We introduce the exclusion–inclusion gap for evaluating finite Pareto approximations constructed from stochastic objective estimates. The gap measures the maximum of two objective-space errors associated with excluding Pareto points from the returned set’s true upper image and including dominated points in the returned set’s true lower image. The terms in its approximation–estimation error decomposition admit general bounds that allow deterministic approximation guarantees to be combined with componentwise stochastic-error control. The gap’s inclusion component is invariant to the return of dominated but weakly nondominated points, enabling performance analysis without positive separation assumptions. Under consistent estimation on a fixed evaluated set, the apparent advantages of such points vanish asymptotically. The results hold across continuous, integer, and mixed-integer settings. We apply the results by performing an approximation–estimation error analysis of a nonadaptive, equal-allocation algorithm for global multiobjective simulation optimization with continuous objective functions and a compact feasible set. The analysis yields finite-sample probabilistic error bounds, budget-allocation rules, sample-complexity results, and convergence rates. Under the infinity norm, we identify conditions under which the sufficient simulation budget grows logarithmically in the number of objectives. For a fixed problem instance, we show that the exclusion–inclusion gap converges at the same total-budget rate as the corresponding single-objective optimality gap, despite accounting for both exclusion and inclusion errors.