Operations Research and Economic Theory pp 291-305 | Cite as

# Continuous Linear Representations of Preference Orderings in Vector Spaces

## Abstract

In operations research and microeconomic modelling it is usual to assume that a decision-maker’s preferences ≼ over prospects x∈X over time, space, or uncertain states-of-nature may be represented by an integral ∫x(ω)dμ(ω) over the underlying set of times, locations, or states-of-nature. In a temporal setting such an integral may be interpreted as the present value of prospect x with respect to a temporal discount function. In a spatial setting, it may be interpreted as accessibility to location pattern x with respect to a spatial discount function. In a choice among uncertain prospects, finally, the integral may be interpreted as the expected value of prospect x with respect to a probability measure.

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### References

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