Friday, November 16, 2007

Universal Scaling at Deadlines

Nature Physics can have a nice, dry sense of humour - here is a plot from the "Correspondence to the Editor" of the November issue, "Conference registration: how people react to a deadline":

Source: Alfi, Parisi, Pietronero, Nature Physics 3, 746 (2007)

Valentina Alfi, Giorgio Parisi and Luciano Pietronero have analysed the distribution of registrations for two conferences (red triangles and blue circles in the main figure), and after a normalisation with respect to the total number of participants, they can describe this distribution by a simple model, assuming that the "pressure to register" is inversely proportional to the time left before the deadline - that's the solid line.

This same simple model seems not work for the distribution of the payment of the conference fee - the dashed line in the inset. However, since the registration is reversible, while the payment is not, there may be a tendency to postpone the payment until closer to the deadline. Describing this tendency to postpone with a Boltzmann factor, the model can also fit distribution of payments very well - that's the solid line in the inset.

Alfi, Parisi and Pietronero conclude, "People’s behaviour around a deadline does indeed seem to be universal. If the action is reversible ..., the pressure to do it is inversely proportional to the available time before the deadline. For an irreversible action ..., there is a tendency to postpone it until even closer to the deadline, which can be described by a utility function." And they even come up with a rule of thumb to estimate the final number of participants "that may be useful for organisers of future events": Just extrapolate the initial linear behaviour and multiply it by three.

People can behave so predictably!

Source: Nature Physics 3, 746 (2007), doi:10.1038/nphys761 (alas, subscription required for the full text)


  1. I assume the airlines industry knows this?

  2. Dear Stefan,

    Hmm, they've omitted the problem of 'soft' and 'hard' deadlines, where the challenge with the first is not letting people know it's a 'soft' deadline. I had to notice that people increasingly come to rely on a deadline not 'really' being a deadline. Surely, there is always some way to do it afterwards, no? In a certain respect its a very interesting collective action problem - people tend to assume something is okay because they believe everybody else will do the same. Like, sure, these letters of recommendation should be send out by Nov 15th, but they know everybody is terribly busy in that time, so it will be fine doing it next week. etc.

    Also, I'd have expected some sub-structure each time a reminder was send out?

    The problem with the late payment is in most cases self-inflicted. Organizers of conferences with open application decide too late whether an applicant can give a talk, and if so under which conditions, and which day. Many people, me included, will only come if they can give a talk (of sensible length), or might not be able to stay the whole week. Others will only come because they are interested in hearing person X speaking about Y, so if the programme isn't out, they will wait. Under such conditions, the irreversibility of the payment will result in delay. (Though I've had cases where I requested a return after payment because I was pissed off by the conference organization, and I got a complete refund).

    Dear Arun,

    Good point :-) I think they will know the general trend - that's why their tickets become increasingly expensive the less time left for booking to counteract this tendency. A tactic that btw seems to have been adapted by many conferences (early/late/on site registration etc). Not sure though if they have a sensible extrapolation based on the early registration, given the repeatedly occurring disasters with overbooked flights, it seems they rely on some other rather insufficient model.



  3. A brilliant, insightful, and useful paper. And it doesn't require E8. I wonder what happens when the organizers extend the deadline.

    By the way, you might enjoy my new E8 root rotation simulation. It starts with random values, but you can type in whatever rotation you want. I'm going to add a better color interface so you can color the particles according to Lisi's paper.

  4. When I was in high school, one of my teachers had a posting up about "Edward's time-effort law: the amount of effort put into a project is inversely proportional to the amount of time remaining before the deadline." I wonder if that "law" is related to this result. It seems similar.

    (There was a correlary to Edward's time-effort law: if it weren't for the last minute, nothing would get done.).

  5. Are we seeing the Ideal Gas Law for adrenaline pressurization? Now we need an assignment corresponding to absolute temperature plus an overall scaling factor and a universal proportionality constant. Call the result the (Hari) Seldon equation.

  6. The upward curve must be due to some mysterious "dark energy." Scientists must now bury any alternative explanations and present a united front as they ask the government for bilion so find more dark energy.

  7. Could someone re-do those curves on semi-log paper, I'm having a hard time "seeing" the two different constant slopes.

  8. Dear Bee,

    they've omitted the problem of 'soft' and 'hard' deadlines

    yes, indeed - the examples seem to deal with hard deadlines only - soft deadlines and reminders may make the coefficient c of the c/(t-t*) law time-dependent, or require the use of two terms inversely proprtional to t-t* and t-t*', which makes the situation more murky ;-)

    In case the deadline is extented at a specific time, as in the situation suggested by Carl, I would guess the distribution switches instantanously to a new distribution inversely proportional to t-t*(new).

