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.

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3 Responses to “The Lessons of Arrow’s Theorem”

  1. Lot’s of people think “independence of irrelevant alternatives” can be easily discarded. What do you think?

  2. Lots of people also think our political system is functional, and that one of the candidates we’re presented with is suitable to take the position of Chief Executive.

    I tend to disregard the positions of most people.

    In regards to the Theorem: irrelevance changes, and things we consider to be unimportant often become important later on. I wouldn’t be so quick to discard that point.

  3. […] could have resulted in President Perot). Caledonian/melendwyr has a post on Arrow’s Theorem here. […]

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