Overcrowding

Very interesting take on overcrowding.  I must admit I hadn’t thought too much about the physical volumetric notion of overcrowding until you brought it up, but it is an interesting idea.  As you know, things in high dimensions do get concentrated; as Han wrote on p. 7 of his book Information-Spectrum Methods in Information Theory, “That is, almost all probability is concentrated on the dust Tn if n is sufficiently large.”  But with people, I’m not sure what exactly is the notion of dimension, or of surface area, or of volume.  

Notwithstanding, a recent paper by Boudreau, Lacetera, and Lakhani on crowdsourcing contests makes the following statement:

Research in economics suggests that increasing the number of competitors who are admitted to a contest will reduce the likelihood of any one competitor winning, thereby reducing incentives to invest or exert effort and lowering overall innovation outcomes (Che and Gale 2003, Fullerton and McAfee 1999, Taylor 1995).  Similar predictions and findings on negative incentive effects have been found in research in sociology and psychology (Bothner et al. 2007, Garcia and Tor 2009). Overall, the literature has generally recommended against free entry into contests, with some models specifically determining the ideal number of competitors to be just two (Che and Gale 2003, Fullerton and McAfee 1999).

Relatedly, I assume you’ve heard of Metcalfe’s Law, right?  This asserts that the value of a network is the square of the number of members.  Such a law doesn’t take overcrowding into effect at all.  Indeed, McAfee and Oliveau argued against Metcalfe’s Law by citing several effects: saturation, cacophony, contamination, clustering, and search costs.  Cacophony is clearly an effect of overcrowding: “When too many users of a network make interaction difficult—in a crowded Internet chat room, for example—cacophony is the result.”  Disappointingly, the solution to cacophony that they propose is to limit new members or to kick out existing members.

A totally different kind of overcrowding is in scientific fields due to herding behavior.  It seems like many people jump on bandwagons when new tools emerge that allow previously unknowable things to become knowable: this could be a newish mathematical insight as in compressed sensing or a newish sensing technology like electron microscopy.  By the way, what happened to your electron micrographs?  Anyway, I recently followed a link from Solomon Hsiang‘s blog, Fight Entropy, about Eurekometrics.  One of the points is that the ease of scientific discovery decays with time, so maybe that explains some of these bandwagons.

Speaking of ease of accomplishment as a function of time, what do you think of Klosterman’s view on the 100m world record?  For those who like visuals, here is a graphical depiction from Wikipedia:

and for good measure, here is the 200m world record:

I wonder if there is some record value distribution method to study scientific progress, as there is for flood levels or world records in athletics.  Moreover, how does overcrowding play into it?

Nobody Goes There Anymore. It’s Too Crowded.

Señor Henri de Toulouse-Lautrec, that number of connections doesn’t include people from the past that you might encounter during Midnights in Paris, does it?

At the SSP Workshop last week, in which I presented a bound on reject option risk for ensemble classification and our work on minimax Bayes risk error quantization, Vikram Krishnamurthy brought up the paper A Global Game with Strategic Substitutes and Complements in his plenary talk.  One key notion in that work is summarized by the following quote by Yogi Berra:

Nobody goes there anymore.  It’s too crowded.

The idea is that when frequenting an establishment, your utility depends on the number of other patrons also frequenting that establishment.  When there is no one else there, you receive no utility.  As it fills up, you get more utility.  When it starts becoming crowded, however, your utility goes down.  This utility function is quasiconcave and applies equally well to sensor networks and cognitive radio as pointed out by Krishnamurthy.  An example of such a function is below, where α is the filling fraction of the establishment.

Does this sort of utility function arise in the crowdsourcing you have been studying?  Do you think that this utility model is at all related to Figure 2(A) of your neuroscience paper or to the surface area of hyperspheres that you pointed out here previously?  (In your neuroscience work, there is a volume constraint with neurons occupying some volume.  Similarly, in an establishment, there is a volume constraint with patrons occupying some volume.  In both cases, more is better until the space starts getting crowded.  For the hypersphere, again there is a volume constraint.)