There are 21 judges whose probabilty for making correct decision(binary decision of accept or reject) is all 0.7. They will aggregate their decision with the simple majority rule(more than half the number wins the decision). What is their probability for correct decision?
pr=:21#0.7 len=:#pr cor=:|: (#~ (>.2%~len) <: +/"1) #: i. 2^len wro=:-. cor +/ */ (pr* cor) + (1-pr)* wro 0.97361 Suprisingly, the probability goes quite high than their original correctness probability. Now, play it with five judges: 0.95, 0.95, 0.90, 0.90, 0.80 pr=:0.95 0.95 0.90 0.90 0.80 len=:#pr cor=:|: (#~ (>.2%~len) <: +/"1) #: i. 2^len wro=:-. cor +/ */ (pr* cor) + (1-pr)* wro 0.992945 1) Could you come up with more elegant, efficient solutions? 2) What would happen if the least correct judge(0.80) from the second case just follows the first judge(0.95)'s decision? 3) What is the condition that the result probabilty is higher than the best person's correct decision probability? ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
