Arrow’s other theorem

I received the following email from someone who’d like to remain anonymous:

Lately I [the anonymous correspondent] witnessed that Bruno Frey has published two articles in two well known referreed journals on the Titanic disaster that try to explain survival rates of passenger on board.

The articles were published in the Journal of Economic Perspectives and Rationality & Society. While looking up the name of the second journal where I stumbled across the article I even saw that they put the message in a third journal, the Proceedings of the National Academy of Sciences United States of America.

To say it in Sopranos like style – with all due respect, I know Bruno Frey from conferences, I really appreciate his take on economics as a social science and he has really published more interesting stuff that most economists ever will. But putting the same message into three journals gives me headaches for at least two reasons:

1) When building a track record and scientific reputation, it’s publish or perish. What about young scholars that may have interesting stuff to say, but get rejected for (sometimes) obscure reasons, especially if you have innovative ideas that run against the mainstream. Meanwhile acceptance is granted to papers with identical messages in three journals that causes both congestion in the review procedures in biases acceptance, assuming that for two of three articles that are not entirely unique two other manuscripts will be rejected from an editorial point of view to preserve exclusivity by sticking to low or constant acceptance rates. Do you see this as a problem? Or is the main point against this argument that if the other papers would have the quality they would be published.

2) As an author one usually gets the question on “are the results published in another journal” (and therefore not original) or “is this paper under review in an another journal”. In their case the answer should be no for both answers as they report different results and use different methods in every paper. But if you check the descriptive statistics in the papers, they are awkwardly similar. At what point do these questions and the content overlap that it really causes problems for authors? Have you ever heard about any stories about double publications that were not authorized reprints or translations in other languages (which usually should not be problematic, as shown by the way in Frey publication list) and had to be withdrawn? Barely happens I guess.

Best regards and thank you for providing an open forum to discuss stuff like that.

I followed the links and read the abstracts. The three papers do indeed seem to describe similar work. But the abstracts are in remarkably different styles. The Rationality and Society abstract is short and doesn’t say much. The Journal of Economic Perspectives abstract is long with lots of detail but, oddly, no conclusions! This abstract has the form of a movie trailer: lots of explosions, lots of drama, but no revealing of the plot. Finally, here’s the PNAS abstract, which tells us what they found:

To understand human behavior, it is important to know under what conditions people deviate from selfish rationality. This study explores the interaction of natural survival instincts and internalized social norms using data on the sinking of the Titanic and the Lusitania. We show that time pressure appears to be crucial when explaining behavior under extreme conditions of life and death. Even though the two vessels and the composition of their passengers were quite similar, the behavior of the individuals on board was dramatically different. On the Lusitania, selfish behavior dominated (which corresponds to the classical homo economicus); on the Titanic, social norms and social status (class) dominated, which contradicts standard economics. This difference could be attributed to the fact that the Lusitania sank in 18 min, creating a situation in which the short-run flight impulse dominated behavior. On the slowly sinking Titanic (2 h, 40 min), there was time for socially determined behavioral patterns to reemerge. Maritime disasters are traditionally not analyzed in a comparative manner with advanced statistical (econometric) techniques using individual data of the passengers and crew. Knowing human behavior under extreme conditions provides insight into how widely human behavior can vary, depending on differing external conditions.

Interesting. My only quibble here is with the phrase “selfish rationality,” which comes up in the very first sentence. As Aaron Edlin, Noah Kaplan, and I have stressed, rationality doesn’t have to imply selfishness, and selfishness doesn’t have to imply rationality. One can achieve unselfish goals rationally. For example, if I decide not to go on a lifeboat, I can still work to keep the peace and to efficiently pack people onto existing lifeboat slots. I don’t think this comment of mine affects the substance of the Frey et al. papers; it’s just a slight change of emphasis.

Regarding the other question, of how could the same paper be published three times, my guess is that a paper on the Titanic can partly get published for its novelty value: even serious journals like to sometimes run articles on offbeat topics. I wouldn’t be surprised if the editors of each journal thought: Hey, this is fun. We don’t usually publish this sort of thing, but, hey, why not? And then it appeared, three times.

How did this happen? Arrow’s theorem. Let me explain.

One day in graduate school, my friend Tex asked me if I knew what Arrow’s Theorem was. I said, yeah, it’s something about the impossibility of a voting rule—No, he interrupted. Not that one. I’m talking about the other Arrow’s Theorem.

The other Arrow’s Theorem? What’s that, I asked. Tex replied: the theorem is that any result can only be published at most five times.

Hmm. I thought about this one for a bit, and then Tex interrupted me again, saying: That’s the weak form of Arrow’s Theorem.

I took the bait and asked, What’s the strong form?

Tex replied; The weak form of Arrow’s Theorem is that any result can be published no more than five times. The strong form is that every result will be published five times.

Fast forward a few years.

It’s 1995, and I’m wandering the fourth floor of Evans Hall in a daze, stunned that my colleagues have just voted by a 2-1 margin to kick me out of the statistics department. Various conversations from the previous few years came to mind: I gave one of my (non-Bayesian) colleagues a prepublication manuscript of Bayesian Data Analysis, and a couple days later he responded in a note that hierarchical models weren’t new, he’d used them back in the late 1940s when he did applied statistics . . . another colleague who, after I’d given an entertaining pre-election talk to the department in late October, 1992 (this being Berkeley and Bill Clinton being way ahead in the polls, it was a festive occasion), had cornered me and said that before seeing my talk he’d never realized how little there was to this political science stuff . . . and after that same talk one of my more applied (!) colleagues asking me why, since votes are discrete, I wasn’t using a discrete-data model such as a Poisson (and, no, he wasn’t persuaded by my argument that if you have 100,000 votes in a congressional district, it’s ok to model it as continuous) . . . and–and here’s the point of this particular digression–one of my more genial colleagues, who’d asked me about my work on monitoring convergence of iterative simulations. I assured him that the work was influential as well as innovative, to which he replied: But if it’s a good idea, why do you have only one paper on the topic? A good research project will have several papers . . .

