Everyone Is Above Average: Is It Possible? Is It Good?

Laxman Bokati, The University of Texas at El Paso
Vladik Kreinovich, The University of Texas at El Paso

Technical Report: UTEP-CS-22-85


Starting with the 1980s, a popular US satirical radio show described a fictitious town Lake Wobegon where ``all children are above average'' -- parodying the way parents like to talk about their children. This everyone-above-average situation was part of the fiction since, if we interpret the average in the precise mathematical sense, as average over all the town's children, then such a situation is clearly impossible. However, usually, when parents make this claim, they do not mean town-wise average, they mean average over all the kids with whom their child directly interacts. Somewhat surprisingly, it turns out that if we interpret average this way, then the everyone-above-average situation becomes quite possible. But is it good? At first glance, this situation seems to imply fairness and equality, but, as we show, in reality, it may lead to much more inequality than in other cases.