Hick's law

Hick's Law is one of the few results in cognitve psychology with a precise formulation, namely that the time taken to make a choice increases with the logarithm of the number of choices. That is, if someone has to make a choice between N alternatives, the reaction time T is given by:
      T   ∝   log( N )

In fact, the original experiments that gave to this were based on highly structured inputs that enabled 'binary chop' style decision strategies. Given a long list of randomly sorted alternatives there is at least a linear time to read the list. However, whether the exact time is logarithmic or linear, the qualitative result still holds: the more alternatives the longer it takes a person to make the decsion.

This is important when designing intelligent human-in-the-loop systems, as it is sensible to present muliple alternatives to the human, but not too many.