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In the case of the US per capita GDP just means that we are a country containing many rich people, not a rich country. Income inequality is extreme. When the government or private industry refuses to redistribute money downward, poor people will just take it.

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https://en.wikipedia.org/wiki/List_of_countries_by_income_eq...

According to the "Gini coefficient" wealth inequality is actually slightly higher in China. Any other theories?

That depends on whose figures you use. According to the CIA, income inequality is higher in the U.S. That's also a figure for the entire country, not within the cities where these bike share companies operate, and I would guess that there's a much more stark divide between rich and poor in American cities.

The CIA gini coefficient is slightly higher for the US, a few percentage points, while the World Bank Gini coefficient is slightly higher for China. Your conjecture about the starker divide between rich and poor in US cities is just that, conjecture. I could guess the same about Chinese cities.

So we have no evidence yet that China has less income inequality than the US. Which makes it a very unconvincing reason for differences in crime.

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