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2.1 Categorical Routine

Once the decision-space has been established, the user enters the decision options describing the problem. For each axis in the space (i.e., each variable), the user enters the numerical data as it appears in the decision problem. An element of the problem may not be explicitly specified (for example, in the DP, where the probabilities in options A and C are not given, even though they are implicitly assumed to be 100%). In such cases the user leaves the field blank, and is subsequently prompted to enter the implicit value. The computer implementation of the theory uses an internal representation corresponding to the categories of the space in which each decision complement is located. These categories are then compared in a pairwise fashion – for each pair of different decision complements that are in different decision options, the user is prompted to indicate which complement is preferred, corresponding to the decision-maker's valenced affect; values are required to choose between categories.

2.2 Ordinal Routine

If two decision-options fall into the same category the decision-maker is indifferent between these complements at the categorical level. Our theory predicts that the decision-maker will descend the gist hierarchy, and revert to a more precise ordinal representation of the decision options. When this happens in our computer implementation, the user is asked to indicate the preferred direction along each of the axes in our decision space. The decision-options are then compared independently along each axis. For example, if our hypothetical adolescent knew for certain that the parents would not break up the party (thereby removing the categorical possibility of no fun), she would face a choice between two options, which advertise “some fun with certainty.” She would choose the party because it would be “more fun” in contrast to the sleepover, which would be “less fun.” If one of the options is preferred along at least one axis, and equal to or preferred along each of the other axes, then this option is chosen.

It may occur that the options are equal along all dimensions, or preferred along one dimension, but not preferred along at least one other dimension. For example, if, instead of parental intervention, our hypothetical adolescent suspected that there was a 10% chance that adult supervision would be present at the party to ensure that it remained dry – an option that would be half as much fun as the sleepover – then the adolescent would have to choose between an option that is interpreted as more fun with some chance and less fun with some chance, and an option that is some fun with certainty. Here the decision-maker is also indifferent at the ordinal level.

2.3 Interval Routine

Our theory predicts that all decision-makers also use yet a more precise interval representation. Here, the user is asked to indicate if there were any implicit decision options that had been left out in earlier routines. For example, truncated complements or implicit probabilities might be added. In this case, our computer implementation calculates the expected utility value of each of the decision options, and chooses the options with the highest such value. In the adolescent example, the adolescent would choose to go to the party because it would be 1.85 times as fun (that is 2 * 0.9 + 0.1 * 0.5), on average, than the sleepover. If one option's expected utility dominates, then this option is chosen; otherwise the decision-maker is indifferent at the interval level.

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