Units are the formal standards that convert observed decision behavior into evidence. In Choice, units specify how individual decisions, comparisons, and responses are measured, stabilized, and rendered comparable across agents, observers, and contexts. Without units, choice observations remain descriptive or anecdotal; with units, they become evaluable.
A unit in Choice is not a label. It is a conventional mapping between a conceptual element of decision-making and a repeatable observational or elicitation procedure. This mapping is what allows observed choices to enter the evidence layer.
Function of Units
Within the SAT framework, units in Choice perform four irreducible functions:
- Stabilization — ensure repeated observations refer to the same kind of choice behavior.
Units fix what counts as the same decision, same option, or same response across repetitions, agents, and contexts, preventing drift in what is being measured. - Comparability — allow choices to be evaluated across agents, situations, and time.
Units make it possible to compare decisions without assuming identical preferences, utilities, or internal states, relying instead on observable decision criteria. - Aggregation — enable individual choice observations to be combined into frequencies, distributions, or patterns.
This supports movement from single decisions to population-level regularities while respecting the limits of interpersonal comparison. - Transmission — preserve semantic meaning as choice data move between observers, datasets, and analytical frameworks.
Units ensure that recorded decisions retain their meaning when transferred from subject to experimenter, experiment to dataset, or dataset to analysis.
If any function fails, evidence about choice degrades into impression, narrative, or ungrounded interpretation.
Conceptual Boundaries
Units in Choice must be distinguished from related concepts:
- Variables identify what choice behavior is observed; units define how it is quantified.
- Scales order or space observed responses; units anchor those responses to a defined decision magnitude or category.
- Indicators / proxies approximate latent preferences or utilities; units define the observable choice outcome itself.
- Dimensions describe abstract decision attributes (time, risk, value); units are the concrete instantiations used to record behavior.
Confusing these categories produces structural errors in choice evidence, often leading to false inference about preferences or rationality.
Validity Conditions
For a unit to function within the Evidence Layer for Choice, it must satisfy most of the following:
- Operational definability — tied to a repeatable choice task, elicitation method, or observation protocol.
- Stability — meaning does not drift across repetitions, agents, or contexts without explicit redefinition of the choice environment.
- Resolution — sufficient granularity to distinguish meaningful differences in decision behavior.
- Characterizable error — noise from inconsistency, framing effects, or elicitation procedures can be bounded or described.
- Inter-observer consistency — different observers record compatible choice outcomes under similar conditions.
Variation across individuals and contexts is expected and informative, but unit definitions must remain fixed.
Structural Types of Units
Fundamental Units
Fundamental units in Choice are the independently defined measurement standards that Choice relies on to record decision situations and outcomes. They are not created by economic theory, preference models, or choice frameworks; they are imported into Choice from physical, mathematical, or institutional systems and used directly.
These units do not rely on combinations, normalization, ranking, counting, or rule-based classification to exist. They remain meaningful even if all higher-level choice constructs are removed. In this sense, they form the measurement substrate on which all other choice evidence is built.
In microeconomic analysis, fundamental units anchor choice behavior to time, quantity, and probability as they are presented to agents at the moment of decision. They allow choices to be recorded as events occurring under specified conditions, without assuming anything about preferences, rationality, or optimization.
All derived, count, ordinal, index, and threshold units used in Choice ultimately depend on these fundamental units. If a fundamental unit is misdefined or unstable, every higher-level measure constructed from it inherits that instability.
Derived Units
Derived units in Choice are units that are constructed from combinations of other units through arithmetic or formal operations. They do not exist independently; their meaning and validity depend entirely on the definition, scale, and stability of the units from which they are built.
In microeconomic analysis, derived units combine fundamental units such as time, monetary amount, and probability to express structured properties of decision situations—differences between options, tradeoffs over time, and relationships between costs and outcomes. These units allow choice behavior to be compared and evaluated without invoking unobservable internal states.
Because derived units inherit all assumptions and limitations of their component units, they are conditionally valid. Any change in the reference, resolution, or interpretation of an underlying unit directly alters the derived unit. As a result, derived units are powerful for analysis but sensitive to mis-specification, especially when used across contexts or agents.