    Dear Arun,

    I assume the airlines industry knows this?

    maybe they know it intuitively, and are not aware of the fact that they are actually relying on the Alfi-Parisi-Pietronero scaling law!

    Cher Blaise Pascal,

    thanks for the pointer to the "Edward's time-effort law" - that's interesting! This law seems to be indeed closely related to the APP scaling, wich then should be called EAPP scaling. Do you know any other reference to Edwards's law?

    Scaling laws Parisi is involved with apparently have a high chance to have been known before - Altarelli-Parisi is now DGLAP, and APP may actually be EAPP, or ESAPP ;-)

    Best, Stefan

  9. Googling for Edward's law produced this fun site, where you can learn among others about

    Bell's Theorem : When a body is immersed in water, the telephone rings.


  10. That curve looks as if it is best fit by an equation of the form

    N = A*exp(B*t)

  11. Nah, the initial slope is too linear, and it looks as if it diverges at the deadline.

  12. I feel left out. I also have a Ph.D. in theoretical physics, obtained over 20 years ago, but I don't have any wild theories to push, and I've never written an "internet book". If anyone has a discarded hair-brained scheme they'd care to lend me, I'll get back to work. :)

  13. Hi anonymous_1,

    Could someone re-do those curves on semi-log paper

    I guess the authors will do that in a full-fledeged publication, where they definitely would have to include more samples, and give details about the fit, such as robustness, chi^2, and the like ;-)

    Hi anonymous,

    hat curve looks as if it is best fit by an [exponential]

    You're talking about the "payments" distribution? The registration curve for sure doesn't fit to an exponential, as Bee says - for the other one, I would be cautious, that's quite hard to say "by inspection". Of course, they should check if an exponential doesn't provide a better fit than this funny Boltzmann-weighted hyperbola.

    But I should add, in my opinion the letter is to a large part a kind of "inside" joke and may not claim to be taken dead-serious without much more checks:

    The authors are well-known statistical physicists, data are from conferences about statistical physics, and "playing around" with such scaling laws while searching for universal patterns is standard business in today's statistical physics. So, I would firmly put this law in the category of semi-serious laws, such as Murphy's law, Bell's law - thank you, Bee, for the pointer ;-) - or Edward's law.

    Best, Stefan

  14. hare-brained


    1. Said of people, actions, etc: foolish; rash; heedless.

    Thesaurus: foolish, asinine, daft, flighty, scatterbrained, dizzy, irresponsible, rash, reckless, wild; Antonym: sensible.

    If you are asking for ideas on the status of being 'not even wrong' I have plenty of these :-) I can't really recommend working on them though, that's why they are in my desk drawer, buried under gummy bears.

    Love your profile pic :-)


  15. lol

    I stumbled into your den through a circuitous route via Garrett's new-found fame. I had to do a little Google work to connect some of the comments on that their "internet books". What a cast of characters! Regarding Garrett's paper -- hep was never my field, so I have no opinion. But the discussion was fascinating!

  16. Hi Anonymous_1,

    Yeah, for a blog discussion it went fairly well. You should have seen our visits statistics, yesterday it peaked at more than 10k (the usual average is around 900). Totally weird. For once I was happy that the blog is running at blogspot and we've no problems with the CPU quota. Though it attracted too many people who didn't actually know what they were talking about, but wanted to say something nevertheless. So I decided to close the comments. As I mentioned in my last comment there, I think about having a follow-up post so those who are still interested when things have calmed down can weigh the arguments in a calmer environment. Best,


  17. I want to post a comment, but I think I will wait until the deadline...

  18. > stefan
    > I guess the authors will do that
    > in a full-fledeged publication...

    Dictum #248 -- Everything looks better on semi-log paper. ;)

    > bee
    > I think about having a follow-up
    > post so those who are still
    > interested when things have
    > calmed down can weigh the
    > arguments in a calmer environment.

    I look forward to reading another discussion on the E8. I just finished listening to Garrett's ILQGS talk. The heavy-hitters sound intrigued, and he deftly handled that presentation.

  19. It gets better - add in weekends, holidays, timezones, etc and you can model the take-up even more accurately!

    The real killer is payment deadlines ... optimising for total revenue isn't as easy as you might expect, based on just these findings ...

  20. (I stumbled onto this site while googling reviews of Lee Smolin's book, which I'm in the middle of, but I have 2 cents to stick into this discussion.)

    1. We put on seminars, so I watch how people sign up. Your curve has a sharp but small peak at the beginning because some people always register immediately.

    2. When I sign up for an event, I aim for the window before the "early bird discount cutoff" but after my credit card charges close for the month. I'll leave it to a math wiz to show how this would affect your curve if lots of people did this.

    By the way, I really like "The Trouble with Physics." The first half is the best description I've ever read of the tension and synergy between theoreticians and experimentalists in scientific exploration. And I'm no physicist: I'm just one of these "educated laypeople."


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