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:

EMM grade distribution

Suggestive, no?

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?

Calculus 1 grade distribution

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.