In this paper we present some results for preference aggregation functionals defined on rich admissible sets. Our results are concerned with an Independence of Irrelevant Alternatives assumption due to Alan D. Taylor suitably adjusted to be applicable in the framework of preference aggregation functionals. The initial step towards this adjustment is a version of Taylor’s property due to Prasanta Pattanaik. We obtain several results which all point to its non-compatibility with a combination of other well-known assumptions that are often invoked in the literature concerning aggregation of preferences. A novel feature of our analysis is the mild requirement on the admissible set of utility profiles on which the preference aggregation functionals are defined for several of our results.