  The main goal of this paper is to investigate which normative requirements,
or axioms, lead to exponential and quasi-hyperbolic forms of discounting.
Exponential discounting has a well-established axiomatic foundation originally
developed by Koopmans (1960, 1972) and Koopmans et al. (1964) with subsequent
contributions by several other authors, including Bleichrodt et al. (2008). The
papers by Hayashi (2003) and Olea and Strzalecki (2014) axiomatize
quasi-hyperbolic discounting. The main contribution of this paper is to provide
an alternative foundation for exponential and quasi-hyperbolic discounting,
with simple, transparent axioms and relatively straightforward proofs. Using
techniques by Fishburn (1982) and Harvey (1986), we show that Anscombe and
Aumann's (1963) version of Subjective Expected Utility theory can be readily
adapted to axiomatize the aforementioned types of discounting, in both finite
and infinite horizon settings.
