What is a priority?

What does it mean to say that something is a 'priority'? Priority setting is used to balance competing claims for resources, but the nature of the exercise is ambiguous. The priorities which are claimed might be for time, resources, process, rights or service. The setting of priorities might refer to importance, relative value, precedence, special status or lexical ordering. And there are different ways of ranking priorities including simple ordering, optimization, triage and satisficing. There is a fundamental distinction between preference rankings and precedence rankings, which can lead to strongly different conclusions from the same initial information. Because there is no definitive understanding of what a priority is, there can be no authoritative formula for deciding between competing claims.