Weighted Majoritarian Rules for the Location of Multiple Public Facilities

We consider collective decision problems given by a profile of single-peaked preferences defined over the real line and a set of pure public facilities to be located on the line. In this context, Bochet and Gordon (2012) provide a large class of priority rules based on efficiency, object-population monotonicity and sovereignty. Each such rule is described by a fixed priority ordering among interest groups. We show that any priority rule which treats agents symmetrically — anonymity — respects some form of coherence across collective decision problems — reinforcement — and only depends on peak information — peakonly — is a weighted majoritarian rule. Each such rule defines priorities based on the relative size of the interest groups and specific weights attached to locations. We give an explicit account of the richness of this class of rules.

Trends in incidence of oesophageal and gastric cancer according to morphology and anatomical location, in Switzerland 1982-2011.

QUESTION UNDER STUDY/PRINCIPLES This study aimed to evaluate trends in the incidence of oesophageal and gastric cancer by anatomical location and histology using nationally representative Swiss data. METHODS We included all oesophageal and gastric cancers recorded in 10 Swiss population-based cancer registries 1982-2011. We calculated age-standardised incidence rates (ASIRs) per 100 000 person-years (PY) (European standard) for both cancer sites stratified by sex, language region (German, French-Italian), morphology and anatomical location. To assess time trends, we estimated annual percentage changes (APCs) with 95% confidence intervals (95% CIs). RESULTS ASIR of oesophageal adenocarcinoma increased in both sexes and language regions (p <0.001). The steepest increase occurred in males of the German-speaking region (APC 6.8%, 95% CI 5.8-7.8) with ASIRs of 0.8 per 100,000 PY in 1982-1987 and 3.9 per 100.000 PY in 2007-2011. Incidence of oesophageal squamous cell carcinoma decreased significantly in males of both language regions by around -1.5% per year. In contrast, a slight but significant increase (APC 1.4%, 95% CI 0.3-2.4]) of oesophageal squamous cell carcinoma was observed in females of the German-speaking region. We observed stable rates for cancer of the gastric cardia. The incidence of noncardia gastric cancer decreased substantially in both sexes and language regions (p <0.001). CONCLUSION In Switzerland, the incidence of oesophageal adenocarcinoma has risen whereas incidence of noncardia gastric cancer has decreased substantially as observed in other developed countries.