On the utility representation of asymmetric single-peaked preferences

We introduce two natural types of asymmetric single-peaked preferences, which we name biased-above and biased-below, depending on whether the asymmetry (or preference-bias) favors alternatives above or below the peak. We de ne a rich family of utility functions, the generalized distance-metric utility functions, that can represent preferences biased-above or biased-below, besides accommodating any degree of asymmetry. We also identify restrictions on di¤erentiable utility representations that guarantee the underlying preferences to be biased-above or below, and allow to compare degrees of asymmetry. Finally, we consider a speci c application agents preferences over government size to illustrate the role of factors such as risk aversion and tax distortions in shaping asymmetric preferences.