Thinking Outside the Euclidean Box: Riemannian Geometry and Inter-Temporal Decision-Making

Area of Science:

• Cognitive Science
• Neuroscience
• Behavioral Economics

Background:

• Inter-temporal decisions involve valuing payoffs at different times.
• Existing models use exponential or hyperbolic discounting, assuming a Euclidean decision space.
• This research challenges the Euclidean assumption in decision-making models.

Purpose of the Study:

• To propose and test a novel decision space for inter-temporal choices.
• To introduce a discount function based on Riemannian geometry (Constant Negative Curvature).
• To explain empirical findings in inter-temporal decision-making literature more effectively.

Main Methods:

• Developed a discount function using distance in a Constant Negative Curvature space.
• Incorporated perceived values of both time and money into the distance function.
• Employed manifold learning algorithms to estimate decision space curvature.

Main Results:

• The proposed discount function explains empirical findings in inter-temporal decision-making.
• Manifold learning confirmed that the decision space's metric properties resemble Negative Curvature space.
• Evidence supports a Riemannian, rather than Euclidean, model of decision space.

Conclusions:

• The decision space for inter-temporal choices is better modeled as a Riemannian space of Constant Negative Curvature.
• This geometric approach offers a more flexible framework for understanding value-based decision-making.
• New theoretical predictions and implications for defining non-normative behavior are presented.