As the combined results of Tables 1 and 2 suggest, our theory successfully predicted the outcomes of the fourteen effects studied. These results support our theory and its implementation. These studies showed that individuals tend to exhibit framing effects when decision options encode different gists (prediction 1), as in the standard, as opposed to non-zero-truncated, DP, and the first decision of the Allais Paradox. Furthermore these choices are based on valenced affect (prediction 2) – i.e., some money is better than no money; some lives saved is better than no lives saved, but some die is worse than none die, etc. When categorical contrasts are not possible, decisionmakers will revert to more precise representations (prediction 3). Thus, we see indifference in the zero-complement-truncated DP, and maximization of expected utility in the second gamble of the Allais paradox because both options have the gist of “some money with some chance, or no money with some chance.” Finally, gist categories are encoded based upon interpretations which, when changed, can change subjects' behaviors (prediction 4). Thus, adding the word “all” to the standard DP attenuates the framing effect because a decision-maker must choose between an option that advertises “some saved with some chance” and an option that advertises “none saved with some chance OR all saved with some chance.” To our knowledge, no rival theories are able to explain these several different effects within one unified framework. Furthermore, our approach is the only one to explain the circumstances under which subjects will use qualitative and categorical (i.e., discrete) representations of numbers, rather than continuous and quantitative representations. Critics might take issue with our notion of constraints, because it is in principle possible to find some constraint that will yield results consistent with data after the fact. Our reaction to this claim is that we only use constraints that are grounded in empirically validated patterns – i.e., some-none or all-some distinctions. For these, our model predicts an attenuated framing effect, and the data from several studies bears out this prediction. The effects explained by our model are therefore robust and novel, lending support to our hypothesis that risky decisions are made upon information that is encoded simultaneously at multiple levels of abstraction, and that resulting categories are culturally contingent.

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