The Bush and Kennedy families are currently four-generation political dynasties, while Clinton is a single generation. That'd be a very low upper limit compared to most of history if it does turn out to be an upper limit, but of course there's no way for us to know now if the current generation will also be the final one.
You need to add the influence those families play in local (e.g. state and city) politics, how they intermarry and extend their reach, how extended family (e.g. different-surname cousins) hold political roles and help each other out into power, and so on.
Even going strictly for families:
(...) "my research has thus far identified 167 families with members elected to public office for at least three consecutive generations. Twenty-two families have had at least four consecutive generations elected to public office, while four families – Bachhuber/Doyle, Cocke, Lee and Washburn – have had at least five generations."
Thanks for this and the other links. Does make me wonder whether nepotism or brand recognition plays the bigger role. The more things are accounted for by the latter, the more I want to chalk this up to democracies getting the leaders they deserve, no more.
