A comparison of intertemporal choices for oneself versus someone else based on Tsallis' statistics

Acknowledgements: The research reported in this paper was supported by a grant from the Grant-in-Aid for Scientific Research (" 21st century center of excellence " grant) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. Summary Impulsivity and inconsistency in intertemporal choice (discounting) have drawn attention in econophysics and neuroeconomics. Although it is well established that most people often show irrational discounting (e.g. hyperbolic discounting), little is known regarding whether the irrationality is mitigated or not, when the choice was performed by someone else instead of subject herself. This point is important for economic policy-making. In order to compare consistency and impulsivity in choices for oneself versus someone else, we experimentally estimated the consistency parameter q in Tsallis' statistics-based discount function for oneself and someone else, by assessing the points of subjective equality (indifference points) at seven delays (one week-25 years) in humans. We observed that (i) most people are more inconsistent when the outcomes of intertemporal choice are only relevant to someone else (q= 8.89) than when relevant to oneself (q=2.63), and (ii) impulsivity, distinguished from inconsistency by utilizing the Tsallis statistics-based q-exponential discount function, is also larger in the choice for someone else than for oneself. Our results indicate that (i) leaving decision-making processes with some others may neither reduce impulsivity nor correct inconsistency, and (ii) when q-exponential discount is utilized, the definition range of q-parameter should be extended to q<0, and smaller q<1 and larger q>1 indicate more inconsistent discounting. Together, the usefulness of the q-exponential discounting for analyzing the dynamic consistency of economic policy was demonstrated in the present study.