### abstract ###
MISC	similar to research on risky choice, the traditional analysis of intertemporal choice takes the view that an individual behaves so as to maximize the discounted sum of all future utilities
MISC	the well-known allais paradox contradicts the fundamental postulates of maximizing the expected value or utility of a risky option
AIMX	we describe a violation of the law of diminishing marginal utility as well as an intertemporal version of the allais paradox
### introduction ###
MISC	in the field of intertemporal choice, the discounted-utility du theory proposed by paul samuelson in 1937 was presented not only as a valid normative standard but also as a descriptive theory of actual intertemporal choice behavior  CITATION
MISC	in its general form, the du theory proposes that the value of an option, x; t, is the product of its present utility, ux, and an exponential temporal discounting function, ft, where t is the time at which x is acquired
MISC	the overall value of a mixed option, a = {x, t, x, t, }, denoted va, is simply the sum of these products
MISC	that is, va = sigma  ux ft
MISC	an option a will be preferred to an option b if and only if va  greater than  vb
MISC	however, a large body of empirical evidence demonstrates that people systematically violate this theory
MISC	this includes the common difference effect, the magnitude effect, the gain-loss asymmetry, the delay-speedup asymmetry, and so on  CITATION
MISC	this situation has led researchers to consider extensions and modifications of the du theory to reconcile it with the experimental data
MISC	the most prominent idea to account for these anomalies is the hyperbolic discounting model  CITATION
MISC	this model suggests that the discount rate is not dynamically consistent but that the rate is higher between the present and near future and lower between the near and far distant future
MISC	numerous theories have been developed by transforming the discount function to other forms, from one-parameter hyperbolic discounting  CITATION  to generalized hyperbolic discounting  CITATION , to proportional discounting  CITATION , and to quasi-hyperbolic discounting  CITATION
MISC	however, these models focus on intertemporal choice between pairs of single-dated outcomes represented as pure gains or losses
MISC	when these models are applied to intertemporal choice between pairs of multiple-dated outcomes in mixed contexts, there is general agreement on the additive assumption and the independence assumption
MISC	with an apt transformation of the discounting rate, the additive assumption means that preferences for outcome sequences are based on a simple aggregation of their individual components within intertemporal choice  CITATION
MISC	the independence assumption means that the value or utility of an outcome in one period is independent of outcomes in other periods  CITATION
MISC	because risk and delay might be psychologically equivalent, or at least analogous, and because similar psychological processes might underlie risk and intertemporal choice  CITATION , theoretical development in intertemporal choice has progressed steadily along a similar route as that of risky choice  CITATION
MISC	both lines of research have spawned a large number of variant models
MISC	although the functional forms differ, most theories assume a maximization principle; that is, people calculate the mathematical expectation of each outcome and add them together before choosing the option that maximizes overall value or utility
CONT	a minor difference is that the existing models of intertemporal choice are relatively underdeveloped and are less flexible in dealing with empirical challenges
CONT	for example, research on risky decision making does not treat risky choice as limited to pure gains or pure losses but has been extended to include mixed outcomes involving both gains and losses
CONT	examples include the sign-dependent utility model  CITATION , the rank- and sign-dependent utility model  CITATION , and the transfer of attention exchange model  CITATION
MISC	the well-known allais paradox  CITATION  contradicts the fundamental postulates of maximizing the expected utility of a risky option
MISC	the paradox presents a violation of the cancellation axiom, which asserts that, if two options have a common consequence under a particular event, the preference order of the options should be independent of the value of that consequence  CITATION
MISC	since then, many new descriptive theories of risky choice have abandoned the maximization assumption  CITATION
MISC	most models of intertemporal choice have not yet abandoned the additive assumption and the independence assumption
MISC	these two assumptions would lead to the cancellation axiom, which indicates that a preference between two sequences with elements in common does not depend on the nature of the common elements
MISC	table 1 illustrates an example of the multiple-dated outcomes problem, which would be used to test the cancellation axiom
MISC	in problem i, the additive models predict that adding a common element x at time 2 to both option a and option b would not change the preference orderings
MISC	the violation of cancellation would be observed if the preference orderings were different between problem i and problem i
MISC	however, if allais's proposition applies to intertemporal choice, we will eventually encounter an intertemporal version of the allais paradox
AIMX	we first illustrate our point with a paradox that is an intertemporal-type violation of the cancellation axiom
