is certainly a tradition we can well trace back to the Adams family, with the 2nd and 6th Presidents, to the Harrisons, with two presidents separated by a generation, and of course to the Bushes with two Presidents, and possibly a third.
I was thinking about this phenomenon, and without having to do any research came up with this:
Kathleen Sebelius - father Rep. John Gilligan
Nancy Pelosi - father Mayor and Rep. Tommy D’Allessandro
Patrick Kennedy - father Bobby Kennedy, Uncle Ted Kennedy - Grandfather Joe Kennedy
Kathleen Kennedy Towndsend - same
Rep. Joe Kennedy II - same
Joe Kennedy III - son of Joe Kennedy II, and thus 4th generation
Andrew Cuomo - father Governor Mario Cuomo
Mark Prior - father Sen. David Prior
George W Bush & Jeb Bush - father Pres. George H. W. Bush, grandfather Sen. Prescott Bush - and note, George P. Bush, elected in TX, is now the 4th generation
John Dingell - father Rep. John Dingell Sr.
Mitt Romney - father Gov. George Romney
Jay Rockefellar - nephew of Govs Nelson and Winthrop Rockefellar
Sen. Shelley Moore Capito - daugher of Gov. Arch Moore
Former Rep Alan Mollohan - son of Rep Robert Mollohan
Former Rep. Dan Boren - son of former Senator David Boren
Robin Carnahan - daughter of Mel and of Jean
Rep. Russ Carnahan - the same
Connie Mack IV - son of Connie Mack III - and if you go back several generations you will find more politicians in the family tree
There are of course many more
In New York there was Hamilton Fish after Hamilton Fish. Going back to the early years of the Republic.
Howard Baker had both of his parents serve in Congress, and of course he married another Senator.
Rep. Susan Molinaro was the daughter of a politician and married another Congressman
And I have not even begun to examine all the examples of spouses who were both in politics, sometimes with the wife appointed to fill the seat of a deceased husband, or running
The thing is, we may not officially be an aristocracy, but far too often people get elected because they have a well-known name.
We may be less egalitarian and non-aristocratic than we think, eh?
Add more examples (there are hundreds) in the comments if you like.
Peace.