292 research outputs found
An improved version of a theorem concerning finite row-column exchangeable arrays
No full textsummary:We improve a result of Bassan and Scarsini (1998) concerning necessary conditions for finite and infinite extendibility of a finite row-column exchangeable array, and provide a simpler proof for the result
Sull'accumulo di un capitale in condizioni di incertezza [On the accumulation of capital under conditions of uncertainty]
No full text
Fear of loss, inframodularity, and transfers
No full textThere exist several characterizations of concavity for univariate functions. One of them states that a function is concave if and only if it has nonincreasing differences. This definition provides a natural generalization of concavity for multivariate functions called inframodularity. Inframodular transfers are defined and it is shown that a finite lottery is preferred to another by all expected utility maximizers with an inframodular utility if and only if the first lottery can be obtained from the second via a sequence of inframodular transfers. This result is a natural multivariate generalization of Rothschild and Stiglitzʼs construction based on mean preserving spreads
On Information Distortions in Online Ratings
No full textConsumer reviews and ratings of products and services have become ubiquitous on the Internet. This paper analyzes, given the
sequential nature of reviews and the limited feedback of such past reviews, the information content they communicate to future
customers. We consider a model with heterogeneous customers who buy a product of unknown quality and we focus on two different informational settings. In the first setting, customers observe the whole history of past reviews. In the second one they only observe the sample mean of past reviews. We examine under which conditions, in each setting, customers can recover the true quality of the product based on the feedback they observe.In the case of total monitoring, if consumers adopt a fully rational Bayesian updating paradigm, then they asymptotically learn the unknown quality. With access to only the sample mean of past reviews, inference becomes intricate for customers and it is not clear if, when, and how social learning can take place. We first analyze the setting when customers interpret the mean as the proxy of quality. We show that in the long run, the sample mean of reviews stabilizes and, in general, customers overestimate the underlying quality of the product. We establish properties of the bias, stemming from the selection associated with observing only reviews of customers who purchase. Then, we show the existence of a simple non-Bayesian quality inference rule that leads to social learning when all customers use such a rule. The results point to the strong information content of even limited statistics of past reviews as long as customers have minimal sophistication
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