The Lessons of Arrow’s Theorem
A full discussion of Arrow’s Theorem, how it was produced, and what it means, is beyond the scope of this blog.
Suffice it to say that an economist thought about preference ranking systems (which political voting systems are a subset of), identified certain properties we might reasonably want them to possess, and established functional definitions of what those properties are. Rigorous, specific, formal definitions, that lent themselves to logical analysis; definitions with clear meanings.
And once he did that, he was able to show that those desirable properties could not all belong to a single system simultaneously.
If you had set for yourself the goal of creating a voting system that possessed all of the properties you wanted them to have, without establishing precisely what those properties were, you’d find yourself trapped in an endless search, never understanding why every effort ended in failure.
Arrow’s Theorem teaches us once again one of the most basic commandments of rationality: YOU MUST ALWAYS DEFINE YOUR TERMS.