11-06-2017A set of N employees or workgroup, denoted UA = {u1, u2, . . . , uN }. ui can be thought of employee i’s name.
For each employee, ui, his or her longevity (i.e., years of service) with the firm, denoted yi.
An ordering, or seniority ranking of the employees names, denoted as a set of integer-name pairs of length N, SA = {(1,ui),...,(N,uj)}. Denote sAi as the seniority rank of worker ui, with sAi = 1 representing the most senior worker and sAi = N representing the most junior member.
For any set of real numbers X = {x1, . . . , xN }, we define Γ(xi|X) to be xi’s rank among 6 the elements of X in descending order (i.e., Γ(xi|X) = 1 for max{x1,...,xN} and Γ(xi|X) = N for min{x1, . . . , xN }).
Likewise, we define ψ(xi|X) to be xi’s rank among the elements of X in ascending order (i.e., ψ(xi|X) = 1 for min{x1, . . . , xN } and ψ(xi|X) = N for max{x1, . . . , xN }).
Definition 1 Consider firm A with a workgroup of N employees. A seniority list SA is said to be date-of-hire if sAi = Γ(yi|Y ),∀i = 1,2,...,N.
Thus, a “date-of-hire” seniority list simply ranks a members of a workgroup by their longevity, the most senior employee (i.e., seniority rank #1) being the one with the longest service to the firm.12 By construction, a resulting property of a date-of-hire seniority list is that sAi < sAj ⇐⇒ yi > yj , ∀i, j.
http://www.econ.umn.edu/~singe119/pa...ntegration.pdf
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