothered that my father seems to be at least amused by this rubbish, and that my mother sort-of waves-away the fact that there's a stream of misrepresentation, and refuses to acknowledge that the hate is on a par with that of right-wing talk radio.

I end-up closing myself into the principal guest room, away from the television but also then away from my parents.

Amendment (2009:04/10): My father stated, last night, that while my mother likes Rachel Maddow, he finds Maddow unpleasant. Now, if only he would reject some of the other folk on MSNBC.

The Classic Monty Hall Problem

Andy is a contestant in a game. In this game, each contestant makes a choice amongst three tags. Each tag is committed to an outcome, with the commitment concealed from each contestant. Two outcomes are undesirable; one is desirable. Nothing reveals a pattern to assignments.

After Andy makes his choice, it is revealed to him that a specific tag that he did not choose is committed to an undesirable outcome. Andy is offered a chance to change his selection. Should he change?

Three Contestants

Andy, Barb, and Pat are contestants in a game. In this game, each contestant makes an independent choice amongst three tags. Each tag is committed to an outcome, with the commitment concealed from each contestant. Two outcomes are undesirable; one is desirable. Nothing reveals a pattern to assignments. In the event that multiple players select the same tag, outcomes are duplicated.

After all contestants make their choices, it is revealed that Andy, Barb, and Pat have selected tags each different from those of the other two contestants. And it is revealed that Pat's tag is associated with an undesirable outcome. Andy and Barb are each offerd a chance to change their selections. What should each do?

This story

is not getting much attention from the main-stream media.

I will be working on a Gadsden-flag bumper-sticker for my car.

[Up-Date (2009:07/17): Some time after this entry was posted, CoolShaving.com removed its fraudulent claims, which had been up since at least 19 July 2006.]

At CoolShaving.com, they claim

Believe it or not, a young man actually thought we killed badgers to get these bristles for our shaving brushes. Nothing could be further from the truth. The manufacturer of these superior quality brushes maintains a flock of badgers that are more pampered and coddled than any badger in the wild, or any domestic animal for that matter.

The page on which they advertise the line of shave brushes doesn't identify the maker in text, but on the handles one can see that these brushes are branded Col. Ichabod Conk.

The Conk brushes are manufactured by Progress-Vulfix Ltd and by Dovo.

Progress-Vulfix Ltd makes no claims about a flock of badgers[1] nor of not using the bristles of killed badgers on the page where they describe their brushes at VulfixOldOriginal.com nor on that at Progress-Vulfix.com. Neither the string cruelty-free nor vegan are found at VulfixOldOriginal.com, nor at Progress-Vulfix.com

The brush that Dovo supplies to Conk isn't listed on the page of brushes sold by CoolShaving.com. But, for the record, the strings ohne Grausamkeit [without cruelty], Grausamkeit-frei, cruelty-free, and vegan do not appear at the Dovo site.

CoolShaving.com is registered to Jim H. Hedgepath of 129 Minnie Fallaw Road, Lexington, SC 29073-8226.

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[1] A company of badgers is called a cete /sit/.

I've been taking another run at Subjective Probability: The Real Thing (2004) by Richard C. Jeffrey. I'd started reading it a while back, but got distracted. Anyway, Jeffrey was an important subjectivist — someone who argued that probability is a measure of belief, and that any degree of belief that does not violate certain rationality constraints is permitted. (As I have noted earlier, the subjectivism here is in the assignment of quantities not specifically required by objective criteria. The subjectivists believe either that quantity by reason must be assigned, albeït often arbitrarily, or that Ockham's Razor is not a binding constraint.) And the posthumous Subjective Probability was his final statement.

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At some point, I encountered the following entry in the index:

Nozick, Robert, 119, 123

which entry was almost immediately annoying. Page 119 is in the References section, and indeed has the references for Nozick, but that's a pretty punk thing to drop in an index. Even more punk would be an index entry that refers to itself; and, indeed, page 123 is in the index, and it is on that page that one finds Nozick, Robert, 119, 123.

Well, actually, I'd forgot something about this book, which is probably an artefact of its being posthumous: Most or all of the index entries are off by ten pages, such that one ought to translate Nozick, Robert, 119, 123 to Nozick, Robert, 109, 113. And, yes, there are references to Nozick on those pages (which are part of a discussion of Newcomb's Problem and of related puzzles). It was just chance-coïncidence that ten pages later one found the listings in the references and in the index.

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In decision theory, there are propositions call independence axiomata. The first such proposition to be explicitly advanced for discussion (in an article by Paul Anthony Samuelson) is the Strong Independence Axiom, the gist of which is that the value of a reälized outcome is independent of the probability that it had before it was reälized. Say that we had a lottery of possible outcomes X₁, X₂,… X_n, each X_i having associated probability p_i. If we assert that the expected value of this lottery were

Σ[p_i · u(X_i)]

where u( ) is some utility function, then (amongst other things) we've accepted an independence proposition. Otherwise, we may have to assert something such as that the expect value were

Σ[p_i · u(X_i,p_i)]

to account for such things as people taking an unlikely million dollars to be somehow better than a likely million dollars.

Anyway, there's another proposition which to most of us doesn't look like the Strong Independence Axiom, and yet is pretty much the same thing, the Sure Thing Principle, which is associated with Leonard Jimmie Savage (an important subjectivist, whom I much admire, and with whom I markèdly disagree). Formally, it's thus:

{[(A ∧ B) pref C] ∧ [(A ∧ ¬B) pref C]} ⇒ (A pref C)

Less formally,

If the combination of A and B is preferred to C, and the combination of A without B is preferred to C, then A is just plain preferred to C, regardless of B.

Savage gives us the example of a businessman trying to decide whether to buy a piece of property with an election coming-up. He thinks-through whether he would be better off with the property if a Democrat is elected, and decides that he would prefer that he had bought the property in that case. He thinks-through whether he would be better off with the property if a Republican is elected, and decides that he would prefer that he had bought the property in that case. So he buys the property. This seems very reasonable.

But there is a famous class of counter-examples, presented by Jeffrey in the form of the case of the Marlboro Man. The hypothetical Marlboro Man is trying to decide whether to smoke. He considers that, if he should live a long life, he would wish at its end that he had enjoyed the pleasure of smoking. He considers that, if he should live a short life, he would wish at its end that he had enjoyed the pleasure of smoking. So he smokes. That doesn't seem nearly so reasonable.

There is an underlying difference between our two examples. The businessman would not normally expect his choice to affect the outcome of the election; the Marlboro Man ought to expect his choice to affect the length of his life. Jeffrey asserts that Savage only meant the Sure Thing Principle to hold in cases where the probability of B were independent of A.

But what makes the discussion poignant is this: Jeffrey, dying of surfeit of Pall Malls, wrote this book as his last, and passed-away from lung cancer on 9 November 2002.