A BALANCE SCALE PROBLEM
Mark Brown · Probability in the Engineering and Informational Sciences · 2013
Suppose we have n objects of different weights. We randomly sample pairs of objects, and for each sampled pair use a balance scale to determine which of the two objects is heavier. It is assumed that the sequence of sampled pairs is iid, each selection uniformly distributed on the set of n(n−1)/2 pairs. We continue sampling until the first time that we can definitively identify the heaviest of the n objects. The problem of interest is to compute the expected number of selected pairs.