In the paper “A Preliminary Model of Jury Decision Making as a Function of Jury

Question

In the paper “A Preliminary Model of Jury Decision Making as a Function of Jury Size, Effective Jury Decision Rule, and Mean Juror Judgmental Competence”, Frontiers of Eco- nomics, Vol. 3, 1980, pp. 98-110, the author Bernard Grofman modeled, that the probability for a three person jury to make a correct decision is given by

P (r, s) = a[3r^2(1 r) + r^3] + (1 a)[3s^2(1 s) + s^3],

where r is the probability that a given jury member will vote “guilty” when the defendant is indeed guilty of the crime, s is the probability that a given jury member will vote “innocent”, when the defendant is indeed innocent and parameter a is the probability that the person is guilty of the crime.

What values of r and s would maximize the jury’s probability of making the correct verdict?

Explanation / Answer

if we see equation

ther expression in r and s is similar

then maxima will occure at symmetry

ie r=s=1/2=0.5

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