Posts Tagged ‘qualitative probability’

Again into the Breach

Monday, 15 January 2018

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.

Just a Note

Thursday, 12 June 2014

Years ago, I planned to write a paper on decision-making under uncertainty when possible outcomes were completely ordered neither by desirability nor by plausibility.

On the way to writing that paper, I was impressed by Mark Machina with the need for a paper that would explain how an incompleteness of preferences would operationalize, so I wrote that article before exploring the logic of the dual incompleteness that interested me.

Returning to the previously planned paper, I did not find existing work on qualitative probability that was adequate to my purposes, so I began trying to formulating just that as a part of the paper, and found that the work was growing large and cumbersome. I have enough trouble getting my hyper-modernistic work read without delivering it in large quantities! So I began developing a paper concerned only with qualitative probability as such.

In the course of writing that spin-off paper, I noticed that a rather well-established proposition concerning the axiomata of probability contains an unnecessary restriction; and that, over the course of more than 80 years, the proposition has repeatedly been discussed without the excessiveness of the restriction being noted. Yet it's one of those points that will be taken as obvious once it has been made. I originally planned to note that dispensibility in the paper on qualitative probability, but I have to be concerned about increasing clutter in that paper. Yester-day, I decided to write a note — a very brief paper — that draws attention to the needlessness of the restriction. The note didn't take very long to write; I spent more time with the process of submission than with that of writing.

So, yes, a spin-off of a spin-off; but at least it is spun-off, instead of being one more thing pending. Meanwhile, as well as there now being three papers developed or being developed prior to that originally planned, I long ago saw that the original paper ought to have at least two sequels. If I complete the whole project, what was to be one paper will have become at least six.

The note has been submitted to a journal of logic, rather than of economics; likewise, I plan to submit the paper on qualitative probability to such a journal. While economics draws upon theories of probability, work that does not itself go beyond such theories would not typically be seen as economics. The body of the note just submitted is only about a hundred words and three formulæ. On top of the usual reasons for not knowing whether a paper will be accepted, a problem in this case is exactly that the point made by the paper will seem obvious, in spite of being repeatedly overlooked.

As to the remainder of the paper on qualitative probability, I'm working to get its axiomata into a presentable state. At present, it has more of them than I'd like.