# The Mathematics of Politics

## E. Arthur Robinson, Daniel H. Ullman

# The Mathematics of Politics

## E. Arthur Robinson, Daniel H. Ullman

## About This Book

It is because mathematics is often misunderstood, it is commonly

believed it has nothing to say about politics. The high school

experience with mathematics, for so many the lasting impression

of the subject, suggests that mathematics is the study of numbers,

operations, formulas, and manipulations of symbols. Those

believing this is the extent of mathematics might conclude

mathematics has no relevance to politics. This book counters this impression.

The second edition of this popular book focuses on mathematical reasoning

about politics. In the search for ideal ways to make certain kinds

of decisions, a lot of wasted effort can be averted if mathematics can determine that

finding such an ideal is actually impossible in the first place.

In the first three parts of this book, we address the following three

political questions:

(1) Is there a good way to choose winners of elections?

(2) Is there a good way to apportion congressional seats?

(3) Is there a good way to make decisions in situations of conflict and

uncertainty?

In the fourth and final part of this book, we examine the Electoral

College system that is used in the United States to select a president.

There we bring together ideas that are introduced in each of the three

earlier parts of the book.

## Information

**Part III**

Conflict

Conflict

**Introduction to Part III**

**Introduction to Part III**

*how*does a person make decisions? Sometimes, when presented with a decision problem, one can determine precisely what choices exist, ascertain what the outcome of every choice is, and evaluate these choices on a linear scale (by, for example, measuring the dollar value of each outcome). In such cases, decision-making is easy. One simply opts for the choice that maximizes benefit. But in the real world, decision-making is more difficult, because one faces uncertainty that may be of two types. The first type is uncertainty about nature. Nature may be thought of as random and unconcerned with our welfare. For example, to decide whether to carry an umbrella, we should factor in the probability of rain. The second type is uncertainty about people. A person, unlike nature, may be our friend or our adversary, and a person may have a stake in the decision process that is unrelated to ours. We assume that other people do not act randomly but rather act in their own self-interest. In other words, they act like we do. For example, to decide how to negotiate a treaty, we need to contemplate the point of view of other signatories.

**13**

*Strategies and Outcomes*

**13.0 Scenario**

**Game 13.1**A simple matrix game.

**13.1 Zero-Sum Games**

**two-person zero-sum game**. We start by looking at a familiar example: a children’s game called Roshambo. Lest the reader feel that game theory is not serious, however, we also consider a game that models a naval battle from World War II.

**Roshambo**, known more familiarly in the United States as Rock-Paper-Scissors, is played by children throughout the world. Recently, Roshambo has also become a popular tournament game in bars. To play Roshambo, two players face each other, and, on the count of three, each makes a finger gesture representing Rock, Paper, or Scissors. The gesture for Rock is a closed fist, the gesture for Paper is an open palm, and the gesture for Scissors is two fingers. Certain gestures defeat others: Rock beats Scissors (i.e., rock dulls scissors), Scissors beats Paper (scissors cut paper), and Paper beats Rock (paper covers rock). If both players make the same gesture, then the outcome is considered to be a tie.

**strategies**. We generally call the two players Row and Column. For the purpose of choosing appropriate pronouns, we often imagine that Row is female and Column is male. In Roshambo, each player has three strategies from which to choose: Rock, Paper, and Scissors. A single round of play involves the players choosing strategies, and then, at a prescribed moment, simultaneously revealing their strategy choices. A strategy choice by each player determines an

**outcome**of the game. For example, in Roshambo, if Row chooses Rock and Column chooses Paper, then the outcome is (Rock, Paper). Since Paper beat...

## Table of contents

*The Mathematics of Politics*(2nd ed.). CRC Press. Retrieved from https://www.perlego.com/book/2192918/the-mathematics-of-politics-pdf (Original work published 2016)

*The Mathematics of Politics*. 2nd ed. CRC Press. https://www.perlego.com/book/2192918/the-mathematics-of-politics-pdf.

*The Mathematics of Politics*. 2nd edn. CRC Press. Available at: https://www.perlego.com/book/2192918/the-mathematics-of-politics-pdf (Accessed: 15 October 2022).

*The Mathematics of Politics*. 2nd ed. CRC Press, 2016. Web. 15 Oct. 2022.