It seems reasonable to expect that the difference between the probability of happiness of people on upper incomes and those on lower incomes would depend on the degree of income inequality in the country in which they live.
This proposition can be tested simply by calculating the gap between the percentage of upper and lower income people who claim to be satisfied with life in each of a large number of countries and then ranking them by the gini coefficient (or some other measure of income inequality) and calculating gap averages for groups of countries. I have used data on percentages of lower, middle and upper income groups who are satisfied with life as a whole for 66 countries. The data was sourced from surveys conducted over the period 1999 - 2002 (see Ronald Inglehart et al, Human Beliefs and Values, Siglo XXI Editores, Mexico, 2004, A 170).
The results are shown below.
If income inequality causes happiness inequality we should expect to see lower average gaps between happiness of people on upper and lower income in countries with relatively low levels of income inequality. That is not what the chart shows.
Similar results have been found in a study by Jan Ott. In a study covering 64 countries this researcher found that inequality of income tends to go together with higher levels of happiness and more inequality of happiness. The correlations are not substantial, but the result challenges conventional wisdom. (See: ‘Level and inequality of happiness in nations’, Journal of Happiness Studies, 2005, p 408-9).