We propose an efficient algorithm for estimation of possibility based qualitative expected utility. It is useful for decision making mechanisms where each possible decision is assigned a multi-attribute possibility distribution. The computational complexity of ordinary methods calculating the expected utility based on discretization is growing exponentially with the number of attributes, and may become infeasible with a high number of these attributes. We present series of theorems and lemmas proving the correctness of our algorithm that exibits a linear computational complexity. Our algorithm has been applied in the context of selecting the most prospective partners in multi-party multi-attribute negotiation, and can also be used in making decisions about potential offers during the negotiation as other similar problems.