# Why is entropy formula defined as what it is? [duplicate]

This is probably a naive question. Why is Entropy formula defined as the way what it is intead of more simpler formula? for example just P(x)*P(y) which I imagine can express uncertainty as well (0.5*0.5 > 0.4*0.6 > 0.3*0.7).

• Sum of squared probabilities (or its complement, or its reciprocal) is often used, with multiple names such as Gini, Turing, Simpson, Hirschman-Herfindahl, repeat rate, match probability, heterozygosity and (!!!) quadratic entropy. – Nick Cox Mar 29 '19 at 8:30