On 20 February, I submitted my paper on probability to yet another academic journal. To my surprise, the journal in question gave me a choice as to whether my review would be doubly blind — with my identity withheld from the reviewers; I chose that option.

Although in my initial reading of the longer of the two reviews that I most recently received I found no worthwhile criticism, I thought that I should pore over that review carefully, to ensure that I didn't overlook anything in it that would cause me to improve my paper. However, though the review was not written with abusive intent, it is none-the-less abusive, and I was averse to reading it. To impel myself to read it carefully, I decided to write a response to each of the criticisms within it, as I would then have to take care to find and to consider each criticism. I completed a draft of the response without finding any good reason to revise my paper. Having gone that far with the draft, I proofread it on 21 February, and posted a version on-line. It is written more in the manner of a 'blog entry than of something intended to go into a journal or book; and I don't know that any of you would want to bother with reading it in any case. But it's available.

Between the time that I previously submitted the paper and the time that received the most recent decision, I more efficiently organized the citations in one paragraph and I compressed one appendix by removing formula numbers and by suppressing logical quantifiers so that its eleven formulæ could be placed into a one-page grid.

In the early morning of 2 March, I received e.mail indicating that my probability paper had been assigned to a handling editor (who was named), and that I would be contacted after a reviewer had returned a report. It seems that the threat of a desk rejection has passed. I made a very cursory check on the handling editor; she seems quite qualified.

On 15 January, in response to a friend, I wrote

But I'm not particularly hopeful. The paper presents a confluence of challenges to philosophers, and I've come to doubt that most of them even with supposedly relevant expertise will recognize the hurdles and attempt to clear them until Authority has told them that they ought to do so.

The reported status of my probability paper remained Reviews Completed into 21 January, but became Reject some time in the morning. (I did not observe an intermediate status of Editor Has a Decision.) The editors wrote

Thanks for submitting your manuscript to [journal] and for your patience during the process. One reviewer hasn't submitted their report for very long after accepting the task, despite the numerous reminder sent. We decided to seek for a third reviewer, who kindly agree to read the paper with a very short delay. Unfortunately, both reports point to a number of problems in the manuscript, we therefore decided not to offer publication at this stage.
Thanks again for your patience in waiting for the editorial decision.

(Note that the last reviewer was said to have agreed to read the paper with a very short delay.) The reporting reviewers were identified with Reviwer #2 and Reviewer #3, which suggests that the reviewer who never returned a report was the earliest to accept.

Reviewer #2 wrote

I think there are some good ideas in the paper, but it needs to be significantly more polished and tightly focused to be publishable. Please see attached report for more comments.

Unfortunately, the attached report was not attached to the e.mail that I received, nor made available to me by way of Editorial Manager; so I am completely unable to consider whatever it may assert. I have written both to the Journals Editorial Office and to the handling editor noting that the report has not been furnished to me.

Reviewer #3 wrote

This is not an easy paper to judge; in a different type of journal I could come to a different judgment. However, I think that the paper is, in spite of its merits, not suited for the [journal]. I have four main concerns:

1. The argument relies on research in logic and artificial intelligence. The average [journal] reader cannot be expected to be familiar with that formalism (in fact, I am not although I work on probability myself). It would be more appropriate for Reviw of Symbolic Logic, Artificial Intelligence or a similar journal.
2. It is not fully clear whether the paper gives an original account of whether it is mainly a summary/presentation of results in the qualitative probability research program. So it is hard to assess the originality of the research.
3. The author tries to embed the formal part of the paper into considerations about the history of probability and its use in science (e.g., confidence intervals in statistics), but these links remain tenuous and sometimes outright unconvincing. With respect to the coherence of the conceptual, philosophical and the formal part, the paper could be improved substantially.
4. The writing could be clearer.

With respect to these concerns, I would have four responses:

1. The formal logic as such of my paper is strictly material that can be found in undergraduate introductory courses, and I very deliberately made no reference to artificial intelligence as such, nor employed research peculiar to what is generally recognized as artificial intelligence.[1] I did cite one article from a journal that is primarily consumed by such researchers, but that article was written to be accessible by a wider audience, and I cited the article only to support a claim that use of intervals (as opposed to bare preörderings) has not been completely satisfactory.
   
   The formalisms that wouldn't be found in an undergraduate course in formal logic but are found in my paper are very simple and clearly defined. There are single symbols for each of the probability relations; for example, ▷ for is more probable than. And there is (X|c) for X, given c; so that (X|c)▷(Y|d) would be read as X given c is more probable than Y given d. That's it. Now, in everyday probability theory p(X|c) already means the [measure of] probability of X given c, so my (X|c) should be easily understood. Keynes and Koopman instead wrote X/c (with a slash instead of a vertical bar, and without parentheses), which looks like arithmetic division.
   
