We describe a prediction method called "Attractivity Weighting" (AW). In the case of cue-based paired comparison tasks, AW's prediction is based on a weighted average of the cue values of the most successful cues. In many situations, AW's prediction is based on the cue value of the most successful cue, resulting in behavior similar to Take-the-Best (TTB). Unlike TTB, AW has a desirable characteristic called "access optimality": Its long-run success is guaranteed to be at least as great as the most successful cue. While access optimality is a desirable characteristic, concerns may be raised about the short-term performance of AW. To evaluate such concerns, we here present a study of AW's short-term performance. The results suggest that there is little reason to worry about the short-run performance of AW. Our study also shows that, in random sequences of paired comparison tasks, the behavior of AW and TTB is nearly indiscernible.