General theory of best variants choice: Some aspects

Abstract

The conventional mechanisms of making the best choice, in particular, optimization mechanisms, make explicit or implicit use of the structural principle of "pair comparability" for variants and of the specific logic of the "dominant" rule for choice. This paper argues for going beyond the framework of "pairness-dominance" on the structures and rules of choice and for using "nonconventiond" structures and rules. This is showto be possible if the notions of "multitudinal influences of variants" is formalized in determining the best choices.

State dependent choice

“…Then x ∈ (C (B) ∩ A) \C (A), an immediate contradiction of sd-WARP (restated). 22 A small choice theoretic observation: this formulation makes it clear that sd-WARP is a stronger version of the classic axiom by Aizerman (see Aizerman and Malishevski [2]), which adds to the premise in sd-WARP the requirement that the sets A and B are nested, i.e. B ⊂ A.…”

“…For example, the relationship between 'mood' and choice is documented in an impressively large body of empirical evidence from psychology and economics. 2 In the large literature on menu choice (Kreps [34]; Dekel, Lipman and Rustichini [14]), an agent anticipates being in one of different preference determining states. And there exist several models of the effects on choice of specific psychological states, such as 'anticipatory feelings' (Caplin and Leahy [8]).…”

Rationality As Conformity

“…(Aizerman andMalishevski, 1981, p.1030) It is clear then, that as far as the characterisation of rational choice is concerned, what distinguishes the choice-functions approach from the one endorsed by the conventional theory of rational choice illustrated above is that it leads to a definition of "optimization" by means of constraints (i.e. properties, axioms, desiderata, etc.)…”

“…Stated very informally, Theorem 1 of Aizerman and Malishevski (1981) asserts that certain combinations of the above properties are necessary and sufficient to represent rational choice functions in terms of the choice of the "best elements" from a given set of options K. A prominent, specific, consequence of this is that Property α is proven to be necessary and sufficient to ensure the rationalizability of a choice set by means of a simple ordering. We shall come back to this sort of characterisation of rational choice, which is not beyond internal criticism (see, e.g.…”

“…However in presenting the problem like this we should be aware that as far as the agents are concerned there is not supposed to be any structure on A. Hence there is no further structure on K beyond the fact that it is the (unordered) set In their discussion of a General theory of best variants choice (Aizerman and Malishevski, 1981), they define several mechanisms for distinguishing among "variants"…”