In the homogeneous case of one type of goods or objects, we prove the existence of an additive utility function without assuming transitivity of indifference and independence. The representation reveals a positive factor smaller than 1 that infuences rational choice beyond the utility function...

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...

What are the best voting systems in terms of utilitarianism? Or in terms of maximin, or maximax? We study these questions for the case of three alternatives and a class of structurally equivalent voting rules. We show that plurality, arguably the most widely used voting system, performs very...

We present a model of price discrimination where a monopolist faces a consumer who is privately informed about the distribution of his valuation for an indivisible unit of good but has yet to learn privately the actual valuation. The monopolist sequentially screens the consumer with a menu of...

We study the complexity of rationalizing choice behavior. We do so by analyzing two polar cases, and a number of intermediate ones. In our most structured case, that is where choice behavior is defined in universal choice domains and satisfies the "weak axiom of revealed preference," finding the...

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...

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to...

The well--known Minkowski's? $(x)$ function is presented as the asymptotic distribution function of an enumeration of the rationals in (0,1] based on their continued fraction representation. Besides, the singularity of ?$(x)$ is clearly proved in two ways: by exhibiting a set of measure one in...