Decision makers often have to choose alternatives which appear in an exogenous structure. For example, consider choosing a dish in a restaurant after going through different menu cards (a menu card for buffet, another for combo offers etc.). The decision maker observes the items displayed (as a list) on a menu card and she switches to another menu card to see the items displayed on it (again in the form of another list). Thus the set of all items appears as an “ordered-tree” to the decision maker. There are other examples of decision making where alternatives appear in the form of an ordered-tree. In this paper we consider the cases of choice from ordered-trees (in particular, “lists of lists”) and characterize the choice functions. We impose the axioms of Backward Consistency and Replacement Indifference on choice functions and obtain characterization results for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$k$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>k</mi> </math> </EquationSource> </InlineEquation>-ary ordered-trees and more general ordered-trees. We show that the results for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$k=2$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mrow> </math> </EquationSource> </InlineEquation> are similar to those of (Rubinstein and Salant <CitationRef CitationID="CR13">2006</CitationRef>), in which the cases of choice from lists are considered. However the results for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$k \ge 3$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>k</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math> </EquationSource> </InlineEquation> and general ordered-trees are different and allow for instance, a richer class of tie-breaking rules in special cases. Copyright Springer-Verlag Berlin Heidelberg 2014
