macrocephalopod

This seems counterintuitive. The most social mobility is usually in places with the greatest range of income isn't it? What do you mean most equality, the bands of income are equal in size?

No! The way you measure social mobility is the likelihood of a child being in a different income quartile (or decile) to their parents. Much more likely in countries with less distance between income bands.

Doesn't that make your claim a consequence of measuring social mobility this way, rather than a statement about social mobility?

How else would you define social mobility in a way that was measurable?

For example: probability that a child will have 5x the income per person vs their parents

Isn't that only social mobility if having x5 income places them in a different part of society?

When would 5x income increase NOT put a person into a different part of society?