Perfect Representative Democracy:
Single-Winner Score Voting vs. Multi-Winner PR
In a perfect representative democracy, the laws being written, passed, and repealed by The Legislature at any given juncture perfectly match the laws “The People” (the entire electorate) would write, pass, and repeal themselves if given the opportunity.
Therefore, to evaluate the efficacy of any representative democracy (whether with single-winner or multi-winner districts, a single ‘elected dictator’ vs. multiple branches of government, etc.) we must compare, in aggregate, the Bayesian Regret between what The People want their government to do and what their government actually does.
To begin to do this, I propose creating a simple scenario involving 5 bill options: A, B, C, D, and E. (I understand this is not how government actually works, as bills are of course drafted and revised in committees before being brought to the floor for a ‘yes’ or ‘no’ vote; but I think this example may serve to illuminate the underlying complexity of modeling Bayesian Regret for other types of political systems beyond Single Winner districts.)
If proposed to the electorate directly in a referendum using a utility-based voting method (in this case, Score Voting)—and, just for the sake of this model, assuming totally ‘sincere’ voters—the bill that was passed would be indicative of “The Will of the People.”
Now, zoom out and have that same electorate vote for representatives. What form of government (Single-Winner ‘dictator,’ President/House/Senate, etc.) plus voting method (Single-Winner Score Voting, Multi-Winner Proportional [Reweighted] Score Voting, etc.) would best effectuate this same outcome? That is, if you were asked to start a representative democracy from scratch, how would you propose to best effectuate “The Will of the People” on any given piece of legislation? And can you mathematically prove that one cumulative approach is superior to another (as Warren has with his original Single-Winner Bayesian Regret charts)?