The paradox of alloreactivity and self MHC restriction: Quantitative analysis and statistics

Although 1–24% of T cells are alloreactive, i.e., respond to MHC molecules encoded by a foreign haplotype, it is generally believed that T cells cannot recognize foreign peptides binding foreign MHC molecules. We show using a quantitative model that, if T cell selection and activation are affinity-driven, then an alloreactivity of 1–24% is incompatible with the textbook notion that self MHC restriction is absolute. If an average of 1% of clones are alloreactive, then according to our model, at most 20-fold more clones should, on average, be activated by antigens presented on self MHC than by antigens presented on foreign MHC. This ratio is at best 5 if alloreactivity is 5%. These results describe average properties of the murine immune system, but not the outcome of individual experiments. Using supercomputer technology, we simulated 100,000 MHC restriction experiments. Although the average restriction ratio was 7.1, restriction was absolute in 10% of the simulated experiments, greater than 100, although not absolute, in 29%, and below 6 in 24%. This extreme variability agrees with experimental estimates. Our analysis suggests that alloreactivity and average self MHC restriction both cannot be high, but that a low average restriction level is compatible with high levels in a significant number of experiments.

The unpredictability paradox: review of empirical comparisons of randomised and non-randomised clinical trials

Objective To summarise comparisons of randomised clinical trials and non-randomised clinical trials, trials with adequately concealed random allocation versus inadequately concealed random allocation, and high quality trials versus low quality trials where the effect of randomisation could not be separated from the effects of other methodological manoeuvres.

Chaos, but in voting and apportionments?

Mathematical chaos and related concepts are used to explain and resolve issues ranging from voting paradoxes to the apportioning of congressional seats.

Elections, information aggregation, and strategic voting

A central role of elections is the aggregation of information dispersed within a population. This article surveys recent work on elections as mechanisms for aggregating information and on the incentives for voters to vote strategically in such elections.