# An Impossibility Result for the Best System Account

This colloquium was given by Sungwon Woo (University of Maryland) at the University of Maryland (KEY 0103) on December 2, 2015 from 3:30PM to 5:30PM.

This talk was based on Woo’s doctoral thesis, “From Social Choice to System Choice: A Problem Lewis’s Best System Analysis.”

## Thesis

David Lewis’s Best System Account of the laws of nature are threatened by Arrow’s Impossibility. He argues that the BSA implies all of Arrow’s conditions, U, D, I, and ND and therefore is subject to it’s conclusion. Namely that there is no scheme that can declare a definitive best system.

## The Best System Analysis

One particular conception of the laws of nature that falls under the regularity school is Lewis’s Best System Account. An ideal theory is that which maximizes the standards of science (e.g. simplicity, strength, fit) over the entire history of the world.

## Arrow’s Impossibility Theorem

Arrow’s Impossibility Theorem proves that given the rational conditions U, D, I, and ND, at least one must be violated under any choice procedure. Therefore if BSA implies that U, D, I, and ND must be true, then even with perfect information and clear criterion, no best system could be found even in principle.

Woo then must justify that BSA implies Arrow’s conditions.

## Condition U

Which system rankings should be excluded from the domain? There is no obvious choice (e.g. should it be to reduce number of parameters or number of total equations in the system).

## Condition I

Woo sees the best escape as the possibility of relaxing Condition I. Here Sen’s enriched information may come into place. Considering two rankings where the ordinal rankings are equivalent, but the cardinal measures are not, one may disagree with I.

This requires some inter-standard commensurability. However, Woo rejects this on both an epistemeic basis and a metaphysical one.

The epistemic basis is that standard comparison like Akaike Information Criterion was built to correct overfit. Since BSA assumes complete information, we are at no risk for overfit and therefore the classical statistical models for this are not applicable.

The metaphysical basis is that these statistical models assume true parameters which the regularity school (and hence BSA) reject outright.