Conclusion
Mathematicians have provided vital understanding and tools for conflict theorists. Descriptive statistics provide an efficient way to summarize large amounts of information. Inferential statistics help in testing hypotheses that follow logically from conflict theories.
Mathematical games and models help us to think clearly about conflicts, although we should not expect the clarity to eliminate the passions. Pareto optimization provides a method for identifying efficient solutions to conflicts. Strategic choice provides a method for identifying stable solutions. Risk analysis and game theory provide tools for factoring uncertainty into decisions. Adjusted winner, proportional allocation, the Steinhaus procedure, and imaginary auctions provide methods for resolving conflicts over division of property.Mathematicians have identified four desirable characteristics of any procedure for resolving a conflict involving division of property. First, it should encourage truthfulness and discourage deception. Second, it should be efficient, in that no better solution is possible for one person without hurting someone else. Third, it should be proportional in that claimants feel that the share received equals their entitlement. Fourth, it should be envy-free (and thus stable), in that no disputant wants the share another with the same entitlement received. Envy-freeness can be achieved only if we understand which of three possible concepts of fairness, equity, equality, or need each claimant means or values most. Of course, all this assumes fairness should always be the goal, an assumption that Asma (2012) sees as an obsession that weakens other virtues such as compassion and has become a collective faith in some quarters that sometimes has comical results, as when schools try to ensure “equal valentine outcomes.”
Mathematical models involving human behavior are fundamentally different from those involving the physical universe. Formal models have difficulty quantifying and reliably predicting the irrational element in human motivation and behavior, which requires attention to character. It is a mistake to put too much faith in models predicting human behavior, because people can change their minds or figure out how to manipulate the theory to their advantage. As theorists, we must not sacrifice reality for elegance (Derman 2011), nor must we be misled by mathematical errors or worse meaningless gibberish disguised as mathematics to provide undeserved credibility such as much of the work of Jacques Lacan and Julia Kristeva (Sokal and Brimont 1998).