We present a graphical framework containing certain in nite pro les of probability distributions that result from an attack on an anonymity system. We represent currently popular anonymity metrics within our framework to show that existing metrics base their decisions on just some small piece of information contained in a distribution. This explains the counterintuitive, thus unsatisfactory, anonymity evaluation performed by any of these metrics for carefully constructed examples in literature. We then propose a new anonymity metric that takes entire pro les into consideration in arriving at the degree of anonymity associated with a probability distribution. The comprehensive approach of our metric results in correct measurement. A detailed comparison of our new metric, especially with the popular metrics based on Shannon entropy, gives the rationale and degree of disagreement between these approaches. vi