Three Roles for Mathematics in Conflict Theory

Mathematics has three major roles in the study of conflict. First, descriptive statistics summarize information and makes it easier to understand. Examples include batting averages, defensive gun incidents, divorce rates, income data, sales reports, terror attacks, voter turnout, and workdays lost to strikes.

Second, scientists test ideas by research design and inferential statistics. Reduced to essentials, the process is easy to understand. First, a “null” or “no difference” hypothesis is stated (e.g., handedness is unrelated to aggressiveness ¹ ). Then, the researcher devises a strategy to test the hypothesis. Minimally, the strategy specifies a population, a sampling plan, the type of data needed, and how to collect and analyze the data. The sample, those from whom or about whom data actually is collected, should be representative of a populatio n, those about whom one desires to draw conclusions. Data is collected by recognized methods such as content analysis, clinical trial, laboratory experiment, observation, or survey research. An appropriate inferential statistic determines whether to retain or reject the hypothesis at a predetermined level of risk. The sources and possibilities for error being great, no single experiment is conclusive (Chapter 1).

The third role of mathematics, game theory, makes four main assumptions:

· Interests are quantifiable

· Players try to minimize losses and maximize gains

· The outcome is based on what each player does

· Every possible outcome is theoretically knowable to all players

The potentially frivolous connotation of “game” theory is unfortunate. In World War II it solved the problem of how to set depth charges to maximize the odds of sinking German submarines, 70% of which were destroyed—the highest fatality rate in any service of any belligerent in the World War II. Game theory helps in assessing risk, making decisions under uncertain conditions, analyzing conflicts, and understanding fairness. Baseball became more sophisticated when Oakland A’s manager Billy Beane evaluated players using sabermetrics (Lewis 2003).

This chapter takes up topics and methods that are vital to understanding conflict theory at virtually every level from the intrapersonal to the international. It provides several methods for dividing property among claimants such as siblings sharing an inheritance. It also describes a sophisticated method for identifying potentially stable solutions to complex conflicts.