I incorporated some changes to my paper that I wished (almost immediately after I'd submitted it) that I had made sooner. Then I chose the next journal to which to submit it, read their submission guidelines, made some changes in the form of the citations, and submitted it to that next journal.

I received a decidedly uninformative rejection letter yester-day from the first journal to which I submitted my paper. Said rejection was a form letter explaining that a member of the editorial board, rather than a referee, read the paper, and that, when in such cases they decided to reject a paper, they save time by not producing a report. In most cases we are not rejecting papers because they have a particular flaw. (Although, presumably, in other cases they are, and they haven't even told me into which of these two categories my paper falls.)

Anyway, I need to decide to which journal I will next submit, look at their submission guidelines, reformat it and see how much more or less I can fit into it, and then send it off again.

Meanwhile, Andrew Sullivan notes the The Results as They Came In for the Iranian Presidential election. Specifically, as the official figures were up-dated, they fell almost perfectly along a straight line. The fit has an R² of .998, which is a virtual impossibility. So the official figures are a bald lie. That doesn't mean that Ahmadinejad wouldn't have won under a fair count, but it means that he chose to steal the election rather than to risk losing under a fair count.

I submitted a version of Indifference, Indecision, and Coin-Flipping to a journal this morning. In that context, I'm going make the working version more generally available.

For those who want to wade through the mathematics but find mysterious some of the notation or the formal notion of a Cartesian product or of a relation, there is a quick-and-dirty explanation of some of that infrastructure.

For those who, instead, want to get the basic ideas without carefully following the math or confronting the proofs, there is a Gentler Guide. It would be helpful, though perhaps not necessary, to have the original paper at hand when reading the Gentler Guide.

I might someday write a Gentler-Still Guide, with even less of the mathematical formalities, but such a treatment would either replace those formalities with verbal constructions that were themselves difficult to follow, or would necessarily discard an even greater amount of the content from the original paper.

If one has a question or questions (concerning this work) not answered by one of the three papers, a comment to this 'blog entry is about as good a way of asking as any.

By far, most submissions to the better reputed economics journals are simply rejected, and I have submitted to what may be the most prestigious economics journal. I am hoping to receive either a simple acceptance or a directive to revise and resubmit. (With economics papers in general, the latter is more common that the former, and is typically seen as good news.) If the paper is simply rejected, then (assuming that no fatal and irreparable flaws were found in the work) the next thing to do is to modify it, as much as seems reasonable, in light of any comments from the referees (reviewers) and from the editor, and submit it to one of the best remaining journals that I think might accept it.

It can take months for referees to actually read a given paper, and between the time that a paper is first submitted to its first journal and it is published in some journal (assuming that the paper is indeed ever published) can be a matter of years. Unsurprisingly, I hope for a faster resolution than that.

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.

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.

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.

The current version of my paper operationalizing and formalizing preferences that are not totally ordered can probably be pushed out the door now. I'm running or going to run it past two more academic economists whom I know before I submit it to a journal, but that's just pronounced caution, and more concerned with the quality of the exposition than with that of the ideas themselves.

Unfortunately, while I'm reasonably sure that the work is correct, I no longer have a gut sense that it's important. Intellectually, I see this lack of such a sense as stemming from a confluence of three things.

The first two are my extended efforts to understand and to communicate matters clearly; these efforts result in those matters now seeming very clear and thus seeming rather obvious to me. I have to remind myself that it was all very murky when I began.

But, additionally, through my life, I've repeatedly had the experience that I just don't feel the significance of completed work. I'm not sure why. Perhaps it's just constitutional anhedonia. I do know that things such as ceremonies and celebrations don't help.

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I've cobbled-together a sort of cheat-sheet for some of my readers who might not be familiar with some of the notation, mathematical notions, and economics jargon that I use in the paper; I'll make it openly available when I make the paper itself more openly available. (In the mean time, anyone with access to the paper who wants a copy of the cheat-sheet should let me know.) At some point, I hope to write-up a sort-of informal translation of the ideas of the paper into far less technical language.