This paper briefly demonstrates a few of the possibilities of a systematic application of robustness theory, concentrating on the estimation of ability when the true item response model does and does not fit the data. The definition of the maximum likelihood estimator (MLE) of ability is briefly reviewed. After introducing the notion of outlier-pair observation, the effect of the model's lack of fit to the data is demonstrated. Then, a new estimator not as influenced as the MLE by outlier pairs is introduced. Based on the motivation for the new estimator, an entire class of new estimators is provided as a vehicle for understanding two notions of robustness theory: (1) the influence function, which compactly yields the majority of the behavioral results about an estimator; and (2) asymptotic relative efficiency (ARE), a concept in classical statistics and used in item response theory (IRT). Although the notion of ARE has had limited application in IRT, it is a useful alternative to expensive monte carlo simulations of the efficiencies of estimators. One of the drawbacks to determining the ARE of an estimator is the analytic derivation of the asymptotic; however, an expansion using the influence function easily yields the needed asymptotic variances. (PN)