Abstract
We define and axiomatically characterize a new proportional influence measure for sequential projects with imperfect reliability. We consider a model in which a finite set of players aims to complete a project, consisting of a finite number of tasks, which can only be carried out by certain specific players. Moreover, we assume the players to be imperfectly reliable, i.e., players are not guaranteed to carry out a task successfully. To determine which players are most important for the completion of a project, we use a proportional influence measure. This paper provides two characterizations of this influence measure. The most prominent property in the first characterization is task decomposability. This property describes the relationship between the influence measure of a project and the measures of influence one would obtain if one divides the tasks of the project over multiple independent smaller projects. Invariance under replacement is the most prominent property of the second characterization. If in a certain task group a specific player is replaced by a new player who was not in the original player set, this property states that this should have no effect on the allocated measure of influence of any other original player.
Highlights
We define and axiomatically characterize a new proportional influence measure for projects with imperfect reliability. These characterizations are still valid when restricting to projects with perfect reliability
We assume that the tasks of a project can be carried out sequentially, and that all players in a task group can attempt to carry out this task
We assume that a success probability is fixed for each player-task combination, independent of, e.g., the realized success of other players within the same task group, or which players carry out the other tasks
Summary
The question at hand is which players are most influential for the completion of a project To this aim, we define and axiomatically characterize a new proportional influence measure based on the task structure of a project. Our paper serves as a starting point of quantitative research on the relative influence of imperfectly reliable players on the completion of a project, based on the task structure of this project. For each task players can carry out, the increase in value of their influence measure corresponds to their relative success probability within the task group. We axiomatically characterize our proportional influence measure by proving it is the only allocation mechanism for sequential projects with imperfect reliability that satisfies two sets of logically independent properties.
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