Arrow’s Impossibility Theorem, voting and the inevitability of occasional suboptimal outcomes

This is a very good explanatory video on a topical subject:Voting Paradoxes.

Most people grasp that a straightforward direct democracy has the advantage that the majority always wins, but it also has the disadvantage of the minority always losing – referred to by the founding fathers in the Federalist papers as the tyranny of the majority. It is an important defect which the founding fathers addressed through the combination of a republican structure (National, State, Local) and the divided branches (Executive, Legislative, Judicial) with the hope that the resulting divisions would facilitate compromise among groups.

It has broadly been a successful model but people are always frustrated that it is 1) slow, and 2) produces less than optimal outcomes under particular (usually transient) circumstances. Fair enough criticisms until you begin to examine what are the alternative mechanisms. That is what the video highlights. Arrow’s Impossibility Theorem dictates that there is no ranked ordering system that makes logical sense. What you gain in one arena of perceived fairness, you lose as much or more in another.

Our political system is not broken. It is merely demonstrating the strains arising from the reality that if there are multiple choices and everyone’s vote counts, then there is no optimum outcome that always maximizes the greater utility of everyone. All models fail under particular circumstances.

The good thing we have is that our model fails less often than most which sounds like damning with faint praise, but is pretty accurate.

All alternatives that get proposed yield a better outcome for particular circumstances but worse outcomes overall.