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Enveloped choice functions and path-independent rationality

Gleb Koshevoy () and Ernesto Savaglio ()

Department of Economics University of Siena from Department of Economics, University of Siena

Abstract: We analyse the rationality of a Decision Maker (DM) who chooses from lists of sets of alternatives. We show that the DM's choice behaviour, rep-resented by a choice function f dened on such lists, can be `improved' bya two-step procedure. We rst construct the list-envelop of f that is the union of all choice sets induced by f on every possible partition (lists) of a set of alternatives. Then, we take among the list-envelop choice functionsthose that are Plott functions (see [4]) and characterize such a family by using a suitable property, allowing a DM to disregard alternatives that are worthless for the choice process. Then, using a rule that breaks the ties that could occur in every choice set, we characterize the set of Plott functions that has a prescribed shelling (see (5) below) of the choice sets. Finally, we study the 'relational system' that satises some compelling properties and rationalizes the class of choice functions studied in the present work.

Keywords: Envelop Choice Function; Plott function; Sequential Rationality; Path-independency; Shuffle of Linear Orders (search for similar items in EconPapers)
JEL-codes: D01 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-mic and nep-upt
Date: 2017-12
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