Theory
======

PrefGraph's theory docs are organized as a linear path. Read the phases in
order if you are new to revealed preference, or jump to the phase that matches
the kind of data you are scoring.

Phase 1 - Foundations
---------------------

Start with notation, maintained assumptions, and the axiom hierarchy. This
phase explains what the observed prices, bundles, menus, and choices must mean
before any score should be trusted.

- :doc:`Budget foundations <../budget/theory_foundations>`
- :doc:`Method landscape <methods>`

Phase 2 - Budget Consistency
----------------------------

Budget choices are price-quantity observations. This phase covers WARP, GARP,
SARP, and related consistency tests, including the strict edge that makes a
revealed-preference cycle a GARP violation.

- :doc:`Budget consistency tests <../budget/theory_consistency>`

Phase 3 - Budget Efficiency
---------------------------

Once consistency is defined, the next question is distance from consistency.
This phase covers CCEI/AEI, MPI, Houtman-Maks, Bronars power, and related
scores.

- :doc:`Budget efficiency scores <../budget/theory_efficiency>`

Phase 4 - Budget Structure and Recovery
---------------------------------------

This phase covers stronger structure: homotheticity, quasilinearity,
separability, integrability, and recovered utility.

- :doc:`Budget structure and utility recovery <../budget/theory_structure>`

Phase 5 - Deterministic Menu Choice
-----------------------------------

Menu choices replace budgets with finite feasible sets. This phase covers
abstract choice, WARP/SARP for menus, congruence, and ordinal utility recovery.

- :doc:`Abstract menu choice <../menu/theory_abstract>`

Phase 6 - Stochastic Menus and Attention
----------------------------------------

The final menu phase covers choice frequencies, random utility, random
attention, limited attention, and attention filters.

- :doc:`Stochastic menu choice <../menu/theory_stochastic>`
- :doc:`Limited attention <../menu/theory_attention>`

Contents
--------

.. toctree::
   :maxdepth: 2

   methods
   ../budget/theory_foundations
   ../budget/theory_consistency
   ../budget/theory_efficiency
   ../budget/theory_structure
   ../menu/theory_abstract
   ../menu/theory_stochastic
   ../menu/theory_attention