They do, actually, though the process by which those seats are assigned is a bit complicated.
Regulations for the student section in Camp Randall have changed a lot over the years. A century ago, all seating was general admission — whether student or otherwise, everyone squeezed onto wooden bleachers. And it was a tight squeeze: in 1915, the official capacity of the bleachers was just 3,000, but the Daily Cardinal reported that as many as 15,000 fans showed up for games.
Today’s Camp Randall accommodates 80,321 people, and 14,000 of those seats are set aside for students. In case you’re curious, those seats are situated in sections K, L, M, N, O, and P, as well as part of section J. Though today’s Badger students pay $168 for a season’s worth of tickets (plus a $20 processing fee), they don’t know which of those 14,000 seats they’ll stand and jump in front of until Game Day.
The thing is, students don’t actually purchase football tickets — instead, they purchase football ticket vouchers, which they take to Camp Randall starting at 8:30 a.m. on Game Days. They then exchange the vouchers for tickets, with seat assignments given out first come, first served. This ensures that the student sections will fill from best seats to worst. (Which, and I’m sure this is purely coincidental, makes the stadium look more attractive and energetic to people watching on television.)
Much of the motivation for experimenting with different seating systems came as a reaction to the tragedy of 1993, when, after a Wisconsin victory over Michigan, the student crowd surged toward the field, injuring 73 people (six seriously). Since then, the number-one concern has been ensuring that no similar issue ever happens again.