Imagine taking a math class with no exams all semester. It sounds impossible, yet it exists at CA in the course Game Theory: A Mathematical Study of Politics, taught by Shawn Bartok. This interdisciplinary class explores social and political structures through a mathematical lens. While students quantify concepts like democracy, fairness, and power, the core of the class emphasizes reading, writing, and critical thinking rather than computation. Lessons extend into the real world, reflecting on historical moments like the Yom Kippur War—exploring strategies the United States and the Soviet Union might have pursued—and examining contemporary issues such as the uneven distribution of influence in the United Nations Security Council, where some nations hold veto power and others do not.
In unit one, students explore voting systems, specifically ranked-choice voting, and methods for determining a social choice, or winner, from ballots. For instance, the Condorcet method identifies a candidate who would beat every other candidate in head-to-head matchups, while the Hare system, or instant-runoff voting, eliminates the candidate with the fewest first-choice votes in successive rounds until one reaches a majority. Students evaluate these methods using criteria such as the Pareto condition—which requires that if every voter prefers one candidate over another, the system should reflect that—and monotonicity, meaning ranking a candidate higher should not hurt their chances. A key takeaway is that no system satisfies all criteria, so there is no singular ideal method for ranked-choice elections. These concepts are applied to real-world cases such as the 2000 U.S. presidential election with Bush, Gore, and Nader, demonstrating how different methods can yield disparate outcomes.
Unit two introduces yes-no voting, commonly used when legislators vote “yea” or “nay” on a bill or amendment, and weighted voting systems, where certain countries or politicians hold more influence than others. Examples include the European Economic Community, where France has four votes, the Netherlands two, and Luxembourg one, as well as the United Nations Security Council where veto power gives certain nations disproportionate sway.
Expanding on the second unit, unit three uses probability and combinatorics to quantify the effective power of each player in weighted systems. Instead of just counting votes, students calculate the percentage of influence a country or individual wields. For example, in the European Economic Community, France holds significantly more operative power than the Netherlands. This unit also divulges paradoxes. Although Luxembourg has one vote, it holds no real power as its vote cannot change a losing coalition into a winning one. Compared to other units, this one is more math-intensive as it assumes prior knowledge of probability and statistics.
Unit four introduces conflict and strategic decision-making via simplified two-by-two games. The Cuban Missile Crisis of 1962 illustrates this: the U.S. could blockade or airstrike, while the Soviet Union could withdraw or maintain missiles. By analyzing outcomes, such as the U.S. airstriking while the Soviets withdraw (most favorable for the U.S.) or the U.S. blockading while the Soviets maintain missiles (most favorable for the Soviets), students determine each player’s dominant strategy. While full analyses involve more complex diagrams and payoffs, this example captures the essence of strategic interaction and the interdependence of choices.
Finally, unit Five examines fairness through apportionment and fair division, geared towards equitable allocation of goods or resources. These methods also apply to intangible disputes—for instance, two political parties negotiating debate rules. One case study is the Electoral College, where the fixed size of the House of Representatives complicates perfectly proportional representation between the states, especially with fractional allocations. Historical approaches like Hamilton’s and Jefferson’s methods of apportionment are analyzed. Everyday examples include dividing a cake via the divide-and-choose method or splitting assets in divorce using the adjusted winner method, demonstrating fairness in a variety of contexts.
Game Theory explores intricate and theoretical connections between math, politics, and social systems. While the material is not overly difficult compared to other math courses, success relies on strong reading comprehension and the ability to write clearly and concisely rather than knowing how to do routine calculations. Students less passionate about math but keen on humanities and civic matters should definitely consider enrolling in this course!