Buridan’s Principle

I have observed that the arbiter problem, discussed in [22], occurs in daily life. Perhaps the most common example is when I find myself unable to decide for a fraction of a second whether to stop for a traffic light that just turned yellow or to go through. I suspect that it is actually a cause of serious accidents, and that people do drive into telephone poles because they can’t decide in time whether to go to the left or the right.

A little research revealed that psychologists are totally unaware of the phenomenon. I found one paper in the psychology literature on the time taken by subjects to choose between two alternatives based on how nearly equal they were. The author’s theoretical calculation yielded a formula with a singularity at zero, as there should be. He compared the experimental data with this theoretical curve, and the fit was perfect. He then drew, as the curve fitting the data, a bounded continuous graph. The singularity at zero was never mentioned in the paper.

I feel that the arbiter problem is important and should be made known to scientists outside the field of computing. So, in December of 1984 I wrote this paper. It describes the problem in its classical formulation as the problem of Buridan’s ass–an ass that starves to death because it is placed equidistant between two bales of hay and has no reason to prefer one to the other. Philosophers have discussed Buridan’s ass for centuries, but it apparently never occurred to any of them that the planet is not littered with dead asses only because the probability of the ass being in just the right spot is infinitesimal.

I wrote this paper for the general scientific community. I probably could have published it in some computer journal, but that wasn’t the point. I submitted it first to Science. The four reviews ranged from “This well-written paper is of major philosophical importance” to “This may be an elaborate joke.” One of the other reviews was more mildly positive, and the fourth said simply “My feeling is that it is rather superficial.” The paper was rejected.

Some time later, I submitted the paper to Nature. I don’t like the idea of sending the same paper to different journals hoping that someone will publish it, and I rarely resubmit a rejected paper elsewhere. So, I said in my submission letter that it had been rejected by Science. The editor read the paper and sent me some objections. I answered his objections, which were based on reasonable misunderstandings of the paper. In fact, they made me realize that I should explain things differently for a more general audience. He then replied with further objections of a similar nature. Throughout this exchange, I wasn’t sure if he was taking the matter seriously or if he thought I was some sort of crank. So, after answering his next round of objections, I wrote that I would be happy to revise the paper in light of this discussion if he would then send it out for review, but that I didn’t want to continue this private correspondence. The next letter I received was from another Nature editor saying that the first editor had been reassigned and that he was taking over my paper. He then raised some objections to the paper that were essentially the same as the ones raised initially by the first editor. At that point, I gave up in disgust.

I had no idea where to publish the paper, so I let it drop. In 2011, a reader, Thomas Ray, suggested submitting it to Foundations of Physics. I did, and it was accepted. For the published version, I added a concluding section mentioning some of the things that had happened in the 25 years since I wrote the original version and citing this entry as a source of information about the paper’s history.

My problems in trying to publish this paper and [22] are part of a long tradition. According to one story I’ve heard (but haven’t verified), someone at G. E. discovered the phenomenon in computer circuits in the early 60s, but was unable to convince his managers that there was a problem. He published a short note about it, for which he was fired. Charles Molnar, one of the pioneers in the study of the problem, reported the following in a lecture given on February 11, 1992, at HP Corporate Engineering in Palo Alto, California:

One reviewer made a marvelous comment in rejecting one of the early papers, saying that if this problem really existed it would be so important that everybody knowledgeable in the field would have to know about it, and “I’m an expert and I don’t know about it, so therefore it must not exist.”

Another amusing example occurred in an article by Charles Seif titled Not Every Vote Counts that appeared on the op-ed page of the New York Times on 4 December 2008. Seif proposed that elections be decided by a coin toss if the voting is very close, thereby avoiding litiginous disputes over the exact vote count. While the problem of counting votes is not exactly an instance of Buridan’s Principle, the flaw in his scheme will be obvious to anyone familiar with the principle and the futile attempts to circumvent it. I submitted a letter to the Times explaining the problem and sent email to Seif, but I received no response.