As I noted in an earlier 'blog entry, I use the words choice and choose simply to refer to selection; and, when I say that someone prefers X to Y, I mean that if given a set of mutually exclusive options that include X and Y then Y will never be selected. Some people try to mean something else by one or both of these terms. In the case of choose, they seldom if ever explain what that something might be. R[obert] Duncan Luce proposed to define preference in terms of probability of selection, rather than in an absolute manner as do I; that difference won't bear meaningfully upon what I have to say here.

One might have preferences about one's preferences. For example, preferring-not-to-prefer simultaneously X to Y, Y to Z, and Z to X for any X, Y, and Z. But note that making choices based upon the preferences that one has is different from choosing to have the preferences with which one makes the choice. Choices about preferences are meta-choices; preferences determining meta-choices are meta-preferences.

In theory, all choices could be determined by preferences, all preferences could be meta-chosen, all meta-choices could be determined by meta-preferences, all meta-preferences could be meta-meta-chosen, all meta-meta-choices could be determined by meta-meta-preferences, &c out to any finite level of meta that you might imagine. But the levelling cannot be infinite. At some point, one reaches a level that wasn't chosen. Varieties of choices and preferences that are turtles all the way down are an impossibility. A class of choices cannot have any members if it is defined such that each member is underlain by a choice of that same class. Likewise for preferences.

And hence I come to the expression sexual preference. As introduced and still generally to-day, it refers to what one sexually prefers; it says nothing about what one meta-prefers or meta-chooses. People said to have sexual preferences are thereby said to choose with those preferences, not to have chosen the preferences themselves. Someone said to have heterosexual preferences is not thus said to have chosen heterosexuality itself, and so too of someone said to have homosexual preferences. And if we deny that sexual preferences can be real because they are not underlain by a choice of sexual orientation, then we must claim that all non-sexual preferences are likewise not real, because it's never turtles-all-the-way-down.

The only people who will be offended by the term sexual preference itself will have confused preferences with meta-preferences — or will be those people who have simply embraced the claim that the term is offensive without much thought as to why it should be so. And a rather large group will not actually be offended, but will rôle-play as if offended, because they observe that this behavior is the practice of their political tribe.

In introductory treatments of economics, one often encounters a distinction drawn between what is called positive economics and what is called normative economics. In these names — and in typical discussion — there are problems.

The meaning of positive here is restricted to fact, as opposed to speculation. Now, on the one hand, supposedly positive economics, like all attempts by human beings to understand the world, is permeated by speculations, which in scientific effort are hypotheses. (The philosophic movement called positivism arose with incompetent aspirations.) On the other hand, contrasting the normative with something called positive entails an implication, insinuation, or declaration that the normative cannot be placed on as solid a foundation as the rest of our understanding. Sometimes a lack of present agreement is treated as if proof that there is no objective ethical truth; sometimes the question is just begged. In any case, the distinction is irrational.

Instead using the terms descriptive and prescriptive steps away from the worst aspect of using positive, though it would be less corrosive to refer to non-prescriptive economics as, well, non-prescriptive or as non-normative.

However, in behavioral science, elements drawn from prescriptive theory are often useful non-prescriptively, either as approximations or as bounding cases. Economic rationality and expected-utility maximization (the latter sometimes conflated with the former) are such elements.

Some economists would not even recognize economic rationality or expected-utility maximization as prescriptive in any case, because they are meta-preferential — they express a preference for structures of preference that have ordering properties such as transitivity and acyclicity, but say nothing about ultimate objectives and thus, in themselves, say nothing about whether one should prefer tomatoes to apples or life over death.

The prescriptive arguments for economic rationality and for expected-utility maximization are to the effect that those who conform realize more of their objectives — regardless of what those objectives might be — than those who do not, with it usually treated as tautologic that one desires such maximization.[1]

The non-prescriptive arguments for economic rationality and for expected-utility maximization as approximations note that these are relatively tractable models of behavior for which evolutionary dynamics will select. Because the models are taken from prescriptive work, some people mistake or misrepresent any use of them as necessarily prescriptive, but the claim is neither that social or other biologic evolution ought to select for something approximated by such behavior nor that agents ought to engage in the behavior for which evolution selects. (If anything, what is illuminated is that evolution selects for a propensity to such prescriptions!)

I endorse use of these models as tractable approximations in many cases, but I also embrace use of a weaker notion of economic rationality as a bounding case. A boundary of economic outcomes is given by considering what those outcomes would be were agents economically rational.

Behavioral economics concerns itself with when-and-how people actually behave, and especially with failures of the aforementioned models. Although this research is not what I do, I acknowledge its value. However, a great deal of what passes for behavioral economics involves an inferential leap from identifying a real or apparent deviation of behavior from one of these models to a conclusion that this-or-that result could be obtained by state intervention, with the researcher looking away from any proper examination of the behavior of agents determining practices of the state. Behavioral economics is thus used as the motte for a statist bailey. Additionally, even behavioral researchers with no apparent statist agenda often fail to recognize when behavior that seems at odds with these models is or may be instead at odds with some presumption of the researcher.[2]

[1] The main-stream of economic theory treats completeness of preferences as a feature of economic rationality but I've never seen a prescriptive argument even attempted for this feature. The prescriptive cases for transitivity and for acyclicity seem to presume an absence of conflicting, prior meta-preferences. The prescriptive argument for expected-utility maximization is especially problematic.

[2] While I have problems with some of the work and with much of the rhetoric of Gerd Gigerenzer, he has ably identified important cases of such failure on the part of researchers.

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

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

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

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

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

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

Since some of the recent visits to this 'blog are by way of search strings containing preference symbol, I put together a table of characters frequently used to represent preference relations. Click on the graphic for a PDF file providing symbols, their interpretation, their Unicode values in hexadecimal and in decimal, the names given to these symbols by the Unicode Consortium, and the LAΤΕΧ mark-up that one would enter for each of the symbols.