Monday, 6 June 2011

When the lack of any probability theory knowledge can bring a big unfairness

Recently I enrolled my son for the local music school. As there are always more candidates than places, somebody apparently decided that it would be a good and fair system to do the following:
  1. Sort out all the candidates alphabetically.
  2. Randomly select one of the letters and then choose n candidates (where n is the number of available places), starting with the first candidate whose surname starts with the chosen letter, and just go down the list in 1. (continuing from the beginning if the end of the list is reached) until all available places are taken.
To see how bad a system this is, I just got a list of 106 people that were applying to another local school (I just didn't have the original list with me) and assumed that 25 places are available. The probabilities of getting a place are so unfair, that I'm going to contact the local school to see if they want to change the system for coming years. Two of the extremes:
  1. One person has only a 3.85% probability of being chosen (the last one whose surname starts with S, since there are 14 people whose surname starts with R, and 12 people whose surname starts with S, so the only chance for her is that the randomly chosen letter is S).
  2. Another person has a 42.31% probability of being chosen (the first one with the letter C, since surnames starting with letters from S to B are a very small proportion of the total, and he would be chosen if any of those letters are randomly chosen. The number of surnames for each of these letters is: S: 12; T: 4; U: 1; V: 4; W: 1; X: 0; Y: 0; Z: 0; A: 1; B: 1).
Below I include a chart which, assuming 25 places, gives the probability (as a percentage) of being chosen for all the 106 people included in my test sample.

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