Summary

Project overview

Formal model of horizontal stare decisis — the mutual constraint judges exert on one another through precedent.

Why, and when, does law bind judges? How do binding force, discretion, and doctrinal drift coexist?

"The law" is not a single determinate rule but a set of admissible decision rules consistent with past holdings
Holdings are linear constraints on the parameter space of affine decision rules
Each new holding shrinks the feasible set by intersection
Judges are constrained (binding force) yet retain discretion (feasible set is not a singleton)
Doctrine evolves gradually through constraint accumulation (drift)

Fact vectors: cases are points $z \in \mathbb{R}^k$ — inherently multidimensional
Affine decision rules: $(w, c)$ parameterize the legal rule $f(z) = w^\top z - c$
Holdings: finite sets of linear inequalities on $(w, c)$, restricting the feasible set
Existential plausibility: an outcome is legal if at least one admissible rule produces it
Sanctions: peer-imposed costs for outcomes or holdings outside the feasible set
Overruling: removing past constraints at a fixed cost
Citation incentives: broader holdings increase influence but also risk of overruling
Entailment: holdings must be logically necessitated by the case (no dicta)

Law binds without being determinate — judges are constrained to the admissible set but retain choice within it
Ideology operates through law — judges with different ideal rules select different admissible $(w, c)$
Doctrine drifts — sequential holdings tilt and shrink the feasible set, making previously implausible outcomes plausible

Primary: Journal of Legal Studies (JLS) — flagship law & economics journal; Niblett, Posner & Shleifer (2010), the 1D predecessor, published here; constitutional law applications fit the readership
Primary: JLEO — publishes theory at the law-economics-institutions intersection; Fernández & Ponzetto (2012) published here; good match for the institutional mechanisms (sanctions, overruling, citation incentives)
Stretch: JPE — Gennaioli & Shleifer (2007) and Baker & Mezzetti (2012) published here; requires closed-form results with clean comparative statics from the convex geometry / VC dimension toolkit
Political science alternative: APSR — Callander & Clark (2017), the closest competitor, published here; would require reframing toward judicial politics audience

Key prerequisite for all targets: close the model with formal propositions (not just skeleton + applications).

Introduction and motivation
Formal model (decision rules, holdings, plausibility, sanctions, overruling, citation incentives)
Equal Protection application (constraint accumulation illustrated with Brown, Korematsu, Grutter, Parents Involved)
Due Process application (Mathews balancing, substantive due process, persistent underidentification)
Next steps (closing the model, testable predictions, empirical strategies, policy implications)

paper/intro.tex — informal introduction framing the binding force of law as a coordination/focal-point problem (Schelling → McAdams → this paper)