One if by Land, Two if by Sea, Three if by Four Seas, and More to Come -- Values of Perception, Prediction, Communication, and Common Sense in Decision Making

TL;DR

This paper introduces decision-theoretic and information-theoretic measures for perception, prediction, communication, and common sense in decision making, with implications for autonomous systems and cognitive science.

Contribution

It rigorously defines new quantitative measures for key decision-making values and explores their mathematical properties and practical implications.

Findings

Perception without prediction can have negative value.

Values of perception, prediction, and communication are nonnegative when combined.

The measures provide insights into optimal observation and prediction strategies.

Abstract

This work aims to rigorously define the values of perception, prediction, communication, and common sense in decision making. The defined quantities are decision-theoretic, but have information-theoretic analogues, e.g., they share some simple but key mathematical properties with Shannon entropy and mutual information, and can reduce to these quantities in particular settings. One interesting observation is that, the value of perception without prediction can be negative, while the value of perception together with prediction and the value of prediction alone are always nonnegative. The defined quantities suggest answers to practical questions arising in the design of autonomous decision-making systems. Example questions include: Do we need to observe and predict the behavior of a particular agent? How important is it? What is the best order to observe and predict the agents? The defined quantities may also provide insights to cognitive science and neural science, toward the understanding of how natural decision makers make use of information gained from different sources and operations.