When designing a public transportation network in a country, one may want to minimise the sum of travel duration of all inhabitants. This corresponds to a purely utilitarian view and does not involve any fairness consideration, as the resulting network will typically benefit the capital city and/or large central cities while leaving some peripheral cities behind. On the other hand, a more egalitarian view will allow some people to travel between peripheral cities without having to go through a central city. We define a model, propose algorithms for computing solution networks, and report on experiments based on real data.

We start by introducing a simple example to illustrate the kind of problems we are interested in solving. Consider the problem of estimating a parameter θ using data from a small experiment and a prior distribution constructed from similar previous experiments. The specific problem description is borrowed from [3]: Estimating the risk of tumor in a group of rats. In the evaluation of drugs for possible clinical application, studies are routinely performed on rodents. For a particular study drawn from the statistical literature, suppose the immediate aim is to estimate θ, the probability of tumor in a population of female laboratory rats of type'F344' that receive a zero dose of the drug (a control group). The data show that 4 out of 14 rats developed endometrial stromal polyps (a kind of tumor). Typically, the mean and standard deviation of underlying tumor risks are not available. Rather, historical data are available on previous experiments on similar groups of rats. In the rat tumor example, the historical data were in fact a set of observations of tumor incidence in 70 groups of rats (table 1).