The quartiles of the maximum entropy distribution

The quartile points and interquartile range of the maximum entropy (ME) distribution and sample distribution are compared, using expected values for sampling from a standard normal population. For sample sizes n?20 such that the sample quartile points are uniquely defined, the ME quartile points and interquartile range are found to have lower mean-squared error (MSE).     

The Under-Exploitation of Natural Resources: A Model with Overlapping Generations*

It is well known that competitive markets may fail to generate an optimal rate of extraction of a natural resource-stock. The barrier to optimality may be uncertainty about tenure, commonality of property rights in the resource, or uncertainty about the extent of the resource. In all these cases, suboptimality takes the form of over-extraction. We draw attention to an additional source of suboptimality. In an economy with overlapping generations, the resource-stock plays the double role of repository of savings and source of productive inputs. The decline in the supply of the resource-stock may eventually force its price so high that it ceases to perform its second function. Extraction comes to an end even though the resource has a positive marginal productivity in producing consumption goods. This is inefficient, hence suboptimal. This time, however, suboptimality takes the form of under-extraction.     

Utility theory based on rational probabilities

Classical utility theory assumes that a preference order is defined for all mixtures αa+(1?α)b of pure prospects a,b for all real numbers α between 0 and 1. If α is irrational such mixtures are hard to interpret intuitively. We show here how to modify the usual axiomatisations to deal with the case where α is restricted to rational values, or even further to values of the form m/2ⁿ corresponding to mixtures built up from even bets.     

A note on cross-impact analysis: a calculus for sequence-dependent events

As the example presented demonatrate, the analysis of cross-impactss amount a group of related events is somewhat more complex than perhaps heretofore imagined. Impacts of effects between such events very often carely depend on their temporal sequence. The event outcome space is accordingly multiplied considerably over the case where such dependency is ignored. The result is that high premium is placed on methods that seek to reduce analytical complexity without distorting essential event intrications.