Looking at the probabilistic foundations of collective decision-making rules, the authors challenge much of the existing theoretical wisdom about social choice processes, and seek to restore faith in the possibility of democratic decision-making. In particular, they argue that worries about the supposed prevalence of majority rule cycles, that would preclude groups from reaching a final decision about what alternative they prefer, have been greatly overstated. In practice, majority rule can be expected to work well in most real-world settings. They provide new insights into how alternative model specifications can change our estimates of social orderings.