Choosing the two finalists

Abstract

Choice correspondence, Two-stage choice, Consideration sets, Axiomatization, D01,

Dual random utility maximisation

“…We note a subtle relation between the symmetric case of the theory and the deterministic "top-and-the-top" (TAT) model studied in Eliaz, Richter and Rubinstein [12]. A TAT is a choice procedure in which the agent uses two ordering and deterministically picks all the alternatives in a menu that are top in at least one of the two orderings.…”

“…The logic of Luce and Raiffa's [24] well-known 'frog legs example' is that the presence of a specific item a (frog legs in the example) in a menu triggers the maximisation of a different preference order because a conveys information on the nature of 11 The key property used by Eliaz, Richter and Rubinstein [12] to characterise TAT says that if an x is chosen from two menus A and B and also from A \ B, and if the choice from A \ B consists of exactly two elements, then x is chosen from A [ B. In addition their axiomatisation also includes a direct assumption on the number of chosen alternatives.…”

“…12 12 'Mode' and 'modal' are meant here and elsewhere in the logical and not statistical meaning. The analog of Modal Impact Consistency holds in the menu-independent model, and indeed in any RUM: if b is chosen with positive probability in a menu, then it impacts some alternative in any sub-menu.…”

Partially dominant choice

“…The observation that the PD model is also compatible with the ERR axiom (which, as shown in Eliaz, Richter, and Rubinstein (2011), implies Property α whenever two alternatives are choosable in every non-singleton menu) also puts an upper bound on how irrational the behavior that is described by this model can be. It is also of interest that theories of maximal-element choice that build on (1) as well as others that satisfy many of the axioms in Observation 3 do not obey Partial b-WARP, and hence deviate more fundamentally from the normative b-WARP axiom than does the PD model.…”

“…It is consistent with Ehlers and Sprumont's (2008) Weakened WARP if, for all A, B ∈ M, x ∈ C(A), y ∈ A \ C(A) and y ∈ C(B) implies x ∈ B \ C(B). Finally, it satisfies the "A3" axiom proposed by Eliaz, Richter, and Rubinstein (2011) (henceforth the ERR axiom) if, for all A ∈ M such that |A| ≥ 2 and x, y ∈ A, w ∈ C(A ∪ {x, y}) holds whenever w ∈ C(A ∪ {x}) and w ∈ C(A ∪ {y}).…”