Linear Utility for Partially Ordered Preferences
Part of the Theory and Decision Library book series (TDLU, volume 31)
We have assumed thus far that the preference relation ≻ on ℳ or P is an asymmetric weak order. We now relax this assumption and consider linear utilities for ≻ on P that preserve ≻ in one direction only: for all P, q ∈ P,
$$ p \succ q \Rightarrow u(p) > u(q).$$
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© Springer Science+Business Media Dordrecht 1982