Posts Tagged ‘probability’

Fifth Rejection and Sixth Attempt

Sunday, 30 November 2014

My short article was rejected by one journal yester-day, and submitted to another in the wee hours of this morning. And, yes, that's just how the previous entry began.

This time, an editor at the rejecting journal informed me that an unnamed associate editor felt that the article didn't fit the purposes of the journal. I got no further critique from them than that. (It should be understood that, as many submissions are made, critiquing every one would be very time-consuming.)

With respect to my paper on indecision, I had some fear that I would run out of good journals to which I might submit it. With respect to this short article, I have a fear that I might run out of any journal to which I might submit it. It just falls in an area where the audience seems small, however important I might think these foundational issues.

Fourth Rejection and Fifth Attempt

Tuesday, 11 November 2014

My short article was rejected by one journal yester-day, and submitted to another in the wee hours of this morning.

At the journal that rejected it, the article was approved by one of the two reviewers, but felt to be unsuited to the readership of the journal by the other reviewer and by the associate editor. Additionally, the second reviewer and the associate editor suggested that it be made a more widely ranging discussion of the history of subjectivist thought, which suggestion shows some lack of appreciation that foundational issues are of more than historical interest, and that the axiomata invoked by the subjectivists are typically also invoked by logicists. (I say appreciation rather than understanding, because the reviewer briefly noted that perhaps my concern was with the logic as such.)

I made three tweaks to the article. One was to make the point that axiomata such as de Finetti's are still the subject of active discussion. Another was to deal with the fact that secondary criticism arose from the editor's and the objecting reviewer's not knowing what weak would mean in reference to an ordering relation. The third was simply to move a parenthetical remark to its own (still parenthetical) paragraph.

The journal that now has it tries to provide its first review within three months.

Third Rejection and Fourth Attempt

Friday, 29 August 2014

As expected, my brief paper was quickly rejected by the third journal to which I sent it. The rejection came mid-day on 19 July; the editor said that it didn't fit the general readership of the journal. He suggested sending it to a journal focussed on Bayesian theory, or to a specific journal of the very same association as that of the journal that he edits. I decided to try the latter.

On the one hand, I don't see my paper as of interest only to those whom I would call Bayesian. The principle in question concerns qualitative probability, whether in the development of a subjectivist theory or of a logicist theory, and issues of Bayes' Theorem only arise if one proceeds to develop a quantitative theory. On the other hand, submitting to that other journal of the same association was something that I could do relatively quickly.

I postponed an up-date here because I thought that I'd report both rejections together if indeed another came quickly. But, so far, my paper remains officially under review at that fourth journal.

The paper is so brief — and really so simple — that someone with an expertise in its area could decide upon it minutes. But reviewing it isn't just a matter of cleverness; one must be familiar with the literature to feel assured that its point is novel. A reviewer without that familiarity would surely want to check the papers in the bibliography, and possibly to seek other work.

Additionally, a friend discovered that, if he returned papers as quickly as he could properly review them, then editors began seeking to get him to review many more papers. Quite reasonably, he slowed the pace of at which he returned his reviews.

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.

Notions of Probability

Wednesday, 26 March 2014

I've previously touched on the matter of there being markèdly differing notions all associated with the word probability. Various attempts have been made by various writers to catalogue and to coördinate these notions; this will be one of my own attempts.

[an attempt to discuss conceptions of probability]

Quantifying Evidence

Friday, 12 August 2011
The only novel thing [in the Dark Ages] concerning probability is the following remarkable text, which appears in the False Decretals, an influential mixture of old papal letters, quotations taken out of context, and outright forgeries put together somewhere in Western Europe about 850. The passage itself may be much older. A bishop should not be condemned except with seventy-two witnesses … a cardinal priest should not be condemned except with forty-four witnesses, a cardinal deacon of the city of Rome without thirty-six witnesses, a subdeacon, acolyte, exorcist, lector, or doorkeeper except with seven witnesses.⁹ It is the world's first quantitative theory of probability. Which shows why being quantitative about probability is not necessarily a good thing.
James Franklin
The Science of Conjecture: Evidence and Probability before Pascal
Chapter 2

(Actually, there is some evidence that a quantitative theory of probability developed and then disappeared in ancient India.[10] But Franklin's essential point here is none-the-less well-taken.)

