Science Analysis Template
These are the structural patterns found across all Scientific Disciplines
This section examines whether the core elements of individual choice theory fit together without contradiction. Choice models rely on a small set of primitives—preferences, constraints, beliefs, and decision rules—and much of their power comes from treating these objects as stable and well-defined. Consistency here means that these definitions, rules, and representations do not silently conflict as the analysis moves between axioms, optimization problems, probabilistic choice, and empirical interpretation. The goal of this section is to ensure that what it means to “choose,” “optimize,” or “prefer” remains coherent across formal theory, limiting cases, and measurement, so that choice behavior is not being explained by mutually incompatible assumptions.
The 10 Universal Consistency Families
1) Definitional consistency
What it is:
Core primitives in choice theory—such as agent, preference, option, utility, choice set, and constraint—are defined in ways that do not conflict with each other and are used consistently throughout the analysis. In particular, if utility is used as a numerical representation of preferences, the theory must be clear about what properties that representation has (ordinal vs. cardinal, interpersonal comparability or not, state-dependence or not) and must not switch interpretations mid-stream. All references to “maximization,” “optimal choice,” or “rationality” must be grounded in the same underlying definitions of preference and feasibility.
Typical failure:
The analysis silently shifts meanings between closely related concepts. Common examples include treating utility as ordinal in some arguments (only rankings matter) but then interpreting differences or levels of utility as meaningful in others; using “preferences,” “utility,” and “welfare” interchangeably without defining equivalence; or redefining the choice set implicitly by adding or removing constraints without updating the definition. Another failure mode is invoking “rational choice” without specifying whether it means completeness and transitivity of preferences, expected-utility maximization, or some procedural decision rule—leading to apparent results that rely on incompatible definitions of what “choice” or “rationality” means.
2) Axiomatic / rule consistency
What it is:
The foundational rules governing individual choice—such as the axioms on preferences (completeness, transitivity, continuity, independence, etc.), feasibility constraints, and the decision rule used to select an option—do not contradict one another. Within the formal structure of choice theory, the axioms must jointly permit a well-defined choice correspondence or utility representation, and the rules for “optimal choice” must be derivable from those axioms without generating incompatible implications. You cannot, under the same interpretation, derive both that an option is chosen and that it is not chosen.
Typical failure:
The model combines axioms or decision rules that cannot all hold at once. Common failures include assuming transitive preferences while also allowing cyclical revealed choices; imposing independence-like conditions while later appealing to context-dependent or reference-dependent behavior without revising the axiom set; or asserting both maximization of a stable utility function and procedural or heuristic choice rules that violate that maximization. Another failure mode is adding “reasonable” behavioral restrictions ad hoc (e.g., choice consistency across menus) that, together with the original axioms, overconstrain the system and eliminate the possibility of any coherent choice rule. In such cases, the theory’s rules implicitly negate one another, rendering the notion of rational choice internally inconsistent.
3) Constraint compatibility
What it is:
All constraints imposed on an individual choice problem—such as budget constraints, feasibility restrictions, information limits, and preference axioms—can be satisfied at the same time. There must exist at least one feasible option in the choice set that respects every stated constraint, so the problem defines a non-empty feasible set. The rules governing preferences and choice cannot require outcomes that violate the agent’s opportunity set or internal consistency conditions.
Typical failure:
The model imposes constraints that cannot jointly hold. Common failures include specifying a budget constraint that leaves no affordable option while still requiring a choice; combining satiation or monotonicity assumptions with bounds that forbid consuming any more of a good; or imposing preference axioms that imply a unique optimum while defining a choice set that contains no maximal element. Another frequent error is layering informational or behavioral restrictions (e.g., perfect foresight or strict optimization) onto a choice environment that does not provide enough information or feasible actions to satisfy those requirements. In these cases, the choice problem is ill-posed because no option can meet all constraints simultaneously.
4) Conservation / accounting consistency
What it is:
Any conserved quantity or accounting identity implicit in an individual choice problem is respected by the decision structure. Feasible choices must satisfy budget balance, resource feasibility, and any probability or weighting constraints assumed in the model. If the choice framework treats certain quantities as fixed totals—such as income, time, probability mass, or endowments—then the choice rules and objective function must not create or destroy those quantities without an explicit source or sink.
Typical failure:
The model allows resources or probability mass to appear or disappear through the choice rule. Common failures include specifying a utility maximization problem in which expenditures exceed income without accounting for borrowing or transfers; defining mixed or stochastic choice rules whose probabilities do not sum to one; or allowing time, effort, or attention to be allocated across options in ways that exceed the total available. Another frequent error is implicitly double-counting or omitting parts of the constraint set—so that the “books” of the choice problem do not balance. In these cases, the choice model violates its own conservation requirements, signaling a mis-specified objective, constraint, or accounting identity.
5) Symmetry / invariance consistency
What it is:
If a choice model assumes certain invariances—such as invariance to relabeling of options, units of measurement, or irrelevant transformations of the choice set—then all derived choice predictions must respect those invariances. The outcome of a choice problem should depend only on the underlying preference structure and constraints, not on arbitrary representations such as how options are named, ordered, or numerically encoded. When preferences are assumed to be stable or representation-invariant, equivalent formulations of the same choice problem must yield the same selected option(s).
