Knowledge of transitive relationships between items can contribute to learning the order of a set of stimuli from pairwise comparisons. However, cognitive mechanisms of transitive inferences based on rank order remain unclear, as are relative contributions of reward associations and rule-based inference. To explore these issues, we created a conflict between rule- and reward-based learning during a serial ordering task. Rhesus macaques learned two lists, each containing five stimuli that were trained exclusively with adjacent pairs. Selection of the higher-ranked item resulted in rewards. “Small reward” lists yielded two drops of fluid reward, whereas “large reward” lists yielded five drops. Following training of adjacent pairs, monkeys were tested on novels pairs. One item was selected from each list, such that a ranking rule could conflict with preferences for large rewards. Differences between the corresponding reward magnitudes had a strong influence on accuracy, but we also observed a symbolic distance effect. That provided evidence of a rule-based influence on decisions. RT comparisons suggested a conflict between rule- and reward-based processes. We conclude that performance reflects the contributions of two strategies and that a model-based strategy is employed in the face of a strong countervailing reward incentive.