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For example, it is very difficult to find a weighting function and a utility function within Goldstein-Einhorn that will give us a preference ranking ABDCE (GE-V40): only one in the two million combinations of parameter values that we checked in our grid search of the parameter space for.

For each pattern, we provide the corresponding ranking of gambles (from best to worst), and the portion of the algebraic parameter space corresponding to each preference (based on a grid search), up to and rounded to the first significant nonzero digit. The precision and range of our grid search were as follows.