An apparent limitation of the conditional logit (CL) model is that it assumes that the error terms Xik are independent not only among voters but also among candidates. However, such independence – often referred to as independence of irrelevant alternatives – need not be the case. In a contest among two liberals and one conservative, for example, the two liberals are likely to compete against each other for unmeasured, nonpolicy evaluations (represented by the Xik terms), whereas their competition with the conservative may be more on ideological grounds, represented instead by the Vi (k) terms. As a result, if we specify the two liberals by the subscripts 1 and 2 and the conservative by the subscript 3, we may expect the perturbation terms Xi1 and Xi2 to be negatively correlated (because higher nonpolicy evaluations of one liberal are likely to come at the expense of the other). On the other hand, neither of these two terms may be significantly correlated with Xi3 (because relative evaluation of liberals versus conservatives is more likely to be based on policy). In particular, the ratio between the support of the two liberals is little affected by the presence of the conservative (or an additional liberal) in the race, whereas the ratio between the support of one of the liberals and the support of the conservative would be strongly affected by the entry of an additional candidate.

An alternative model that permits limited correlation structures of the type suggested here is the generalized extreme value (GEV) model.