problemdata: Claims problem data

In ClaimsProblems: Analysis of Conflicting Claims

Claims problem data

Description

The function returns which of the following subdomains the claims problem belongs to: the lower-half, higher-half, and midpoint domains. In addittion, the function returns the minimal rights vector, the truncated claims vector, the sum and the half-sum of claims.

Usage

problemdata(E, d, draw = FALSE)

Arguments

E	The endowment.
d	The vector of claims.
draw	A logical value.

Details

Let N=\{1,\ldots,n\} be the set of claimants, E\ge 0 the endowment to be divided and d\in \mathbb{R}_+^N the vector of claims such that D=\sum_{i \in N} d_i\ge E.

The lower-half domain is the subdomain of claims problems for which the endowment is less or equal than the half-sum of claims, E \le D/2.

The higher-half domain is the subdomain of claims problems for which the endowment is greater or equal than the half-sum of claims, E \ge D/2.

The midpoint domain is the subdomain of claims problems for which the endowment is equal to the half-sum of claims, E = D/2.

The minimal right of claimant i\in N in (E,d) is whatever is left after every other claimant has received his claim, or 0 if that is not possible:

m_i(E,d)=\max\{0,E-d(N\backslash\{i\})\}.

Let m(E,d)=\Bigl(m_1(E,d),\dots,m_n(E,d)\Bigr) be the vector of minimal rights.

The truncated claim of claimant i\in N in (E,d) is the minimum of the claim and the endowment:

t_i(E,d)=\min\{d_i,E\}.

Let t(E,d)=\Bigl(t_1(E,d),\dots,t_n(E,d)\Bigr) be the vector of truncated claims.

Value

The minimal rights vector; the truncated claims vector; the sum, the half-sum of the claims, and the class (lower-half, higher-half, and midpoint domains) to which the claims problem belongs. It returns cod = 1 if the claims problem belong to the lower-half domain, cod = -1 if it belongs to the higher-half domain, and cod = 0 for the midpoint domain. Moreover, if draw = TRUE a plot of the claims, from small to large in the interval [0,D], is given.

See Also

allrules, setofawards.

Examples

E=10
d=c(2,4,7,8)
problemdata(E,d,draw=TRUE)

ClaimsProblems documentation built on April 4, 2025, 2:21 a.m.