TL;DR
This paper investigates the concept of top monotonicity in preference domains, providing a characterization, extending it to partial orders, and proving that testing it is NP-complete.
Contribution
It offers a new characterization of top monotonicity via non-betweenness constraints and proves the computational complexity for partial orders.
Findings
Characterization of top monotonicity using non-betweenness constraints
Extension of top monotonicity to partial orders
NP-completeness of testing top monotonicity in partial orders
Abstract
Top monotonicity is a relaxation of various well-known domain restrictions such as single-peaked and single-crossing for which negative impossibility results are circumvented and for which the median-voter theorem still holds. We examine the problem of testing top monotonicity and present a characterization of top monotonicity with respect to non-betweenness constraints. We then extend the definition of top monotonicity to partial orders and show that testing top monotonicity of partial orders is NP-complete.
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Game Theory and Voting Systems · Advanced Graph Theory Research