On the maximum-likelihood estimator for the location parameter of a cauchy distribution

In the literature of point estimation, the Cauchy distribution with location parameter is often cited as an example for the failure of maximum-likelihood method and hence the failure of the likelihood principle in general. Contrary to the above notion, we prove that even in this case the likelihood equation has multiple roots and that the maximum-likelihood estimator (the global maximum) remains as an asymptotically optimal estimator in the Bahadur sense.