Game of Thrones fans already know this, but apparently it's not great for governance when close relatives produce offspring. But this actually isn't a story about tangled royal bloodlines. As Michael Woodley and Edward Bell argue in the Journal of Cross-Cultural Psychology, it's something a little more broad-based:
This article examines the hypothesis that although the level of democracy in a society is a complex phenomenon involving many antecedents, consanguinity (marriage and subsequent mating between second cousins or closer relatives) is an important though often overlooked predictor of it. Measures of the two variables correlate substantially in a sample of 70 nations (r = –0.632, p < 0.001), and consanguinity remains a significant predictor of democracy in multiple regression and path analyses involving several additional independent variables. The data suggest that where consanguineous kinship networks are numerically predominant and have been made to share a common statehood, democracy is unlikely to develop. Possible explanations for these findings include the idea that restricted gene flow arising from consanguineous marriage facilitates a rigid collectivism that is inimical to individualism and the recognition of individual rights, which are key elements of the democratic ethos. Furthermore, high levels of within-group genetic similarity may discourage cooperation between different large-scale kin groupings sharing the same nation, inhibiting democracy. Finally, genetic similarity stemming from consanguinity may encourage resource predation by members of socially elite kinship networks as an inclusive fitness enhancing behavior.
As a counterpoint, Iceland -- a country so isolated and sparsely populated that people need an Android app to keep them from hooking up with a close relative -- has had a representative parliament since the 10th century and a culture of individualism so strong they write Nobel Prize-winning novels about it. So there.