This page collects work by Mark C. Wilson and coauthors on collective decision-making without monetary transfers. This area includes topics such as single-winner voting rules and allocation (fair division) of resources. The motivation is to find ``better" methods for making such decisions, where "better" is defined usually in terms of social welfare outcomes. It has been shown in the last several decades that every reasonable voting rule is susceptible to various ``paradoxes" (undesirable behaviour such as being strategically manipulable. It therefore (apparently) makes sense to quantify the extent to which this behaviour can occur, and this brings in probability theory. In earlier papers we adopted this viewpoint, refining the methodology and (in my opinion) being more rigorous than some previous authors. More recently, we realized that since dictatorship rules out these paradoxes, minimizing their occurrence is not a good idea in itself. The reason that dictatorships are not desirable is because it typically leads to low social welfare outcomes. So we now focus on maximizing welfare. This has some difficulties, in that interpersonal comparisons of utility cannot now be avoided. Also, different strategic behaviours lead to different answers. The space of voting rules is vast, and there is little reason to suspect that we have found all the good ones. Some papers here explore this space in more detail.