Combinatorial diversity metrics for the analysis of policy processes

We present several completely general diversity metrics to quantify the problem-solving capacity of any public policy decision making process. This is performed by modelling the policy process using a declarative process paradigm in conjunction with constraints modelled by expressions in linear temporal logic. We introduce a class of traces, called first-passage traces, to represent the different executions of the declarative processes. Heuristics of what properties a diversity measure of such processes ought to satisfy are used to derive two different metrics for these processes in terms of the set of first-passage traces. These metrics turn out to have formulations in terms of the entropies of two different random variables on the set of traces of the processes. In addition, we introduce a measure of `goodness' whereby a trace is termed {\it good} if it satisfies some prescribed linear temporal logic expression. This allows for comparisons of policy processes with respect to the prescribed notion of `goodness'.