A Behavioral Characterization of the Likelihood Ratio Order

Abstract

It is well known that stochastic dominance is equivalent to a unanimity property for monotone expected utilities. For lotteries over a finite set of prizes, we establish an analogous relationship between likelihood ratio dominance and monotone betweenness preferences, which are an important generalization of expected utility. (JEL D11, D44)

Information aggregation in competitive markets

“…Given a weak order on signals ▹, a quasi‐linear function is monotone if implies . In Mihm and Siga (2020a), we show that an environment satisfies the MLRP if and only if there is a weak order ▹ on signals such that implies for every monotone quasi‐linear function. The relation between the MLRP and monotone quasi‐linear functions is, therefore, analogous to the well known relation between first‐order stochastic dominance and monotone linear functions.…”

“…In fact, the MLRP can also be characterized in terms of quasilinear functions. Given a weak order on signals , a quasi-linear function Mihm and Siga (2020a), we show that an environment satisfies the MLRP if and only if there is a weak order on signals such that v(ω) > v(ω ) implies V (P ω ) > V (P ω ) for every monotone quasi-linear function. The relation between the MLRP and monotone quasi-linear functions is, therefore, analogous to the well known relation between first-order stochastic dominance and monotone linear functions.…”

Weighted Utility and Optimism/Pessimism: A Decision-Theoretic Foundation of Various Stochastic Dominance Orders

“…Early literature (e.g., Quirk & Saposnik, 1962;Hadar & Russell, 1969) focuses on the first and second-order stochastic dominance and expected utility. However, the behav ioral foundation of the likelihood-ratio order has not been studied until Mihm & Siga (2021). In Mihm & Siga (2021), the authors provide a different characterization of the likelihood-ratio order using the betweenness preference relation (Dekel, 1986).…”

Full Information Equivalence in Large Elections

“…It is straightforward to verify that the betweenness condition implies the existence of a betweenness preference (with linear indifference curves in the simplex that are not necessarily parallel) therefore satisfying the betweenness property in SM.11Mihm and Siga (2021) show that there is a precise connection of the MLRP and the betweenness property: the betweenness property is satisfied if states are separated on the simplex by some betweenness order, while the MLRP is satisfied if states are separated for every betweenness order.…”

“…1111 Mihm and Siga (2021) show that there is a precise connection of the MLRP and the betweenness property: the betweenness property is satisfied if states are separated on the simplex by some betweenness order, while the MLRP is satisfied if states are separated for every betweenness order. …”