In this paper, we are interested in computing preferred abductive explanations for decision trees and random forests. We present two preference models and for each of them, we describe and evaluate an algorithm for computing preferred majoritary reasons, where majoritary reasons are specific abductive explanations, suited to random forests, and which coincide with sufficient reasons in the case of decision trees. We experimentally show the feasibility of the approach. We also show that in practice the preferred majoritary reasons for an instance can be much less numerous than its majoritary reasons.