arXiv subjects

Pierre Nunn

Publications and source records attributed to Pierre Nunn.

4 recordsLinked to original sources

arXiv2026

Non-obvious Manipulability with Groups in Shapley-Scarf Housing Markets

In Shapley-Scarf housing markets, Ma (1994) shows that top trading cycles (TTC) is the unique mechanism satisfying individual rationality (IR), Pareto efficiency (PE), and strategy-proofness. We ask what other mechanisms become possible when strategy-proofness is replaced by a weaker condition called non-obvious manipulability (NOM), introduced by Troyan and Morrill (2020). We first show that this weaker condition does not help on its own: every IR and PE mechanism is already NOM. We therefore introduce a new condition: NOM with groups, under which each agent knows the preferences of the other members of her group, but not those of agents outside the group. This condition reduces to strategy-proofness when all agents belong to one group, and to standard NOM when every group is a singleton. Also, we introduce a participation condition called group rationality (GR), which requires that no group do worse than it would by trading only among its own members. We then define a class of mechanisms called TTC with super-groups, whose members satisfy GR, PE, and NOM with groups. The class includes mechanisms that differ from standard TTC, including mechanisms that are not strategy-proof. Furthermore, we show that every mechanism that satisfies GR, PE, and NOM with groups has the same best- and worst-case outcomes as every TTC with super-groups mechanism.

cs.GT↗

arXiv2026

Distances Between Top-Truncated Elections of Different Sizes

The map of elections framework is a methodology for visualizing and analyzing election datasets. So far, the framework was restricted to elections that have equal numbers of candidates, equal numbers of voters, and where all the (ordinal) votes rank all the candidates. We extend it to the case of elections of different sizes, where the votes can be top-truncated. We use our results to present a visualization of a large fragment of the Preflib database.

cs.GT↗

arXiv2024

A Logic for Reasoning About Aggregate-Combine Graph Neural Networks

We propose a modal logic in which counting modalities appear in linear inequalities. We show that each formula can be transformed into an equivalent graph neural network (GNN). We also show that a broad class of GNNs can be transformed efficiently into a formula, thus significantly improving upon the literature about the logical expressiveness of GNNs. We also show that the satisfiability problem is PSPACE-complete. These results bring together the promise of using standard logical methods for reasoning about GNNs and their properties, particularly in applications such as GNN querying, equivalence checking, etc. We prove that such natural problems can be solved in polynomial space.

cs.AI↗

arXiv2023

A Modal Logic for Explaining some Graph Neural Networks

In this paper, we propose a modal logic in which counting modalities appear in linear inequalities. We show that each formula can be transformed into an equivalent graph neural network (GNN). We also show that each GNN can be transformed into a formula. We show that the satisfiability problem is decidable. We also discuss some variants that are in PSPACE.

cs.AI↗