An $\alpha$-MaxMin Utility Representation for Close and Distant Future Preferences with Temporal Biases

This article introduces an axiomatic approach of utilities streams based upon three preference relations, namely the close future order, the distant future order, and the main order. Assuming all these preferences to be bi-separable, the article derives a unanimous representation for weights over periods. The analysis of two categories of a \emph{potentially better} property allows for the establishment of \textit{MaxMin}, \textit{MaxMax}, and $\alpha-$\textit{MaxMin} representations. This is followed by the presentation of a multiple discounts rates version of $T^{*}$-temporally biased, generalizing quasi-hyperbolic discounting for the close future order. A similar analysis for the distant future is also performed, where it is proved that Banach limits can be considered as the distant future counterpart of exponential discounting in the evaluation of the close future.