Further and detailed statistical analysis of departmental staffs would be inappropriate in such an article as this. It is hoped, however, to reach a tentative conclusion regarding the time likely to elapse between a given official's first appointment and the later appointment of his two or more assistants. Dealing with the problem of pure staff accumulation, all the researches so far completed point to an average increase of about 5¾ per cent per year. This fact established, it now becomes possible to state Parkinson's Law in mathematical form, thus:
Not all of an agent’s desires result in action. In fact, if one has conflicting desires, then it is impossible for an agent to satisfy all her desires. Suppose that Allison not only desires to run, but that she also desires to stay curled up in bed, where it is nice and warm. In such a case, Allison cannot fulfill both of her 1st order desires. If Allison decides to act on her desire to run, we say that her desire to run has moved her to action. An effective desire of this sort is called a volition; a volition is a desire that moves the agent all the way to action. Similarly, one can differentiate between a mere 2nd order desire (simply a desire to have a certain desire) and a 2nd order volition (a desire for a desire to become one’s will, or a desire for a desire to become a volition). According to the hierarchical view of the will, free will consists in having 2nd order volitions. In other words, an agent has a free will if she is able to have the sort of will that she wants to have. An agent acts on her own free will if her action is the result of a 1st order desire that she wants to become a 1st order volition.