Here's a curious finding:
Within-country happiness inequality has fallen in the majority of countries that have experienced a positive income growth over the last forty years, in particular in developed countries...This mean-preserving declining spread of happiness happens via a reduction in both the share of individuals who declare a very low and a very high level of happiness.
This is true for the US since the 1970s, Germany since the 80s and the UK since the mid-90s.
You might find this paradoxical, because during this time income inequality has generally increased, which you might expect to increase inequality of happiness.
However, the paradox is only superficial. Rising income inequality, ceteris paribus, does tend to increase happiness inequality - which is one reason why the US (pdf) has seen a partial reversal of the decline in happiness inequality since the late 90s. It just happens that, over the long-run, economic growth has reduced happiness inequality by more than rising income inequality has increased it.
One possible explanation for this lies in Abraham Maslow's hierarchy of needs. As the economy grows, the basic needs of the poor for nutrition and health are more easily met, and so the numbers of people in misery decline. However, the more neurotic rich increasingly ask "if I'm so rich, why aren't I happier?" and focus upon the lack of fulfilment of their needs for self-actualization. The number of very happy people thus also declines.
So, how embarrassing is this for egalitarians?
It is awkward for green egalitarians, because it means the case for economic growth is stronger than supposed, if you value equality.
It is also awkward if income inequality is necessary for economic growth - because if this is so, then income inequality is a price we must pay for increased equality of happiness.
However, in another sense, it might strengthen egalitarians' arguments.
First, if income inequality (pdf) is bad for growth, as Joe Stiglitz argues, then the case for income equality strengthens - because income equality would raise economic growth and thus increase happiness equality.
Secondly, if the hierarchy of needs explanation for increased happiness equality is correct, then inequalities of power in the workplace become more pernicious as incomes rise because they frustrate demands for self-actualization and so prevent rising incomes from leading to rising happiness. In this sense, egalitarians and utilitarians (and proper libertarians too!) can make common cause.