   If the reviewer works on probability him- or herself, and is not already used to formalism on this order, then he or she is unfortunately committed in practice to sufficient assumptions to ensure measurability of probabilities.
2. The introduction to my paper clearly identifies the prior research and notes what that research failed to do. The body of the paper compares and contrasts my axiomata with those of the previous researcher who got furthest, and cites other work when it approximates my other axiomata.
3. The paper is already too long to be accepted in various journals, but the reviewer wants me to labor issues further. And it would be good if he or she would provide an example of something that he or she found outright unconvincing.
4. Similarly, I would want an example of a passage that the reviewer thought should be made more clear. I expect that what the reviewer truly felt was that the writing were spartan, which is often is, in order to keep its length in check.

I've now seen the report from Reviewer #2. It would probably take a paper of some length to explain everything wrong with it. I'll just furnish a couple of examples.

I use various terms from the English language in their ordinary, everyday senses, but the reviewer presumes that I must be using them in special senses, and then objects that I've not provided definitions. For example, I wrote

A pure frequentism or a pure combinatoric interpretation of probability would force [relation in which there is no relative order of probability] to be empty, as also (trivially) would betting quotients. But logicism and subjectivism in general do not require it to be empty. (An impure frequentism would be one in which [weak supraprobability] and [weak infraprobability] were always about beliefs about frequency; similarly for an impure combinatoric interpretation.)

Note that I even provided a parenthetical note that shows how an impure frequentism would be distinguished from a pure frequentism, but the reviewer insists that I'd introduced undefined jargon.

In my paper, I noted that twelve of what are the thirteen axiomata of my system are theoremata of the Kolmogorov axiomata, and the the remaining axiom conforms to the Kolmogorov axiomata, so that they must be at least as consistent as the Kolmogorov axiomata.[2]

The reader can trivially verify that, while what I offer as axiomata are not sufficient to imply the Kolmogorov axiomata, his axiomata imply (A1) through (A5) and (A7) through (A13), and that (A6) conforms to the Kolmogorov axiomata. Thus, the axiomata are at least as consistent as are those popular systems, and are at least as consistent as are any systems whose axiomata imply those principles which are Kolmogorov’s axiomata.

The reviewer misrepresents me as using conform in some special, undefined way, and as claiming that the thirteen axiomata are consistent for no better reason than because they exhibit such unexplained conformance.

As I will explain in a later 'blog entry, I wrote a response to each of the criticisms found in the longer review. I don't know that this response will be of current use to anyone else, but I have made it available on-line.

[1] There is a very important sense in which logic itself is artificial intelligence, and I'd someday like to labor that point. But the reviewer was referring to intelligence in devices external to the human mind.

[2] Because the Kolmogorov axiomata use arithmetic, they must be incomplete or inconsistent; but I do not raise that issue in my paper.

I have argued that persons outside of any social context can be scientists. Recently, I watched and listened to a recording of an interview of one philosopher by another, in which the two agreed that science is intrinsically social, that persons outside of social contexts cannot be scientists.[1]

Towards explaining what was wrong with their argument, I'll first explain their argument. One of the very most important things that a scientist ought to do is to look for areas of potential vulnerability in theories, and to test those theories against what evidence may practicably be gathered. And any one researcher is imperfect in his or her ability to find such potential vulnerabilites, in knowledge of existing evidence, and in capacity to collect new evidence. It is often particularly difficult for any one researcher to recognize the unconscious presumptions that inform his or her own theories; exposing the work of one researcher to the scrutiny of other researchers may mean that those presumptions are recognized and challenged.

All right; but, just as any one researcher is imperfect, so are jointly any two researchers, or any three researchers, or any n researchers, for all finite values of n. In fact, I am nearly certain that even an infinite number of scientists would be insufficient to overcome weaknesses across the whole body of theories that these scientists could construct; but, in any case, science is not an unattainable limiting case of behavior. One might instead pick a finite n, and insist that one does not have science until one has n participants engaging in behavior of some sort, but the choice of n would seem to be quite arbitrary; and I'd like to know what one should then call the behavior when there are fewer participants.

As a practical matter, it is far from clear that two people each in isolation engaged in that behavior would continue to engage in that behavior when brought together. Social contexts can promote peculiar forms of irrationality. Historically, a great deal of what has been widely taken to be science by participants and by most observers in wider society has often been grossly unscientific behavior resulting exactly from social pressures. A great deal of what passes for science these days is socially required to conform to consensus, which is to say that social mechanisms protect widely shared presumptions from scrutiny.

[1] As it happens both one of those philosophers and I referred to Robinson Crusoe as an individual outside of a social context. It was natural for us each independent of the other to reach for the most famous example within our shared cultural context, but it heightened my sense of annoyance.

