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If empirical data had no variability, it would be natural to treat them as algebraic. But if there is variability in empirical data, a probabilistic framework is more appropriate. In particular, it is common to interpret algebraic models of behavior as assuming that behavior is deterministic, which may be too strong an assumption. While some decision makers display relatively small amounts of variability in their binary choices, the typical picture for actual participants in the Tversky study and the Regenwetter et al.

But we will see that even data like those of HDM warrant quantitative testing.