Tests for independence in contingency tables with ordered categories

Consider an r - c contingency table under the full multinomial model where each category is ordered. The problem is to test the null hypothesis of independence against the alternative that all local log odds ratios are nonnegative with a least one local log odds ratio positive. We find the class of all tests that are simultaneously exact, unbiased, and admissible. The problem is of considerable interest to social scientists. Some discussion of specific tests is given.