Typical failure:
The model’s predictions change under transformations that should leave the choice problem unchanged. Common failures include choices that depend on the labeling or ordering of options rather than their attributes; utility representations that yield different choices under monotonic transformations despite only ordinal preferences being assumed; or menu-dependent results that contradict assumed independence from irrelevant alternatives. Another frequent error is mixing unit-dependent and unit-invariant reasoning—for example, treating utility as ordinal in theory but drawing conclusions from utility differences that vary under rescaling. In these cases, the choice model violates its own symmetry assumptions, indicating an internal inconsistency between representation and prediction.
6) Limit / correspondence (bridge) consistency
What it is:
When multiple choice models or formulations apply to overlapping domains or limiting cases, they must agree where both are supposed to be valid. More general or enriched choice frameworks (e.g., stochastic choice, bounded rationality, dynamic choice) should reduce to simpler, well-established choice models under the appropriate limits (e.g., zero noise, full information, static environments). Likewise, alternative representations of the same choice problem should yield the same predictions in regimes where their assumptions coincide.
Typical failure:
A choice model fails to recover standard results in the limit where it claims to be an approximation. Common failures include stochastic choice models that do not converge to deterministic utility maximization as noise goes to zero; dynamic choice formulations that fail to reduce to static choice when intertemporal considerations are removed; or bounded-rationality models that contradict classical revealed-preference results even when bounds are relaxed. Another frequent error is treating two formulations of choice (e.g., revealed preference vs. utility maximization) as interchangeable without checking that they agree in overlapping cases. In these situations, the bridge between models breaks, signaling an inconsistency in how choice behavior is being generalized or approximated.
7) Statistical / probabilistic consistency
What it is:
All probabilistic elements used to model individual choice are internally coherent. If uncertainty, randomness, or stochastic choice is introduced, probabilities must be properly normalized, assigned consistently, and interpreted under a single probabilistic framework. Expected utility, choice probabilities, and belief updates must align so that probabilistic statements about choice correspond to one another and to the underlying decision environment.
Typical failure:
The model mixes incompatible probabilistic interpretations or violates basic probability rules. Common failures include defining stochastic choice probabilities that do not sum to one; combining frequentist error terms with Bayesian belief updates without reconciling the two; or specifying expectations that do not match the implied probability distribution over outcomes. Another frequent error is introducing randomness at the choice level while simultaneously interpreting outcomes as if they reflected deterministic utility maximization. In these cases, the probabilistic structure of the choice model contradicts itself, making its predictions internally inconsistent.
8) Operational / measurement consistency
What it is:
The theoretical constructs used in choice theory—such as preferences, utility, beliefs, constraints, and expectations—are measured or inferred in ways that genuinely correspond to their definitions in the model. Any empirical proxy or elicitation method (revealed preference, surveys, experiments, observed choices under constraints) must align with the abstract concept it is meant to capture. Procedures for estimating utility, beliefs, or choice rules must be consistent with how those objects are defined in the theory.
Typical failure:
The measurement or inference procedure tracks a different construct than the theory assumes. Common failures include interpreting observed choice frequencies as cardinal utility levels when the theory only supports ordinal preferences; inferring stable preferences from behavior that is actually driven by changing constraints or information; or measuring beliefs or expectations using survey responses that do not correspond to the probabilistic objects assumed in the model. Another frequent error is mixing units or contexts—such as treating stated preferences, revealed preferences, and welfare measures as interchangeable without justification. In these cases, the operational definition breaks alignment with the theoretical construct, undermining consistency between theory and observation.
9) Cross-scale / multi-level consistency
What it is:
Descriptions of choice at different levels—such as moment-to-moment decisions, menu-level choice behavior, and aggregate choice patterns for a single agent over time—do not conflict with one another. When multiple representations of individual choice are used (e.g., static vs. dynamic choice, deterministic vs. stochastic choice), the relationships between these levels must be explicit and coherent. Higher-level summaries of choice behavior must be derivable from, or at least compatible with, the underlying choice rules assumed at the micro level.
Typical failure:
The model’s representations of choice at different levels contradict each other. Common failures include specifying stable preferences at the individual level while deriving aggregate choice patterns that imply systematic preference reversals; modeling dynamic choice behavior that, when collapsed into a static representation, violates the original choice axioms; or assuming consistent revealed preferences over time while introducing state-dependent or context-dependent choice rules without reconciliation. In these cases, the higher-level description of choice demands behavior that the lower-level choice rules cannot produce, signaling a cross-level inconsistency within the choice framework.
10) Numerical / discretization consistency
What it is:
When computational or numerical methods are used to analyze choice problems—such as discretizing choice sets, approximating utility functions, or simulating stochastic choice—the numerical representation must preserve the core constraints and properties of the underlying choice theory. Feasibility, budget balance, probability normalization, and preference orderings must not be violated by the discretization or algorithm. As approximations are refined, numerical results should converge toward the predictions of the theoretical choice model.
Typical failure:
The numerical implementation introduces artifacts that contradict the theory. Common failures include discretized choice sets that eliminate feasible optima; simulated choice probabilities that become negative or fail to sum to one; or numerical maximization routines that select dominated options due to coarse grids or rounding error. Another frequent error is approximating a continuous preference or constraint structure with a discrete one that breaks monotonicity or convexity assumptions relied upon by the theory. In these cases, the numerical results no longer faithfully represent the underlying choice model, and apparent conclusions reflect computational inconsistency rather than properties of choice itself.