How selfish soever man may be supposed, there are evidently some principles in his nature, which interest him in the fortune of others, and render their happiness necessary to him, though he derives nothing from it except the pleasure of seeing it.

Thus begins Adam Smith's first book, in its editions of 1759, 1761, 1767, 1774, 1781, and 1790. In other words, he was saying this both before and after his more famous work, An Inquiry into the Nature and Causes of the Wealth of Nations (1776, 1778, 1784, 1786, & 1789). At some point, I may write a lengthier entry on what Smith was doing with the Wealth of Nations, but I wanted to make the point that Smith didn't make his case for a free market based upon a personal belief that one only cared for others based upon their effects on one's own material well-being. Rather, he made his case (in the Wealth of Nations) for the optimality of a free market without availing himself of the proposition that people otherwise gave a d_mn about each other. Then, as now, many opponents of a free society held that an economy without extensive state control could work only if people had more fellow-feeling than they actually do.

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.

The toe that I injured more than six weeks ago still hurts when flexed in some ordinary ways. I'm fairly sure that I broke the thing. According to what I've read, it may take up to a year to completely heal.

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Recently, two different people at different places on different days have asked me about my having a foreign accent. As far as I'm concerned, I have a very generic American accent. The Woman of Interest and I speculate that the lack of more precisely identifiable regionalization is what has people wondering about my being from elsewhere. That is to say that I cannot be placed from my speech as from the South, Northeast, Midwest, or whatever.

I don't think that I was ever much inclined to adopt regionalisms. For example, my mother had a very strong Arkansan accent when I was a child, my father has a Missouri twang, and from some time in my fourth year until some time in my seventh, my family lived in North Carolina; yet it was noted that neither my brother nor I developed southern accents. Much later, I became very consciously deliberate in selecting the characteristics of what amounts to my personal accent. I wasn't interested to appear to be from a particular place or of a particular social standing; I was interested in things such as clear enunciation and as respect for the language.

Various people on the WWWeb have used the word peosis or peotic. In all the cases that I have examined, these uses appear to be typographical errors, with the intended word being poesis or poetic.

FWIW, the word πέος is Greek for membrum virile. Thus, for example, wax peotic would be equivalent to wax penile.

Working on that less formal explanation of my paper has paid another dividend.

The model in the paper has involved six propositions, which function like axiomata, specifically about choices concerning lotteries. I have known for some time that these weren't orthogonal — that there was overlap amongst what they said. It is at best unfortunate to have that sort of redundancy in foundational propositions. But I'd not seen how to reduce it.

This morning, after describing those propositions less formally, and then considering what to say about the theoremata that follow, I started to see how to turn one of those propositions into a theorem. After a bit of musing and fretting, I've effected the change.

Yester-day, as I was in the course of writing-up a somewhat less formal discussion of the ideas in my decision-theory paper, I reälized that I had fudged something important in that paper.

More specifically, I had erroneously treated an important property of one relation as ex definitione. That property does follow from the combination of the definition with some propositions in the paper, but it's not a fully observable property, whereäs I had tried to make each of the relations as observable as was possible, even at the cost of using somewhat cluttered definitions.

I was, unsurprisingly, very unhappy with the reälization. The confusion had been an act of incompetence on my part, in an area where competence is quite important to me. It meant that I had increased the potential burden upon those who have been or will be kind enough to check-over that work. And I didn't immediately know how much work I would have to do to repair the model.

As to the last, when I buckled-down and started the revision, it proved to be fairly easy. I removed the mistaken assertion in the discussion of the definition, and inserted a quick proof of the property amongst the theoremata.

Had the error not been caught before the paper were submitted to a journal, it might well have caused the paper to be rejected. A referee might have been bright enough to pick-up on the mistake, but (for various possible reasons) not seen that it weren't truly fundamental to the work.

One lesson that is reïnforced by this experience is the value, for one's own understanding, of explaining ideas to others.

Yester-day, I found a rat's nest under the hood of my car. Literally.

I visited my parents in Tucson from late March until last Tuesday. I parked outside, just off their drive-way, and didn't use my car very much during that time. They live far east of the city center, out amongst the cactus, gilla monsters, and pack rats. I spotted the occasional pack rat under my car, but thought very little of it.

On my way home, I was pulled-over by an officer of the Arizona Highway Patrol, because my passenger-side head-light was out. (He was simply concerned that the problem be addressed, and gave me a written warning rather than ticketting me.) I went to an automotive store on the next day or the day after that, and bought new bulbs. But, when I popped the hood to replace the bulb, I found that the wires to the bulb were frayed and broken. There was nothing there to bang-around. The Woman of Interest suggested that they'd been chewed by a mouse. Rodent damage seemed plausible, and I couldn't think of a good rival explanation. Anyway, I decided that the best way to effect a repair was with a new connector and some butt connectors (metal sleeves, which are in turn ensleeved in plastic, and which are crimped to join wires or cables).

Apparently, I was operating with a sort of tunnel vision when I discovered the chewed wires. Although the rat's nest was quite big, I didn't spot it, sitting on the engine behind the valve cover, until yester-day, as I was effecting the repair. The nest was built of twigs, sticks, and some soft fibrous material. I was puzzled about why I hadn't had an engine fire, until I reälized that the soft fiber was produced by shredding swatches of the hood insulator. That rat really did considerable damage.

None-the-less, its actions weren't malicious, and I rather hope that it either wasn't in the car at all when I was driving, or leapt out before I was going more than a few miles per hour. Otherwise, the pack rat almost certainly was cooked to death or was killed when it hit the pavement. Had it cooked, I probably would have found a body. And if the nest was built between my previous use of the car and when I was loading it to go home, then the rat probably fled as the car shook from that loading.

Another one of the many perturbing errors in Jeffrey's Subjective Probability, this from §4.1:

If I am sure that it was one of the years from 1951 to 1959, with equal probabilities, then my ex(X) will be 1951
9 + 1952
9 + … + 1959
9, which works out to be 1954.5.

One doesn't even have to do any arithmetic (I didn't) to spot the error; for a sequence of an odd number of equally-spaced integers, the average is the middle-most value, in this case 1955.

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.