I taught an entry-level math course. Although I had no attendance policy, most students attended regularly (not perfectly, but regularly) throughout the semester. A significant minority had spotty attendance for at least part of the semester, and often only a small part. Take a look at the grade distribution for the class:
The following semester, I taught a slightly higher-level class. Again, I had no attendance policy, but I explained what had happened the previous semester, and showed a version of the chart above. Success! The vast majority attended class regularly throughout the semester. On the other hand, a significant minority skipped at least a quarter of the homework assignments. Doing so had little direct effect on their grades, since homework was only a small part of the course. Were there indirect effects?
I guess that the lesson here is to be responsible in at least two ways. While my previous teaching experience shows that this is not a guarantee of success, the charts above suggest that it might not be too bad of an idea.