A Mathematical Analysis of the Improving Sequence Effect for Monetary Rewards

Abstract

In this paper, we mathematically formalize the concept of improving sequence effect, which is one of the main anomalies of the discounted utility model [1]. The improving sequence effect implies a preference for a given sequence of outcomes, which increase over time, and has been empirically demonstrated for both monetary and nonmonetary results (hedonic experiences and health-related outputs). Nevertheless, to date, there is no mathematical treatment of this anomaly in the context of intertemporal choice, which allows us to relate this paradox to other anomalies, such as the delay and magnitude effects. In this way, the present manuscript has filled this gap. More specifically, we have proved that the improving sequence effect for monetary rewards cannot be rationalized by using a separable discount function but only by considering a non-separable discount function. Moreover, under certain conditions, we have proved that the delay and magnitude effects are necessary conditions for the existence of the improving sequence effect.

Reasons for loan repayment plan preferences.

“…Obviously, we have V(L) ϭ L, for r L ϭ r e ; V(L) Ͼ L, for r L Ͼ r e ; and V(L) Ͻ L, for r L Ͻ r e . Therefore, by using an exponential discount function, for r L Ͼ r e , the subjective present value of the loan V(L) is greater than its principal L. Rambaud, Torrecillas, and Garcia (2018) proved that this result applied to sequences in (increasing or decreasing) arithmetic progression. We found that it also applied to any loan repayment sequences.…”

Price Attractiveness and Price Complexity: Why People Prefer Level-Payment Loans

“…For positive series of future rewards such as incomes, restaurant visits, leisure activities or other gains, the preference for improvement means that individuals prefer to start with the least attractive outcome and end with the most attractive outcome than the opposite, i.e., they prefer the rising sequence over the falling sequence adding up to the same total amount Prelec, 1991, 1993;Loewenstein and Sicherman, 1991;Gigliotti and Sopher, 1997;Thaler, 1999;Matsumoto et al, 2000;Guyse et al, 2002;Duffy and Smith, 2013;Duxbury et al, 2013). Likewise, for negative series of outcomes such as pains, annoying noise, discomfort or other losses, individuals prefer the falling sequence over the rising sequence (Ariely and Loewenstein, 2000;Ariely and Zauberman, 2000;Langer et al, 2005;Rambaud et al, 2018;Garcia et al, 2020). Some researchers examined human preferences for sequences with respect to loan repayment plans.…”