Complexity of Deliberative Coalition Formation
Edith Elkind, Abheek Ghosh, Paul Goldberg

TL;DR
This paper analyzes the computational complexity of deliberative coalition formation models in metric spaces, revealing hardness results, potential exponential length of deliberation sequences, and bounds on compromise sizes.
Contribution
It proves the difficulty of finding highly supported proposals, computes the potential exponential length of deliberation sequences, and strengthens bounds on compromise sizes in hypercube models.
Findings
Finding high-support proposals is computationally hard.
Sequences of 2-compromise transitions can be exponentially long.
Lower bounds on compromise size in hypercube models are significantly increased.
Abstract
Elkind et al. (AAAI, 2021) introduced a model for deliberative coalition formation, where a community wishes to identify a strongly supported proposal from a space of alternatives, in order to change the status quo. In their model, agents and proposals are points in a metric space, agents' preferences are determined by distances, and agents deliberate by dynamically forming coalitions around proposals that they prefer over the status quo. The deliberation process operates via k-compromise transitions, where agents from k (current) coalitions come together to form a larger coalition in order to support a (perhaps new) proposal, possibly leaving behind some of the dissenting agents from their old coalitions. A deliberation succeeds if it terminates by identifying a proposal with the largest possible support. For deliberation in d dimensions, Elkind et al. consider two variants of their…
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Taxonomy
TopicsGame Theory and Voting Systems · Privacy-Preserving Technologies in Data · Game Theory and Applications
