decision support developers

Abstract: The tournament equilibrium set (TEQ), proposed by Schwartz in 1990, is a classical voting rule based on pairwise majority comparisons. Its definition is recursive: an alternative is judged by the alternatives that beat it, called its dominators, and by which of those dominators TEQ itself selects. Deciding whether a given alternative belongs to TEQ was known to be NP-hard and to lie in PSPACE. We close this gap by proving that the problem is PSPACE-complete. To our knowledge, this is the first PSPACE-completeness result for membership in a tournament solution. The hardness persists even when every nonempty subtournament has a unique minimal retentive set, the property conjectured by Schwartz to hold for all tournaments. Moreover, every such subtournament in our hard instances contains an alternative with at most three dominators. We prove that a single alternative with at most four dominators suffices both to guarantee uniqueness and to find a TEQ winner in $O(N^2)$ time. Thus, on our hard instances, finding one winner is efficient even though recognizing a specified winner is PSPACE-complete. We also study how the complexity changes with the dominator bound. If every nonempty subtournament has an alternative with at most one dominator, the entire TEQ can be computed in quadratic time; allowing two dominators makes membership NP-hard. Under the same condition with four dominators, all $t$ winners can be computed in $O(2^t N^2)$ time, where $N$ is the number of alternatives.

Abstract: Humans increasingly use generative AI (GenAI) for decision-making assistance, yet tend to engage in such situations using quick, intuitive (System 1) rather than deliberate, analytical assessment (System 2) as reflected in Dual Process Theory. Such engagement reduces the effectiveness of human-GenAI interactions and increases associated risks. Our research investigates how to design human-GenAI interactions that promote the transition from System 1 to System 2 thinking in decision-making. Based on the Three-Stage-Model, which suggests humans switch to System 2 when conflicts are detected, we conducted an experiment (n=130) testing sequential human-GenAI interaction as a cognitive forcing nudge during problem-solving tasks. This approach, where humans decide first before receiving AI assistance, enables detection of conflicting decisions. Compared to non-sequential settings (concurrent or no AI assistance), results show the sequential condition significantly enhanced both decision performance and GenAI prompt utilization, providing valuable insights for designing more reflective and thus effective human-GenAI interactions.