> I don’t think middle class refers to median income. At least it certainly didn’t used to. How else could a population have a small middle class?

Well, it could if it meant “near median income” if few had near the median income. Median doesn't mean particularly common (or even the most common, which is the mode.)

The median is what you get if you sort all people by income and pick the middle person. If one forces the median to be in the middle class then this forces the upper class to be large when the middle is small: Example with a large middle class:

  |...|...........|...|
    ^       ^       ^
    |     median    |
  (working)      (upper)

Example with small middle class:

  |.......|...|.......|
    ^       ^       ^
    |     median    |
  (working)      (upper)

Real life example with small middle class:

  |.............|...|.|
  (working) ^     ^  ^
          median  | (upper)
                middle

> If one forces the median to be in the middle class then this forces the upper class to be large when the middle is small

It doesn't force the working and upper class to be equally large unless you further assume the distribution is symmetric, but yes, there is a limit to how small the upper class can be since at least half of the distribution has to be split between the upper and middle class.

If you look here [0] it would suggest that median is well within middle class (only 29% are "lower").

[0] http://www.pewresearch.org/fact-tank/2018/09/06/the-american...

Well sure. The point I contest is that the definition of middle class is “the class of the person/household with median income.”

Currently in developed countries it happens to be the case that the people with median income are middle class. However this was not always the case, ie the group referred to as middle class did not always include people with median income and so the above definition does not coincide with what middle class typically referred to.

The entire comment chain was not about some abstract middle class, rather middle class in the US right now.