Preliminaries • A social decision scheme (SDS) is a function that maps a preference profile to a lottery over the alternatives. Formally, an SDS is a function f : RFN → ∆(A). • An SDS is majoritarian if it only depends on the (unweighted) 
 majority comparisons between alternatives. • We compare lotteries using stochastic dominance (SD). A lottery p is preferred to another lottery q if the expe...

We establish that the fraction of preference profiles for which the random serial dictatorship allocation is ordinally efficient vanishes for allocation problems with many object types. We consider also a probabilistic setting where in expectation agents have moderately similar preferences reflecting varying popularity across objects. In this setting we show that the probability that the random...

We consider situations in which n indivisible objects are to be allocated to n agents. A number of recent papers studying such allocation problems have shown various interesting equivalences between randomized mechanisms based on trading and randomized mechanisms based on serial dictatorship. We prove a very general equivalence theorem from which many previous equivalence results immediately fo...

This essay describes how a " democratic " voting can give a dictatorial outcome. In essence, choosing representatives in political systems could be understand as a coarse-graining process or decimation of opinions. Therefore, ideas and techniques from real-space renormalisation group can be used. This is a good example of the application of statistical physics to politics.

In an infinite-horizon setting, Ferejohn and Page showed that Arrow’s axioms and stationarity lead to a dictatorship by the first generation. Packel strengthened this result by proving that no collective choice rule generating complete social preferences can satisfy unlimited domain, weak Pareto and stationarity. We prove that a domain restriction can be imposed and completeness can be dropped ...