On 15 October, I posted an entry on the status of my paper that presented a table showing the reported status of my probability paper, along with the date-stamp associated with that status. I declared

I'm not going to post a separate entry for each change, but will just up-date the table above until the status becomes Reviews Completed.

Those who checked that entry know that, on the next day, the status of the paper changed from Reviewers Assigned to Under review, but that it then languished for more than twleve weeks. In the meantime, I added notes to the entry about the passage of time, about my communication with the editorial office and then with the handling editor, and about a new reviewer having been selected and accepted the assignment on 10 January.

On 14 January, the reported status of the paper became Reviews Completed.

Typically, most of the time between when a reviewer accepts an assignment and when he or she completes it is spent on concerns without meaningful relationship to the review (except in-so-far as they displace it). If reviewers had to turn immediately to the task of reviewing a paper, then far fewer would accept the responsibility. Setting aside all but truly everyday activities, it is quite possible to review a paper in a matter of a very few days, and certainly in less than five.

None-the-less, a review as speedy as must have been the last review has me especially concerned that the job may suffer from some of the deficiencies associated with a rushed review, or that the reviewer may otherwise not have recognized with significance of what were said in my paper.

In a private communication, a friend writes:

I have, several times, been asked by an editor to read a paper over, without being a formal reviewer, and send her my thoughts. Sometimes, I am then made a formal reviewer (whether I have sent my thoughts or not) when one of the other reviews withdraws or is unable or unwilling to complete a review.

I had not considered a possibility of this sort.

In the course of a present investigation of how the main-stream of economics lost sight of the general concept of utility, I looked again at the celebrated article Specimen Theoriæ Novæ de Mensura Sortis by Daniel Bernoulli, in which he proposed to resolve the Saint Petersburg Paradox[1] by revaluing the pay-off in terms of something other than the quantity of money.

The standard translation of his article into English[2] replaces Latin emolument- everywhere with utility, but emolumentum actually meant benefit.[3] Bernoulli's own words in his original paper show no more than that he thought that the actual marginal benefit of money were for some reason diminishing as the quantity of money were increased. However. before Bernoulli arrived at his resolution, Gabriel Cramer arrived at a resolution that had similar characteristics; and, when Bernoulli later learned of this resolution, he quoted Cramer. Cramer declared that money was properly valued à proportion de l' uſage [in proportion to the usage]. The term uſage itself carries exactly the original sense of utility. (Cramer goes on to associate the usefulness of money with plaiſir, but does not make it clear whether he has a purely hedonic notion of usefulness.) Bernoulli did not distinguish his position from that of Cramer on this point, so it is perfectly reasonable to read Bernoulli as having regarded the actual gain from money as measured by its usefulness.

Of course, both Cramer and Bernoulli were presuming that usefulness were a measure, rather than a preördering of some other sort.

[1] The classic version of the Saint Petersburg Paradox imagines a gamble. A coin whose probability of heads is that of tails is to be flipped until it comes-up tails; thus, the chance of the gamble ending on the n-th toss is ¹/2ⁿ. Initially, the payoff is 2 ducats, but this is doubled after each time that the coin comes-up heads; if the coin first comes up tails on the n-th flip, then the pay-off of the gamble will be 2ⁿ ducats. So the expected pay-off of the gamble is ∑[(¹/2ⁿ)·(2ⁿ ducats)] = 1 ducat + 1 ducat + … = ∞ ducats Yet one never sees people buying such contracts for very much; and most people, asked to imagine how much they would pay, say that they wouldn't offer very much.

Cramer's resolution did not account for the preëxisting wealth of an individual offered a gamble, and he suggested that the measure of usefulness of money might be measured as a square root of the quantity of money. Bernoulli's resolution did account for preëxisting wealth, and suggested that the actual benefit of money were measurable as a natural logarithm.

I'm amongst those who note that one cannot buy that which is not sold, and who believe that people asked to imagine what they would pay for such a contract instead imagine what they would pay for what were represented as such a contract, which could not possibly deliver astonishingly large amounts of purchasing power.

[2] Exposition of a New Theory on the Measurement of Risk in Econometrica v22 (1954) #1 (January) pp 22–36.

[3] In a footnote, translator Louise Sommer claims that mean utility is a free translation of emolumentum medium and then that the literal translation would be mean utility; I believe that she had meant to offer something else as the literal translation, but lost her train of thought.

This 'blog has been bit hard by a bug in a plugin.

WP-Sweep includes an ostensible ability to purge categories and tags that are not used for any entries. Unfortunately, the programmer made an error such that the categories and tags purged are any not used in generally accessible entries; tags and categories used exclusively in restricted entries are therefore purged.

Still more unfortunately, I did not discover the bug until after I had made various content changes; simply restoring a previous version of the database would undo those changes. I don't remember what they were, and my only records are the database and saved versions thereöf.

I will, over time, try to repair the damage.

