In QCA set-theoretical relations are the central features of the method, so it is worth explaining these first.

A necessary relation exists where, starting with the outcome we are interested in, we find a range of causal factors that consistently also appear. A simple example will make this clear. To get a graduate job (the outcome), it is necessary to first be a graduate (causal factor). Being a graduate is a necessary condition of getting a graduate job.

However, necessary factors, by themselves, do not guarantee a specific outcome will occur (unless there are also sufficient – which we will explore in a moment). This is because whereas it is necessary to be a graduate to get a graduate job, it is not enough by itself. There are a host of other things that a graduate will probably also have to do – apply for the job, go through a selection and interview process, and so on. So necessary conditions tell us about factors that have to be present (they are ‘necessary’) to lead to an outcome, but they usually are not enough (sufficient) – by themselves, to achieve that outcome as other factors have to be present as well.

A sufficient relation exists where, whenever we have the cause (or combination of causes), then we also get an outcome we are interested in. It is ‘sufficient’ to know that, when these causal factors are present, we will also get the outcome. However, just because a cause is sufficient, it does not mean that it is the only way of achieving the outcome. We may have several sufficient solutions (which we will call ‘pathways’ to an outcome). This is because our causal factors (and others) can be combined in different ways to achieve a specific solution. This approach of having multiple pathways to a solution, rather than a single solution, is called equifinality.

The logic of a sufficient condition is therefore, at least in some respects, the opposite of that of a necessary condition. For a necessary relation we start with the outcome (a graduate job) and then look for consistently present causal factors (being a graduate).