The paper begins by exploring the Path Independence Property. The possibility of a lower and upper approximation of a choice function satisfying Path Independence is dealt with in the paper. A significant property implied by Path Independence is Outcasting. We propose in the paper a unique characterisation of a choice function, called the batch choice function, which satisfies Outcasting. However, the relevant characterisation theorem requires a property stronger than Outcasting called the Choice Acyclicity Property. In an appendix to the paper, we provide a simple proof (without using Zorn's Lemma), of the fact that satisfaction of a property by a choice function is equivalent to the existence of a utility function, whose maximizers on a feasible set are always chosen. This result is originally due to Deb [1983]. This theorem is used in our paper to prove the existence of Path Independent lower approximations.