Combinatorial diversity metrics for the analysis of policy processes

TL;DR

This paper introduces general diversity metrics based on entropy to analyze the problem-solving capacity of policy processes modeled with declarative and temporal logic, enabling evaluation of process diversity and quality.

Contribution

It develops novel diversity metrics for policy processes using first-passage traces and entropy, integrating temporal logic to assess process diversity and goodness.

Findings

Metrics quantify policy process diversity effectively.

Entropy-based measures relate to process trace variability.

Goodness measure enables comparison of policy process quality.

Abstract

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'.