Matthew Yglesias posts a pretty picture showing a negative correlation between income inequality and income redistribution. This relationship is definitionally true, so at first I wasn't sure why he thought it was worth pointing out. But then he goes on to say that this means something else entirely:
I think the links between taxation, spending, and inequality are the most plausible explanation of the fact that the highest-taxed countries are the happiest. It can’t be that paying taxes makes Danes happy. But plausibly, living in a relatively egalitarian society makes people happy.
That certainly is plausible, especially to those (like Yglesias) who are attracted to arguments for progressive social policy from Rawls' "Veil of Ignorance". Unfortunately, as Wilkinson points out, the plausible causal inference isn't true:
Danes say they’re really happy and have the lowest inequality. But Americans are nearly as happy and have high inequality for an OECD country. Mexicans are a quite upbeat lot, but have really, really high income inequality. So there’s not much of a clear pattern in the data. The effect of inequality on happiness appears to be pretty strongly ideologically mediated. Unsurprisingly, high inequality tends to be disquieting to egalitarians. But it doesn’t so much bother meritocrats. Additionally, the causes of high inequality are various. Economic predation by political elites (lots of Latin America and Africa) is pretty likely to create a sense of victimization and injustice. But high levels of wealth creation in more or less fair institutions but with relatively little fiscal redistribution (the U.S.) doesn’t bother people as long as they think the system is more or less fair. So the national income inequality variable itself tends to have little or no independent effect. The effect it does have depends on other things people believe and care about and the specific causes of inequality in different places.
There are a lot of plausible explanations for why Danes are happy. One of them is that Denmark is a small, culturally homogenous country that preserves their homogeneity with strict immigration laws. These strict immigration laws prevent the migration of poorer people into Denmark, which keeps intra-national income inequality low (and possibly broadens the support for domestic redistribution, since the social spending won't go to immigrants) but increases the inter-national income inequality between Denmark and other, poorer, countries.
Yglesias does not describe which he prefers: within-country inequality or between-country inequality, and I'm sure he would recoil from having to make the choice. But there is often a trade-off. Without realizing it, he does seem to think that one of the two makes citizens happier, but I don't think he intends to espouse a "keep them out, keep them poor" attitude towards the developing world. Unfortunately, that appears to be the way it works: keeping immigrants out makes citizens of wealthy countries wealthier (on average), boosts support for income redistribution through social services, and makes people lucky enough to be born there happier than the unlucky ones born in poorer places.
This is why causal inference in the social sciences is so difficult: a plausible explanation isn't always borne out by the data. Sometimes this is made evident if we consider related questions. In this case, if we observe that poor countries are less happy than rich countries, which they are, should we conclude that it's probably because they don't have enough public transportation or a better pension system? Or maybe having access to better economic opportunities might improve the mood.
For the record, the other happiest countries are Finland, the Netherlands, Belgium, Switzerland, New Zealand, Australia, Canada, Sweden, and Norway. Bastions of diversity, they are not.