Nice article. A few notes on terminology:

“Voting system” has an ambiguous meaning. It can mean hardware and/or software; it can mean a mathematical algorithm, as you’re using it in this article; or it can mean the entire set of laws and procedures of a given jurisdiction around voting, which includes both of the former meanings but also things like rules about who gets to vote and when. Thus, “voting method” is a better word, because it unambiguously means the algorithm.

“Bayesian regret” is also a poor term. Rev. Thomas Bayes was indeed a utilitarian philosopher, but he’s mostly known today for his theorem on conditional probabilities; “Bayesian Regret” has nothing to do with conditional probabilities, only with expected value. Thus, the more-current term for “Bayesian Regret” is Voter Satisfaction Efficiency, or VSE: http://electionscience.github.io/vse-sim/VSE/.

You do a good job explaining ordinal and cardinal voting methods, but you don’t mention hybrid methods such as STAR voting or 3-2-1 voting. Although these hybrids forego the provable perfection of either side on certain criteria, in practice it’s been shown they can pass the criteria more often in practice. I believe it’s better to almost-always pass two good criteria than to always pass one but often fail the other.