On 15 October, the reported status of my probability paper reverted from Under review to Reviewers Assigned. That change means that at least one reviewer who had accepted the assignment has since withdrawn. Since the reported status of my paper has ceased to be monotonic, I'm not going to post a separate entry for each change, but will just up-date the table above until the status becomes Reviews Completed.

The reported status and its date-stamp have remained unchanged since 16 October. Since the editor moved relatively rapidly between receipt of the paper and assigning it to reviewers, I'm going to infer that the editor is likely diligent and that the reported status would have been changed had all reviews been returned, or had a reviewer withdrawn since 16 October.

I've read of one journal that requests that reviews be returned within two weeks, but more typically journals ask that they be returned within three weeks, within four weeks, or within a month. I know that many reviewers fail to meet these requests.

I've seen very little data on how long the typical review takes; that data was not partitioned according to outcomes. Useful data partitioned according to whether the review were competent is surely not available.

The reported status and its date-stamp remain unchanged after the passage of two months.

24 December represented the third mensiversary of the most recent submission of my paper. By itself, three months is not a bad figure; in some cases, it might be a month before an editor had read a paper, and it might take another two months to find reviewers.

But 25 December represented the ten-week mark for the paper's reported status of Under review; that is quite a long time. I sent e.mail to the Journals Editorial Office:

For ten weeks, the reported status of my paper has been Under review. Within what interval does your journal ask reviewers to complete their reviews?

My question wasn't rhetorical. (I generally try to avoid rhetorical questions.) It is possible that reviewers are typically given a rather long time by this particular journal; it is also possible that a decision was made to suggest an atypical length of time to one or both reviewers.

The first reply from the Journals Editorial Office, in the morning of 27 December, perfectly failed to answer my question. So I swiftly reïterated my query. This morning, I received what I believe to be the best response that the Office might give:

Please be advised that we are sending reminders to reviewer after 3, 8 and 13 days upon the acceptance of the invitation. More than, we escalate it to the Editor for further action.

I'm surprised that reminders should be sent at three days and at eight, and I'm surprised that escalation should occur at less than three weeks.

But, in any case, as more than ten weeks have past, by the standards of the JEO, at least one of the reviews is wildly overdue. I do not know what the editor imagines.

In the late after-noon of 8 January, I sent e.mail to the handling editor, which message read

My paper has now begun its thirteenth week since the status was last changed to Under review. This span seems quite excessive.

The handling editor responded on 10 January:

One reviewer is very late, despite the numerous reminders sent. We are considering now what to do to speed up the process.
Thanks for your patience,
[editor name]

Sometime during 11 January, the reported status of my paper became Under review with a date-stamp of 10 January. I did not observe an interval when the reported status was Reviewers assigned between when last the date-stamp was 16 October and when the date-stamp became 10 January.

With a date-stamp of 12 October, the reported status of my probability paper has become Under review, indicating that a set of reviewers have accepted the assignment. (Editorial Manager seems to be inconsistent about capitalization.) There were no changes in the date stamp when the status was Reviewers Assigned, so it seems that the first set of reviewers accepted the assignment.

It is possible for reviewers to withdraw, in which case the reported status would revert to Reviewers Assigned. Otherwise, one expects that within about a month the reviewers will complete their task, and the status will become Reviews Completed, followed by Editor Has a Decision.

On previous occasions, rather than saying that my own paper would probability be rejected by reviewers, I've made the statistical claim that most reviews of academic papers result in rejection. But, at this stage, I am more willing to say that my paper will probably be rejected by these reviewers. Still, I hope for a better outcome.

With a date-stamp of 5 October, the reported status of my probability paper has become Reviewers Assigned, which indicates that some person or persons have been asked by the editor to review the paper. If he, she, or they decline, then I will later see a change in the time-stamp but the same reported status. If he, she, or they accept, then the status will become Under Review.

The change in status from Editor Assigned was relatively swift; an editor might more typically take a month before deciding whether to send a paper to reviewers or instead to issue a desk rejection, which rejection is the fate of the majority of papers sent to academic journals (setting aside the various vanity journals).

I will hope that the task of reviewing is quickly accepted by competent reviewers, and certainly that it is not again undertaken by reviewers who will look only inside the box of conventional theory in attempting to understand a paper that primary considers matters outside of that box.

I made two minor tweaks to my paper on probability, to meet the requirements of a specific journal, and then submitted it to that journal. One of those tweaks was to insert a formal citation of a work that I had consulted. (It already appeared in the references, but was not cited in the text because I think that a citation might cause a slight confusion. But better that confusion than to leave the author unacknowledged in the references.) The other tweak was just to ensure that my identity was not suggested by the text.

So, again, most papers are swiftly rejected by editors before being sent to reviewers, and most papers that are reviewed are unconditionally rejected by those reviewers after some weeks.