Should I use a regression or classification framework to predict rankings? My dependent variable is a performance ranking (relative to the other individuals). For example, one individual would be ranked first, another second, another third, etc. Would I use a classification or regression framework to model this?
Sounds like a classification task. Since your $y$ is ordered, you may also consider "ordered probit" or "ordered logit". These methods make sure that the order in $y$ is accounted for.