Advancing Strategic Decision Science Since 2014
How can we divide a set of goods, burdens, or rights among several people in a way that is perceived as fair? How can we aggregate individual preferences into a collective decision that respects certain democratic principles? These are the central questions of fair division and social choice theory, two deeply interrelated fields where the Nevada Institute of Game Theory has made significant contributions. This research is deeply mathematical but profoundly ethical, seeking to turn abstract principles of justice and democracy into concrete, implementable procedures. The work ranges from the whimsical-sounding 'cake-cutting problem' to the deadly serious design of electoral systems and the allocation of scarce medical resources.
Fair division theory provides algorithms for dividing a heterogeneous good (like a cake with different toppings, or an estate with various assets) among n players so that each player believes they received at least 1/n of the total value (a property called proportionality) or, even stronger, so that no player envies another's share (envy-freeness). NIGT researchers have improved upon classic protocols like the Dubins-Spanier moving-knife procedure and the Selfridge-Conway discrete procedure for envy-free division. More urgently, they apply these principles to real-world problems: allocating computational resources in the cloud, dividing airport landing slots among airlines, and assigning public housing units. A particularly critical application is in organ transplantation. Game-theoretic matching algorithms, building on the work of Alvin Roth and Lloyd Shapley (Nobel laureates who have both visited NIGT), are used to run kidney paired donation programs, creating chains and cycles of donors and recipients to save more lives. This is fair division in its most literal and impactful form.
Social choice theory, dating to Condorcet and Borda in the 18th century and revolutionized by Arrow's Impossibility Theorem in the 20th, studies the aggregation of individual preferences into a social preference or choice. NIGT scholars investigate the properties of different voting rules (plurality, Borda count, instant-runoff voting, approval voting) and the trade-offs they entail between criteria like Condorcet consistency, independence of irrelevant alternatives, and resistance to strategic manipulation. They analyze the likelihood of voting paradoxes, like the Condorcet paradox (cyclic majorities), under various models of voter preferences. This research provides an objective, analytical basis for debates on electoral reform, helping to move the discussion beyond partisan advantage to the intrinsic properties of different democratic decision rules.
Beyond ranking candidates, groups often need to aggregate judgments on a set of logically interconnected propositions (e.g., a jury deciding on facts in a trial). This is the domain of judgment aggregation. NIGT research has highlighted 'discursive dilemmas' where majority voting on individual premises can lead to inconsistent collective judgments. They explore alternative aggregation rules, such as premise-based or conclusion-based procedures, and study their strategic properties. This work has implications for the design of deliberative bodies, corporate boards, and any group that must make coherent collective decisions based on multiple criteria or pieces of evidence.
In the modern era, many allocation and ranking decisions are made by algorithms—from credit scoring to college admissions to content recommendation. NIGT researchers are deeply engaged in the intersection of social choice, fair division, and computer science, known as algorithmic fairness or computational social choice. They examine how to define fairness mathematically (e.g., demographic parity, equalized odds) and how to design algorithms that satisfy these definitions while maintaining accuracy and efficiency. They also study the strategic implications: if an algorithm is designed to be fair according to a certain metric, how might individuals or groups game the system? By bringing the rigorous, axiomatic approach of social choice to bear on these pressing issues, the Nevada Institute helps ensure that the algorithms shaping our lives are not only powerful but also just and transparent, embodying our collective values in their design.