⁹ Foot-note in the original, citing Decretales Pseudo-Isidorianae, et Capitula Angilramni edited by Paul Hinschius, and recommending comparison with The Collection in Seventy-Four Titles: A Canon Law Manual of the Gregorian Reform edited by John Gilchrist.

[10] In The Story of Nala and Damayanti within the Mahābhārata, there is a character Rtuparna (aka Rituparna, and mistakenly as Rtupama and as Ritupama) who seems to have a marvelous understanding of sampling and is a master of dice-play. I learned about Rtuparna by way of Ian Hacking's outstanding The Emergence of Probability; Hacking seems to have learned of it by way of V.P. Godambe, who noted the apparent implication in A historical perspective of the recent developments in the theory of sampling from actual populations, Journal of the Indian Society of Agricultural Statistics v. 38 #1 (Apr 1976) pp 1-12.

Disappointment and Disgust

Sunday, 21 March 2010

In his Philosophical Theories of Probability, Donald Gillies proposes what he calls an intersubjective theory of probability. A better name for it would be group-strategy model of probability.

Subjectivists such as Bruno di Finetti ask the reader to consider the following sort of game:

  • Some potential event is identified.
  • Our hero must choose a real number (negative or positive) q, a betting quotient.
  • The nemesis, who is rational, must choose a stake S, which is a positive or negative sum of money or zero.
  • Our hero must, under any circumstance, pay the nemesis q·S. (If the product q·S is negative, then this amounts to the nemesis paying money to our hero.)
  • If the identified event occurs, then the nemesis must pay our hero S (which, if S is negative, then amounts to taking money from our hero). If it does not occur, then our hero gets nothing.
Di Finetti argues that a rational betting quotient will capture a rational degree of personal belief, and that a probability is exactly and only a degree of personal belief.

Gillies asks us to consider games of the very same sort, except that the betting quotients must be chosen jointly amongst a team of players. Such betting quotients would be at least examples of what Gillies calls intersubjective probabilities. Gillies tells us that these are the probabilities of rational consensus. For example, these are ostensibly the probabilities of scientific consensus.

Opponents of subjectivists such as di Finetti have long argued that the sort of game that he proposes fails in one way or another to be formally identical to the general problem for the application of personal degrees of belief. Gillies doesn't even try to show how the game, if played by a team, is formally identical to the general problem of group commitment to propositions. He instead belabors a different point, which should already be obvious to all of his readers, that teamwork is sometimes in the interest of the individual.

Amongst other things, scientific method is about best approximation of the truth. There are some genuine, difficult questions about just what makes one approximation better than another, but an approximation isn't relevantly better for promoting such things as the social standing as such or material wealth as such of a particular clique. It isn't at all clear who or what, in the formation of genuinely scientific consensus, would play a rôle that corresponds to that of the nemesis in the betting game.

Karl Popper, who proposed to explain probabilities in terms of objective propensities (rather than in terms of judgmental orderings or in terms of frequencies), asserted that

Causation is just a special case of propensity: the case of propensity equal to 1, a determining demand, or force, for realization.
Gillies joins others in taking him to task for the simple reason that probabilities can be inverted — one can talk both about the probability of A given B and that of B given A, whereäs presumably if A caused B then B cannot have caused A.

Later, for his own propensity theory, Gillies proposes to define probability to apply only to events that display a sort of independence. Thus, flips of coins might be described by probabilities, but the value of a random-walk process (where changes are independent but present value is a sum of past changes) would not itself have a probability. None-the-less, while the value of a random walk and similar processes would not themselves have probabilities, they'd still be subject to compositions of probabilities which we would previously have called probabilities.

In other words, Gillies has basically taken the liberty of employing a foundational notion of probability, and permitting its extension; he chooses not to call the extension probability, but that's just notation. Well, Popper had a foundational notion of propensity, which is a generalization of causality. He identified this notion with probability, and implicitly extended the notion to include inversions.

