# Symmetry, presumptions, and the judges design

## TL;DR

This paper examines the 'judges design' in social sciences and shows how assumptions about judge behavior can be violated under certain conditions, affecting causal inferences.

## Contribution

The paper extends the understanding of when average monotonicity is violated in judges' decision-making under symmetric signals and presumptions.

## Key findings

- Judges solving Bayesian decision problems violate average monotonicity with symmetric signals and no strong presumptions.
- The violation persists even when judge presumptions are symmetrically distributed.
- The analysis provides insights into the plausibility of assumptions in causal effect identification.

## Abstract

An instrumental variables approach called ‘the judges design’ used frequently in social sciences relies on an assumption called ‘average monotonicity’. This assumption pertains to how different judges’ (or other classifiers’) decision making processes relate to each other. Violations of it are hard to detect, which raises the importance of it being supported by a plausible theory. Decisions of judges who solve Bayesian decision problems violate average monotonicity as long as the signals they process are symmetric and they do not possess strong presumptions. This result is extended to cases where judge presumptions are symmetrically distributed and may include strong presumptions. The analysis reveals factors that can be considered while discussing the plausibility of an assumption made to identify causal effects whose violations are difficult to detect and has important policy implications.

“In other cases, however where instrumental variables are used [monotonicity is] not so plausible. Specifically in what are now called judge lenience designs”

Guido Imbens,

2021 Nobel Prize Lecture