Biased representation of homothetic preferences on homogeneous sets

In the homogeneous case of one-dimensional objects, we show that any preference relation that is positive and homothetic can be represented by a quantitative utility function and unique bias. This bias may favor or disfavor the preference for an object. In the first case, preferences are complete but not transitive and an object may be preferred even when its utility is lower. In the second case, preferences are asymmetric and transitive but not negatively transitive and it may not be sufficient for an object to have a greater utility for be preferred. In this manner, the bias reflects the extent to which preferences depart from the maximization of a utility function.

Biased quantitative measurement of interval ordered homothetic preferences

We represent interval ordered homothetic preferences with a quantitative homothetic utility function and a multiplicative bias. When preferences are weakly ordered (i.e. when indifference is transitive), such a bias equals 1. When indifference is intransitive, the biasing factor is a positive function smaller than 1 and measures a threshold of indifference. We show that the bias is constant if and only if preferences are semiordered, and we identify conditions ensuring a linear utility function. We illustrate our approach with indifference sets on a two dimensional commodity space.

The gain-loss asymmetry and single-self preferences

Kahneman and Tversky asserted a fundamental asymmetry between gains and losses, namely a reflection effect which occurs when an individual prefers a sure gain of $ pz to anuncertain gain of $ z with probability p, while preferring an uncertain loss of $z with probability p to a certain loss of $ pz.We focus on this class of choices (actuarially fair), and explore the extent to which thereflection effect, understood as occurring at a range of wealth levels, is compatible with single-self preferences.We decompose the reflection effect into two components, a probability switch effect,which is compatible with single-self preferences, and a translation effect, which is not. To argue the first point, we analyze two classes of single-self, nonexpected utility preferences, which we label homothetic and weakly homothetic. In both cases, we characterize the switch effect as well as the dependence of risk attitudes on wealth.We also discuss two types of utility functions of a form reminiscent of expected utility but with distorted probabilities. Type I always distorts the probability of the worst outcome downwards, yielding attraction to small risks for all probabilities. Type II distorts low probabilities upwards, and high probabilities downwards, implying risk aversion when the probability of the worst outcome is low. By combining homothetic or weak homothetic preferences with Type I or Type II distortion functions, we present four explicit examples: All four display a switch effect and, hence, a form of reflection effect consistent a single self preferences.

D-String on near horizon geometries and infinite conformal symmetry

We show that the symmetries of effective D-string actions in constant dilaton backgrounds are directly related to homothetic motions of the background metric. In the presence of such motions, there are infinitely many nonlinearly realized rigid symmetries forming a loop (or looplike) algebra. Near horizon (antideSitter) D3 and D1+D5 backgrounds are discussed in detail and shown to provide 2D interacting field theories with infinite conformal symmetry.