Later, Gillies offers dreadful criticism of Keynes. Keynes's judgmental theory of probability implies that every rational person with sufficient intellect and the same information set would ascribe exactly the same probability to a proposition. Gillies asserts

[…] different individuals may come to quite different conclusions even though they have the same background knowledge and expertise in the relevant area, and even though they are all quite rational. A single rational degree of belief on which all rational being should agree seems to be a myth.

So much for the logical interpretation of probability, […].
No two human beings have or could have the same information set. (I am reminded of infuriating claims that monozygotic children raised by the same parents have both the same heredity and the same environment.) Gillies writes of the relevant area, but in the formation of judgments about uncertain matters, we may and as I believe should be informed by a very extensive body of knowledge. Awareness that others might dismiss as irrelevant can provide support for general relationships. And I don't recall Keynes ever suggesting that there would be real-world cases of two people having the same information set and hence not disagreeing unless one of them were of inferior intellect.

After objecting that the traditional subjective theory doesn't satisfactorily cover all manner of judgmental probability, and claiming that his intersubjective notion can describe probabilities imputed by groups, Gillies takes another shot at Keynes:

When Keynes propounded his logical theory of probability, he was a member of an elite group of logically minded Cambridge intellectuals (the Apostles). In these circumstances, what he regarded as a single rational degree of belief valid for the whole of humanity may have been no more than the consensus belief of the Apostles. However admirable the Apostles, their consensus beliefs were very far from being shared by the rest of humanity. This became obvious in the 1930s when the Apostles developed a consensus belief in Soviet communism, a belief which was certainly not shared by everyone else.
Note the insinuation that Keynes thought that there were a single rational degree of belief valid for the whole of humanity, whereäs there is no indication that Keynes felt that everyone did, should, or could have the same information set. Rather than becoming obvious to him in the 1930s, it would have been evident to Keynes much earlier that many of his own beliefs and those of the other Apostles were at odds with those of most of mankind. Gillies' reference to embrace of Marxism in the '30s by most of the Apostles simply looks like irrelevant, Red-baiting ad hominem to me. One doesn't have to like Keynes (as I don't), Marxism (as I don't) or the Apostles (as I don't) to be appalled by this passage (as I am).

A Note to the Other Five

Sunday, 14 March 2010

Probability is one elephant, not two or more formally identical or formally similar elephants.

Dear Sir or Madam, will you read my book?

Saturday, 6 February 2010

Despite the fame of Laplace's Philosophical Essay on Probabilities, it is not in fact a very original work. The classical interpretation of probability emerged from discussion in the period roughly from 1650 to 1800, which saw the introduction which saw the introduction and development of the mathematical theory of probability. Most of the ideas of the classical theory are to be found in Part IV of Jacob Bernoulli's Ars Conjectandi, published in 1713, and Bernoulli had discussed these ideas in correspondence with Leibniz. Nonethless, it was Laplace's essay which introduced the ideas of the classical interpretation of probability to mathematicians and philosophers in the nineteenth century. This may simply have been because Laplace's essay was written in French and Bernoulli's's Ars Conjectandi in Latin, a language which was becoming increasingly unreadable by scientists and mathematicians in the nineteenth century.

Donald Gillies
Philosophical Theories of Probability
Ch 1 §1 (p3)

[…] Laplace generalised and improved the results of his predecessors — particularly those of Bernoulli, De Moivre and Bayes. His massive Théorie analytique des Probabilitiés, published in 1812, was the summary of more than a century and a half of mathematical research together with important developments by the author. This book established probability theory as no longer a minority interest but rather a major branch of mathematics.

Donald Gillies
Philosophical Theories of Probability
Ch 1 §2 (p8)

Essai philosophique sur les probabilitiés was published a couple of years after Théorie analytique des probabilitiés, as a popular introduction to that earlier work. Objecting that Essai is not in fact a very original work, given that Théorie was the summary of more than a century and a half of mathematical research together with important developments by the author, is a bit absurd.

An editor should have brought this dissonance to Gillies' attention. I don't quite know what editors do these days, beyond deciding whether a given work may be expected to sell.

this ebony bird beguiling

Tuesday, 14 April 2009

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.

[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.