[jerzyt]

It could also be argued that "medianism" is the perfect method to hide income inequality, because median is resilient to outliers, so the billionaires will not affect the median at all. Every metric can be "gamed" and so can the median.

[jnwatson]

That’s not how the median works. If we had as many in poverty as billionaires, we’d have a pretty good situation.

[Stupulous]

If half of a country were impoverished and half were billionaires, I'd say they have a pretty serious income inequality issue. A median would randomly conclude that either the typical person is a billionaire or in poverty. Best case scenario, the median would equal the mean and give a result that reflects reality, but it still doesn't convey the issue at all.

Median and mean both compress n data points into one, which is only useful given some assumptions about the distribution. Quintiles (or similar) would work for that scenario, but I'm sure there are more complicated situations where they fall short.

[jnwatson]

Societies in which there are within 100x as many billionaires as poverty stricken don’t exist.

[Stupulous]

Sure, it's a toy example to tease out the underlying shortcomings of the measurement. Societies where the median does not reflect the typical experience do exist.

[notahacker]

But resistance to outliers is the point because people don't take billionaires inflating the per capita GDP as "wow, this country has a problem with inequality", they take it as "wow, this country is getting richer".

With GDP per capita, a few oil billionaires and a very small class of well-paid oil workers make Equatorial Guinea look like a middle income country. Median GDP reveals that the average person there lives on less than $2 a day, because Equatorial Guinea is also the most unequal country in the world. But clearly it's more representative to class Equatorial Guinea as very poor (median income) than moderately wealthy (per capita GDP/mean income) or rich (per capita GDP PPP)

Median income isn't perfect because it can hide things like one country having 5% living in extreme poverty and one country having 25% but with typical real world income distributions, an average not massively skewed upwards by how rich the top 10% or 1% is gives you a much more accurate perspective on which country most people have higher incomes in.