Score contribution per author:
α: calibrated so average coauthorship-adjusted count equals average raw count
In school choice problems, a list of restrictions have been imposed on priorities to achieve desirable properties of rules. However, it is difficult to verify these “acyclicity” conditions and identify the structure of the restricted priority profiles. To improve visibility and verifiability, we provide characterizations of these conditions. We also present the logical relations among the conditions by using our characterizations.