The majority of enrolled students are found in the College of Letters and Sciences vs. Engineering so UCSB has plenty of strong programs besides the STEM areas.
The Econ program at UCSB is considered very strong and ranked in the top 50 of all UC colleges. Regarding Political Science and Sociology, I cannot comment but if the student is interested in Law school, they can major in any subject as long as they achieve a high LSAT score and GPA.
I would suggest you look over the course curriculum’s for any major of interest to see if they fit your goal. Hopefully a current student or parent that has first hand experience with one of these programs can chime in on their experience. UC’s overall have some strong programs in a variety of subjects.