2,112 research outputs found
An impossibility theorem for paired comparisons
In several decision-making problems, alternatives should be ranked on the
basis of paired comparisons between them. We present an axiomatic approach for
the universal ranking problem with arbitrary preference intensities, incomplete
and multiple comparisons. In particular, two basic properties -- independence
of irrelevant matches and self-consistency -- are considered. It is revealed
that there exists no ranking method satisfying both requirements at the same
time. The impossibility result holds under various restrictions on the set of
ranking problems, however, it does not emerge in the case of round-robin
tournaments. An interesting and more general possibility result is obtained by
restricting the domain of independence of irrelevant matches through the
concept of macrovertex.Comment: 18 pages, 4 figure
On the additivity of preference aggregation methods
The paper reviews some axioms of additivity concerning ranking methods used
for generalized tournaments with possible missing values and multiple
comparisons. It is shown that one of the most natural properties, called
consistency, has strong links to independence of irrelevant comparisons, an
axiom judged unfavourable when players have different opponents. Therefore some
directions of weakening consistency are suggested, and several ranking methods,
the score, generalized row sum and least squares as well as fair bets and its
two variants (one of them entirely new) are analysed whether they satisfy the
properties discussed. It turns out that least squares and generalized row sum
with an appropriate parameter choice preserve the relative ranking of two
objects if the ranking problems added have the same comparison structure.Comment: 24 pages, 9 figure
Feasibility Constraints and Protective Behavior in Efficient Kidney Exchange
We propose a model of Kidney-Exchange that incorporates the main European institutional features. We assume that patients do not consider all compatible kidneys homogeneous and patients are endowed with reservation values over the minimal quality of the kidney they may receive. Under feasibility constraints, patients' truthful revelation of reservation values is incompatible with constrained efficiency. In the light of this result, we introduce an alternative behavioral assumption on patients' incentives. Patients choose their revelation strategies as to “protect” themselves from bad outcomes and use a lexicographic refinement of maximin strategies. In this environment, if exchanges are pairwise, then priority rules or rules that maximize a fixed ordering provide incentives for the patients to report their true reservation values. The positive result vanishes if larger exchanges are admitted.Kidney, Matching, Protective Behavior
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