553 research outputs found
Consensus theories: an oriented survey
This article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly â but not exclusively â concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de MathĂ©matique Sociale (CAMS).Consensus theories ; Arrowian results ; aggregation rules ; metric consensus rules ; median ; tournament solutions ; restricted domains ; lower valuations ; median semilattice ; complexity
Behavioral implications of shortlisting procedures
We consider two-stage âshortlisting proceduresâ in which the menu of alternatives is first pruned by some process or criterion and then a binary relation is maximized. Given a particular first-stage process, our main result supplies a necessary and sufficient condition for choice data to be consistent with a procedure in the designated class. This result applies to any class of procedures with a certain lattice structure, including the cases of âconsideration filters,â âsatisficing with salience effects,â and ârational shortlist methods.â The theory avoids background assumptions made for mathematical convenience; in this and other respects following Richterâs classical analysis of preference-maximizing choice in the absence of shortlisting
Arrovian juntas
This article explicitly constructs and classifies all arrovian voting systems
on three or more alternatives. If we demand orderings to be complete, we have,
of course, Arrow's classical dictator theorem, and a closer look reveals the
classification of all such voting systems as dictatorial hierarchies. If we
leave the traditional realm of complete orderings, the picture changes. Here we
consider the more general setting where alternatives may be incomparable, that
is, we allow orderings that are reflexive and transitive but not necessarily
complete. Instead of a dictator we exhibit a junta whose internal hierarchy or
coalition structure can be surprisingly rich. We give an explicit description
of all such voting systems, generalizing and unifying various previous results.Comment: 22 pages, 1 figur
Beyond Language Equivalence on Visibly Pushdown Automata
We study (bi)simulation-like preorder/equivalence checking on the class of
visibly pushdown automata and its natural subclasses visibly BPA (Basic Process
Algebra) and visibly one-counter automata. We describe generic methods for
proving complexity upper and lower bounds for a number of studied preorders and
equivalences like simulation, completed simulation, ready simulation, 2-nested
simulation preorders/equivalences and bisimulation equivalence. Our main
results are that all the mentioned equivalences and preorders are
EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly
one-counter automata and P-complete on visibly BPA. Our PSPACE lower bound for
visibly one-counter automata improves also the previously known DP-hardness
results for ordinary one-counter automata and one-counter nets. Finally, we
study regularity checking problems for visibly pushdown automata and show that
they can be decided in polynomial time.Comment: Final version of paper, accepted by LMC
- âŠ