In what degree?
There are certainly, at least, some guidelines in some instances based on one's relatives. I was called up for a coroner's court jury a few years ago and was perfectly happy to serve, but there was a "tell us anything else that may be relevant" clause in the letter, so I informed the relevant authorities that my father (by then retired) had previously been a Deputy Coroner. On these grounds I was judged ineligible for coroner's court jury service, a decision I've never quite understood the reason for. While there are, no doubt, certain people who shouldn't be allowed to serve on juries, I find it hard to understand exactly why I'm one of them.
Actually, I can think of one or two, but they're more to do with pedantry than ancestry.
Dave