Comment on Jackson and Sonnenschein (2007) "Overcoming Incentive Constraints by Linking Decisions"

TL;DR

This paper clarifies and corrects a bound in the definition of approximate truthfulness in Jackson and Sonnenschein's 2007 work, ensuring the main theorem's validity with a looser bound.

Contribution

It identifies a discrepancy in the original proof and provides a corrected bound that maintains the theorem's validity.

Findings

The original permutation-based proof requires a looser bound for correctness.

The corrected bound still ensures the fraction of lies vanishes as the number of problems increases.

The main theorem remains valid after adjusting the bound.

Abstract

We correct a bound in the definition of approximate truthfulness used in the body of the paper of Jackson and Sonnenschein (2007). The proof of their main theorem uses a different permutation-based definition, implicitly claiming that the permutation-version implies the bound-based version. We show that this claim holds only if the bound is loosened. The new bound is still strong enough to guarantee that the fraction of lies vanishes as the number of problems grows, so the theorem is correct as stated once the bound is loosened.