Procedural Invariance and Its Violations

Economic Violations of Procedural Invariance

One well-known phenomenon, often interpreted as a failure of procedure invariance, is the preference reversal. Reversals of preferences are observed when a so-called $-bet (offering a high money prize with low probability) is assigned a higher selling price than a P-bet (offering a lower money prize but with a higher probability) but is subsequently not chosen in a direct choice between the two. A violation of procedure invariance is currently the prevailing explanation of this pattern of behavior. For instance, when assessing the monetary values of gambles (or delayed payments), people base their actions on a particular value system. When choosing between gambles, however, they base their actions on another value system. Therefore, preferences from choosing are different from those yielded by monetary valuation; this fact constitutes a violation of procedure invariance. The explanations invoking a violation of procedure invariance are mostly based on weighted additive models. These models assume that, both for choosing and for valuation, a person evaluates a gamble-delayed payment ($x, p), where x is the expected monetary reward and p is the probability of obtaining this payoff, by using av(x) + bw(p), where v and w are values for the separate attributes and a > 0 and b > 0 sum to 1 and are importance weights. It is generally assumed that the value functions v and w are the same for choosing and valuation and that only the weights a and b vary. That is, for choosing, particular weights, such as ac and bc, are adopted, and for valuation, other weights, such as av and bv, are adopted. Note that because importance weights are positive, choosing and matching yield the same orderings over single attributes.

...