When I published my first co-authored journal article, my co-author and I took the advice of a senior colleague and adopted the convention of listing our names in alphabetic order by surname.  Because my surname begins with a “T” and I usually end up as the second, third, or even fourth author, I always wondered if that was optimal (for me).  I was therefore pleased to read, many years later, the article by Engers et al. (1999), in one of the top journals in economics, showing that this ordering was an equilibrium, and possibly a unique one.  They further showed that listing the authors in order of relative contribution was never an equilibrium.  Of course, this equilibrium was from the authors’ point of view; they also showed that compelling authors to use priority to signal relative contributions would increase the total quality of research.

Recently, Einav and Yariv (2006) produced evidence consistent with the caveat that Engers et al. (1999) had mentioned, and which they attributed to Merton (1973), that alpha ordering can lead to a reduction in attribution to second and subsequent authors who get lost in the “et al.”  Einav and Yariv (2006) produced evidence that strongly suggested that the alpha order convention in economics might be a cause of the alphabetical discrimination that they discovered.  What they showed was that faculty with earlier surname initials were disproportionately positively represented among tenured faculty at top ten economics departments, fellows of the Econometric Society, and, to a lesser extent recipients of the Clark Medal and the Nobel Prize.    These statistically significant differences remained even after they controlled for country of origin, ethnicity, religion or departmental fixed effects.  However, the effects gradually faded as they increased the sample to include the entire set of top 35 departments.   

Still, in addition to the arguments that Engers et al. (1999) advanced for alpha ordering, there is another, which has a certain social utility.  I am aware of at least one paper that after multiple drafts never progressed even to a working paper because the authors (I was not among them) could not agree on relative contribution, and they were writing in a field in which the convention was that the order of names should represent the order of relative contribution.  This is surely not an isolated case.   Research contribution consists of two inputs, the originality and value of the idea, and the effort expended in bringing the idea to a finished paper.   Originality and value are arguable, and incommensurable with effort, and effort is frequently unobservable among authors.  These factors would suggest that there may well be many potential papers that never get to publication over the issue of relative contribution. 

Alpha order, like “first come, first served” (Cornell and Roll 1981), would be an Evolutionary Stable Strategy that reduces conflict, though at the cost of the biases already mentioned.    The problem is to keep the conflict reduction and other positive aspects of alpha order while overcoming the biases that accompany it. 

One possible solution to the alphabetic bias is random ordering of authors’ names.    This would work for prolific partnerships and for prolific authors who enter into multiple team projects.  Two colleagues of mine have written numerous papers since they were graduate students together; for each paper, just before circulating it, they toss a coin.  The coin toss determines the order, and they announce in the acknowledgements footnote that they have used a randomizing device.  More generally, journals could declare that they will randomize the author order, absent the authors’ attestation that the order they submit reflects relative contributions.

This still leaves the second bias, that of the under-production of quality research.    I have noticed that journals sometimes require the authors of an article to designate a corresponding author.  This may produce a weak and noisy signal of the lead author, and so may be better than nothing.  Still, I suspect that the bias may not be one that we can overcome, though I hope readers of the blog post can suggest a solution.

Cornell, Bradford and Richard Roll. 1981.  Strategies for pairwise competitions in markets and organizations. Bell Journal of Economics 12 (1), 201-213.

Einav, Liran and Leeat Yariv. 2006. What’s in a Surname? The Effects of Surname Initials on Academic Success.   Journal of Economic Perspectives 20 (1), 175–188.

Engers, Maxim, Joshua S. Gans, Simon Grant and Stephen P. King. 1999.   First-Author Conditions. Journal of Political Economy. 107 (4), 859–83. 

Merton, Robert K. 1973.  The Sociology of Science: Theoretical and Empirical Investigations. Chicago: Univ. Chicago Press. 

The first example comes from land navigation, which is the use of compass and map to get from one point to another.  One standard problem is to get from a point in a wood, or other occluded terrain, to a point on a road or the like, some distance away.  The unbiased approach is to take a bearing, i.e., determine a direction, from where one is to where one wants to go, and then follow it.  The problem is that as one follows the bearing, with each step a little random lateral error creeps in so that when one reaches the road one may not be sure whether the point one is seeking is to the right or the left.  The biased approach is to follow a bearing that is sufficiently to the left or right of the objective that when one reaches the road one can assume with a high degree of probability that the objective is to the right or left.

The second example comes from directing artillery fire to strike a target that one can observe, but that is an unknown distance away.  The unbiased approach is to estimate (guess) the distance, notify the gunners, observe the first shot, and then walk subsequent shots towards the target in increments of distance.  (Up 100. Up 100. etc.) The biased approach is “bracketing” the target.  In bracketing, the observer estimates (guesses) the distance, and then adds a large increment to the estimate to ensure that the first shot will fall beyond the target.  The observer then adjusts the fall of the sequence of subsequent shots by halving the distance between subsequent shots.  (ideally, by cycling through a sequence of over and under shots.  As n increases, X plus (0.5) to the nth power, times β sub n, where β is the unknown bias in estimating the unknown range X, will converge on X.  Experiments have shown that on average, bracketing will result in a faster convergence of the fire on the target than will walking.

So long as satellites and batteries don’t go dead, GPS and laser range finders now solve the land navigation and ranging problems in an unbiased manner.  Still, the questions that motivated this post remain: is the notion of useful bias itself useful?  That is, are there other, more pacific examples in the cognitive realm?

In the case of the Million Man March, supporters from the Nation of Islam claimed attendance of 1.5 to 2 million.  The Park Service suggested initially that 400,000 had participated.  The Malatesta Estimator therefore yields an estimate of 800,000.  We can calibrate this by comparing it with an estimate by Dr. Farouk El-Baz and his team at the Boston University Remote Sensing Lab.  Dr. El-Baz and his team used samples of 1 meter square pixels from a number of overhead photos to estimate the density per pixel, and then calculated an estimate for the entire area.  Their estimate was 837,000, with 20% error bounds giving a range from 1 million to 670,000.

Saunders, Frances Stonor. 2004. The Devil’s Broker: Seeking Gold, God, and Glory in Fourteenth-Century Italy. (New York: HarperCollins), p. 93.

BU Remote Sensing Lab Press Release: http://www.bu.edu/remotesensing/Research/MMM/MMMnew.html

Accessed 14 December 2006.