Nobody Goes There Anymore. It’s Too Crowded.

July 6, 2011

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.)


One comment

  1. […] Ashvins The Ultimate Machinists « Nobody Goes There Anymore. It’s Too Crowded. Overcrowding July 17, […]

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