MO {ClaimsProblems} | R Documentation |
Minimal overlap rule
Description
This function returns the awards vector assigned by the minimal overlap rule rule (MO) to a claims problem.
Usage
MO(E, d, name = FALSE)
Arguments
E |
The endowment. |
d |
The vector of claims. |
name |
A logical value. |
Details
Let be the endowment to be divided and
the vector of claims
with
and such that
the sum of claims exceeds the endowment.
The truncated claim of a claimant is the minimum of the claim and the endowment:
Suppose that each agent claims specific parts of E equal to her/his claim. After arranging which parts agents claim so as to “minimize conflict”, equal division prevails among all agents claiming a specific part and each agent receives the sum of the compensations she/he gets from the various parts that he claimed.
Let . The minimal overlap rule is defined, for each problem
and each claimant
, as:
If then
If let
, with
,
be the unique solution to the equation
. Then:
Value
The awards vector selected by the MO rule. If name = TRUE, the name of the function (MO) as a character string.
References
Mirás Calvo, M.A., Núñez Lugilde, I., Quinteiro Sandomingo, C., and Sánchez-Rodríguez, E. (2021). The adjusted proportional and the minimal overlap rules restricted to the lower-half, higher-half, and middle domains. Working paper 2021-02, ECOBAS.
O'Neill, B. (1982). A problem of rights arbitration from the Talmud. Math. Social Sci. 2, 345-371.
Thomson, W. (2019). How to divide when there isn't enough. From Aristotle, the Talmud, and Maimonides to the axiomatics of resource allocation. Cambridge University Press.
See Also
Examples
E=10
d=c(2,4,7,8)
MO(E,d)