Deviation from proportionality and Lorenz-domination for claims problems

Calvo, Miguel Ángel Mirás; Lugilde, Iago Núñez; Sandomingo, Carmen Quinteiro; Sánchez-Rodríguez, E.

doi:10.1007/s10058-022-00300-y

Cited by 4 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To end, we conclude, directly from Figure 4, that

\text{PIN}\succcurlyeq \text{AA}\succcurlyeq \text{MO}

on the entire domain of claims problems. This result was already established by Mirás Calvo et al (2022a) using a different approach.…”

Section: Ranking Of Rulessupporting

confidence: 78%

“…As a corollary of all the different approaches, Bosmans and Lauwers (2011) and Thomson (2019) provide a diagram reflecting the ranking of nine of the central rules discussed in the literature on the full domain. Mirás Calvo et al (2022a) incorporate the average‐of‐awards rule to this ranking. Bosmans and Lauwers (2011) also present a diagram showing the ranking of the nine central rules on the restricted domains.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Refining the Lorenz‐ranking of rules for claims problems on restricted domains

Calvo

Lugilde

Sandomingo

et al. 2022

Int J of Economic Theory

Self Cite

View full text Add to dashboard Cite

The comparison of the central rules for claims problems, according to the Lorenz order, has been studied not only on the entire set of problems but also on some restricted domains. We provide new characterizations of the adjusted proportional rule as being Lorenz‐maximal or Lorenz‐minimal within a class of rules on the half‐domains. Using this result, we rank the adjusted proportional, the minimal overlap, and the average‐of‐awards rules by analyzing whether or not these rules satisfy progressivity and regressivity on the half‐domains. We also find that the adjusted proportional rule violates two well‐known claim monotonicity properties.

show abstract

“…To end, we conclude, directly from Figure 4, that

\text{PIN}\succcurlyeq \text{AA}\succcurlyeq \text{MO}

on the entire domain of claims problems. This result was already established by Mirás Calvo et al (2022a) using a different approach.…”

Section: Ranking Of Rulessupporting

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Refining the Lorenz‐ranking of rules for claims problems on restricted domains

Calvo

Lugilde

Sandomingo

et al. 2022

Int J of Economic Theory

Self Cite

View full text Add to dashboard Cite

show abstract

The average-of-awards rule for claims problems

2022

View full text Add to dashboard Cite

Given a claims problem, the average-of-awards rule ($${\text {AA}}$$ AA ) selects the expected value of the uniform distribution over the set of awards vectors. The $${\text {AA}}$$ AA rule is the center of gravity of the core of the coalitional game associated with a claims problem, so it corresponds to the core-center. We show that this rule satisfies a good number of properties so as to be included in the inventory of division rules. We also provide several representations of the $${\text {AA}}$$ AA rule and a procedure to compute it in terms of the parameters that define the problem.

show abstract

An algorithm to compute the average-of-awards rule for claims problems with an application to the allocation of CO$$_2$$ emissions

et al. 2023

View full text Add to dashboard Cite

The set of awards vectors for a claims problem coincides with the core of the associated coalitional game. We analyze the structure of this set by defining for each group of claimants a, so called, utopia game, whose core comprises the most advantageous imputations available for the group. We show that, given a claims problem, the imputation set of the associated coalitional game can be partitioned by the cores of the utopia games. A rule selects for each claims problem a unique allocation from the set of awards vectors. The average-of-awards rule associates to each claims problem the geometric center of the corresponding set of awards vectors. Based on the decomposition of the imputation set, we obtain an interpretation of the average-of-awards rule as a point of fairness between stable and utopia imputations and provide a backward recurrence algorithm to compute it. To illustrate our analysis, we present an application to the distribution of CO$$_2$$ 2 emissions.

show abstract

Deviation from proportionality and Lorenz-domination for claims problems

Cited by 4 publications

References 12 publications

Refining the Lorenz‐ranking of rules for claims problems on restricted domains

Refining the Lorenz‐ranking of rules for claims problems on restricted domains

The average-of-awards rule for claims problems

An algorithm to compute the average-of-awards rule for claims problems with an application to the allocation of CO$$_2$$ emissions

Contact Info

Product

Resources

About