Arrow’s theorem.

I’m very happy in New York and wouldn’t trade my current life for anything, so Arrow’s theorem did me a favor. But still . . .

What’s happened since then? I never intend to publish the same thing over and over, but sometimes people ask me to write something for a journal, and I need to come with something . . . And sometimes you really do want to reach different audiences. I blog in 4 different places (here and the three “sister blogs” you see on the top of the blogroll here). I certainly don’t mind publishing blog entries in journals. Or, to take a more fully academic example, Jennifer, Masanao, and I are publishing our paper on multiple comparisons in the Journal of Research on Educational Effectiveness: despite the obscure-seeming title, Jennifer assures me this is an influential venue. We’re also working on a related discussion paper for a statistics journal. Different audiences. For yet another example, I’m not the only researcher to get funding from multiple sources to do similar work. And I think this is ok (as long as I do the work!).

And consider George Orwell. He wrote the same thing over and over, hammering out his ideas in different low-circulation magazines. To write is to think.

To return to the articles by Frey et al. discussed at the beginning: Remember the strong form of Arrow’s theorem. Two more publications will come of this, for sure.

P.S. Just to clarify: No, I don’t think Bruno Frey did anything wrong.

12 thoughts on “Arrow’s other theorem

  1. (1) The audience question is a good one. I'm 'way over on the applied side, so I don't find I get much out of theoretical stat articles. I recognize theorems have to be proven, just like sausage needs to be made, but I don't want to watch.

    (2) At least one of the 5 versions should be something that is accessible to the public, particularly if the work was sponsored by public funds. [I'm not complaining about Andrew Gelman here; I think he's a model on this dimension.]

  2. "my colleagues have just voted by a 2-1 margin to kick me out of the statistics department." Gosh, the American system is harsh, isn't it?

  3. Zbicyclist:

    I agree. The norm of publishing things multiple times is probably good in that it provides a positive incentive for scholars to communicate broadly.


    Indeed. Of course, although I'm calling them "my colleagues," I don't think they thought of me as their colleague!

  4. I do not get your objection to the term "selfish rationality". You point out that the term is not redundant, and has a definite meaning that is not captured by either word alone. So what is wrong with using it?

  5. I think it's important to distinguish (for any newbie researchers out there) how a research *project* could lead to several publications, but a research paper should not be published several times in slightly modified forms.

    As to Frey, keep in mind that JEP is not a refereed outlet and it does not "count" as a pub for tenure and promotion. It is however a wide-readership outlet and a sign that one's work is interesting to the profession. My understanding is JEP publishes mostly invited papers, not unsolicited work.

    Given that, and since PNAS is a very different audience, Frey perhaps saw this as an opportunity to reach different audiences. As far as economists are concerned, only one refereed pub was garnered (JEP and PNAS are impressive but don't count).

  6. Has no one else noticed the fourth paper yet? "Noblesse oblige? Determinants of survival in a life and death situation." Journal of Economic Behavior & Organization, 74(1-2), pp. 1-11 ( Multiple publications are not new and t'was ever thus. It's more the statistical modelling and the interpretation of the models that I am not keen on. Given the large number of variables considered, other models would likely have fit almost as well. Needless to say, there are no graphics of any kind (no mosaicplots, no coefficient plots, nothing), so it's difficult to judge how good the models are. A lot of the pseudo R2 values are low.
    Two of the papers cover both the Titanic with the Lusitania. The PNAS paper has four models, two each for each ship. The J Econ Perspectives paper has 6 Titanic models and 1 Lusitania model, which is not directly comparable with any of the 6 Titanic ones, one Titanic model is common to both papers. The other two articles only consider the Titanic and offer 17 Models (Rationality & Society) and 18 (J Economic Behaviour & Org) respectively. There is a little overlap with two of the models appearing in both. The tables are not always clear and in the J Economic Behaviour & Org article the number of women passengers is given as 433, whereas it should surely be 460, as in the J Econ Perspectives paper. Perhaps this is a reason why the remark is made in that article (p18) that "Interestingly, females had a lower probability to survive among crew-members than among passengers.", which I don't believe to be true. The authors' understanding of the crew's behavious is also suspect: "The results show that crew-members had a higher probability of survival which may indicate their taking advantage of their increased opportunities (better possibilities) to acquire resources and to be informed which promoted their survival rate. Thus, such a result is more in line with a self-interested approach." They should take account of the fact that every lifeboat had to leave with several crew members on board, before discussing any other factors.

  7. I guess there is a problem with "selfish rationality" in that it is misleading! The question is when do rational agents act selfishly and when do they not. Then the question is (only) when do rational agents deviate from selfishness in life and death situations? If you read the article you will find out that they have taken self-interested behavior as preferring your life to all others which is, indeed they have taken selfishness as rationality and vice versa. (ignoring the idea of not being able to live with yourself after such an action and hence rationally preferring others to yourself)
    Still this is the smallest problem with this paper in terms of being misleading (or maybe written by misled people)

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