In the community of mamathetitians in a certain country there are mamathetitians in two areas: Anabra (fraction p of the mamathetitians) and Algasis (fraction 1-p of mamathetitians.) There are ten universities with 50 faculty members in each mamathetics department and there is a clear ranking of these universities from best to worse. (So a better university pays higher salary and gives better working conditions.) Every year 40 fresh Ph D’s are in the job market and each university hires two of the fresh Ph. D.’s as new faculty members replacing retired faculty members.
The objective value v(x) of every mamathetitian x is a random variable uniformly distributed in the interval [0,1]. The subjective value of x in the eyes of another mamathetitian y is v(x)+t if they belong to the same area and v(x)-t if they belong to different areas, where t is a small real number.
The top ranked university hires the best two fresh Ph. D.’s according to average value in the eyes of the faculty, the second university hires the second best two students etc.
Let’s assume that to start is p=0.25, so 25% of all faculty are anabraists, and 75% are algasisits and this is the ratio in every university. Let us also assume that among the students for ever 25% are anabraists, and 75% are algasisits.
Test your intuition (and/or, programming skills) 43: What will be the distribution of anabraists and algasisits in the departments as time advances (depending on t), what will be the stationary distribution across departments?
We can also ask about variations to the model:
Further test you intuition, imagination and programming skill: How does the answer change if you change the model in various ways. Change the value of p? Make the initial distribution random across departments? Add noise to the subjective value? Make the bias in subjective evaluation asymmetric? make different assumptions on the fresh Ph. D.s? etc. etc.
References to similar models considered in the literature are most welcome.
Disclaimer: I do not know the answers.
Outcomes by Joshua Paik
Here are very interesting outcomes by Joshua Paik. We see a sort of Zebra-strips patterns between Algasis dominated departments and Anabra dominated departments.