Social choice theory is broadly concerned with the formal study of collective decision making: a set of agents report preferences over a set of candidates that need to be aggregated into a collective decision. In economic theory, the standard approach to evaluating mechanisms for such problems, so-called voting rules, is to formalize desirable behavior of mechanisms as rigorous mathematical axioms and to prove or disprove that a given mechanism satisfies these axioms. Common examples of such axioms are Pareto efficiency, strategyproofness, or proportionality conditions. Unfortunately, it is well-known that it is often not possible to attain several desirable properties at the same time because impossibility theorems show that even rather basic axioms cannot be jointly satisfied by any voting rule. In an attempt to circumvent such impossibility theorems, I will discuss the idea of approximate axioms in this talk. Instead of being binary criteria, such approximate axioms allow for quantifying how close a rule is to satisfying a given axiom, thus allowing for moving past impossibility theorems. Further, I will showcase this approach by discussing how approximate strategyproofness can be used to bypass a far-reaching impossibility result showing that no efficient and strategyproof budget division method can be proportional.