A balance scale problem (Q2845125)

From the text: 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. [\dots] The problem is to compute \(\operatorname{E}T_{n}\), where \(T_{n}\) is the random number of selections made until we determine which of the objects is the heaviest. Our main results is that, \(\frac{\operatorname{E}T_{n}}{\binom{n}{2}}\) is an increasing sequence with limit \(c\), where \(1.254768<c<1.255575.\) [\dots]NEWLINENEWLINE The above problem can be viewed as a coupon collecting problem.