Pohl reported that 89% of inferences accorded with the model in judgments of population, compared to only 54% in judgments of the distance. More generally, there is a positive correlation of r = 0.64 between the recognition validity and the proportion of judgments consistent with the recognition heuristic across 11 studies. Another study by Pachur suggested that the recognition heuristic is more likely a tool for exploring natural rather than induced recognition (i.e. not provoked in a laboratory setting) when inferences have to be made from memory. In one of his experiments, the results showed that there was a difference between participants in an experimental setting vs. a non-experimental setting. If α > β, and α, β are independent of n, then a less-is-more effect will be observed. Here, β is the knowledge validity, measured as C/(C+W) for all pairs in which both alternatives are recognized, and n is the number of alternatives an individual recognizes. A less-is-more effect means that the function between accuracy and n is inversely U-shaped rather than monotonically increasing. Some studies reported less-is-more effects empirically among two, three, or four alternatives and in group decisions), whereas others failed to do so, possibly because the effect is predicted to be small (see Katsikopoulos). Smithson explored the "less-is-more effect" (LIME) with the recognition heuristic and challenges some of the original assumptions. The LIME occurs when a "recognition-dependent agent has a greater probability of choosing the better item than a more knowledgeable agent who recognizes more items." A mathematical model is used in describing the LIME and Smithson’s study used it and attempted to modify it. The study was meant to mathematically provide an understanding of when the LIME occurs and explain the implications of the results. The main implication is "that the advantage of the recognition cue depends not only on the cue validities, but also on the order in which items are learned". The recognition heuristic can also be depicted using neuroimaging techniques. A number of studies have shown that people do not automatically use the recognition heuristic when it can be applied, but evaluate its ecological validity. It is less clear, however, how this evaluation process can be modeled. A functional magnetic resonance imaging study tested whether the two processes, recognition and evaluation, can be separated on a neural basis. Participants were given two tasks; the first involved only a recognition judgment ("Have you ever heard of Modena?