Modeled rank order tests have become a powerful tool to infer discrimination through observational outcome data such as police search success rates or errors in court decisions. The tests predict that outcomes that are born out of prejudice by decisionmakers will violate certain rank order patterns among the treated groups. This paper presents an unnoticed issue in these tests. I advance a rank order model that includes strategic behavior of the treated with respect to the decisionmakers' beliefs about them. This feedback mechanism can give rise to multiple equilibria, which can invalidate the use of the test.