MO | R Documentation |

This function returns the awards vector assigned by the minimal overlap rule rule (MO) to a claims problem.

MO(E, d, name = FALSE)

`E` |
The endowment. |

`d` |
The vector of claims. |

`name` |
A logical value. |

Let *E≥ 0* be the endowment to be divided and *d* the vector of claims
with *d≥ 0* and such that the sum of claims exceeds the endowment.

The truncated claim of a claimant *i* is the minimum of the claim and the endowment:

*ti=min{di,E}, i=1,…,n*

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 *d0=0*. The minimal overlap rule is defined, for each problem *(E,d)* and each claimant *i*, as:

If *E≤ d_n* then

*
MOi(E,d) = t1/n + (t2-t1)/(n-1) + … + (ti-t(i-1))/(n-i+1).*

If *E>d_n* let *dk<s ≤ d(k+1)*, with *0≤ k ≤ n-2*,
be the unique solution to the equation *max{d1-s,0}+…+max{dn-s,0}=E-s*. Then:

*
MOi(E,d) = d1/n + (d2-d1)/(n-1) + … + (di-d(i-1))/(n-i+1), if i≤ k*

*MOi(E,d) = MOi(s,d)+di-s, if i>k+1.*

The awards vector selected by the MO rule. If name = TRUE, the name of the function (MO) as a character string.

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.

allrules, CD.

E=10 d=c(2,4,7,8) MO(E,d)

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