Characterizations of the classes of all choice functions that select the cores or the externally stable cores induced by an underlying revealed dominance digraph are provided. Relying on such characterizations, the basic order-theoretic structure of the corresponding sets of revealed cores is also analyzed. In particular, it is shown that the poset of all revealed cores ordered by set inclusion is a median meet semilattice: therefore, any profile of revealed cores may be aggregated by means of the simple majority rule.
Vannucci, S. (2015). Revealed cores: characterizations and structure. APPLIED MATHEMATICS, 6(13), 2279-2291 [dx.doi.org/10.4236/am.2015.614200].
Revealed cores: characterizations and structure
VANNUCCI, STEFANO
2015-01-01
Abstract
Characterizations of the classes of all choice functions that select the cores or the externally stable cores induced by an underlying revealed dominance digraph are provided. Relying on such characterizations, the basic order-theoretic structure of the corresponding sets of revealed cores is also analyzed. In particular, it is shown that the poset of all revealed cores ordered by set inclusion is a median meet semilattice: therefore, any profile of revealed cores may be aggregated by means of the simple majority rule.
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https://hdl.handle.net/11365/983722