[Symmetry]

Well the traditional alternative is that you inherit your profession from your parent. In terms of political leadership this would be aristocracy but it was pretty common for others too. Men with the last name "smith" expecting to follow their father in becoming smiths for example. But of course levels of employment in different jobs are nowhere near as stable as they were back then. Not too many smiths around and we've gone from 80+% of people working as farmers to less than 5%.

I suppose you could have everybody randomly assigned to jobs. Or you could people have a list of preferences and to the extent that there are more applicants to a given job than open slots randomly assign them then move the other applicants to their next slot.