Derived units occupy the intermediate layer of Choice evidence: more informative than raw measurements, but still grounded in observable quantities. All higher-order constructions in Choice—such as indices, thresholds, and model-based parameters—ultimately depend on the correct specification of these derived units.
Count Units
Count units in Choice are units that represent discrete tallies of entities or events. They answer “how many”, not “how much”, “how intense”, or “how ranked.” Count units advance in integer steps and carry no internal magnitude beyond their numerical count.
In microeconomic analysis, count units are used to enumerate decision events, observations, agents, and outcomes under clearly specified definitions. They provide the raw quantitative backbone for summarizing choice data without imposing structure related to value, preference strength, or probability.
Count units are additive over identical entities or events, which makes them essential for aggregation and comparison across samples, experiments, and contexts. Their validity depends entirely on stable definitions of what is being counted; if the definition of an event, option, or agent changes, the count unit immediately loses comparability.
Within the Evidence Layer, count units serve a strictly descriptive role. They support statistical analysis and pattern detection, but they do not themselves explain behavior. Any interpretive meaning arises only when count units are combined with other unit types, such as derived, ordinal, or index units.
Ordinal Units
Ordinal units in Choice are units that encode order only, without conveying any information about magnitude, distance, or intensity. They specify which option comes before or after another within a defined choice set, but they do not indicate how much one option is preferred over another.
In microeconomic evidence, ordinal units are used to record positional relationships among options at a single moment of decision or elicitation. They operate strictly within a given choice context and do not require aggregation across trials or inference about underlying preferences. As such, they remain agnostic about utility, strength of preference, or rationality assumptions.
Ordinal units permit only order-preserving transformations. Any operation that treats rank positions as numerically spaced or metrically meaningful violates their evidentiary role. For this reason, ordinal units support comparisons of ordering but not arithmetic manipulation.
Within the Evidence Layer, ordinal units sit between raw counts and constructed indices. They provide structure without imposing measurement intensity. Their validity depends entirely on the stability of the choice set and elicitation protocol; if either changes, ordinal comparability immediately breaks.
Index Units
Index units in Choice are normalized or composite measures whose values are meaningful only relative to an explicit baseline. They do not represent raw observations or magnitudes; instead, they express how observed choice behavior compares to a reference condition built into the unit’s definition.
In microeconomic evidence, index units are constructed from more primitive units—typically counts or derived measures—and then normalized against a fixed benchmark, such as a designated reference option or a uniform choice distribution. Because the baseline is intrinsic, the absolute value of an index has no standalone interpretation outside that reference.
Index units enable comparison across options, contexts, or datasets without imposing behavioral rules or model assumptions. Their evidentiary role is comparative rather than descriptive: they show deviation from a baseline, not the underlying causes of that deviation.
The validity of index units depends entirely on the stability and explicitness of their baseline. If the reference option or distribution changes, index values lose comparability immediately. For this reason, index units must always be reported together with their defining baseline to preserve evidentiary integrity within the SAT framework.
Threshold Units
Threshold units in Choice are units that represent categorical cutoffs tied to explicit rules. They convert continuous or complex inputs—such as time, resources, or eligibility conditions—into binary states where only the act of crossing the cutoff matters, not the distance from it.
In microeconomic evidence, threshold units are used to record whether a decision situation satisfies or violates a rule that conditions available actions or outcomes. Examples include budget constraints, eligibility requirements, and time limits. These units do not measure preference strength, value, or probability; they record rule activation.
Threshold units permit no arithmetic or order-based operations beyond classification. Treating them as magnitudes or rankings violates their evidentiary role. Their usefulness lies in clearly demarcating feasible versus infeasible, allowed versus disallowed, or on-time versus late states within a choice environment.
The validity of threshold units depends entirely on the stability and explicitness of the underlying rule. If the rule definition changes, threshold outcomes lose comparability immediately. Within the SAT framework, threshold units mark the boundary where institutional, procedural, or contextual constraints enter choice evidence.
SAT – Evidence – Units – Choice (Microeconomic Foundations)
| Unit | Unit Type | Measurement Structure | Reference Dependence | Transformability | Temporal Behavior | Error Profile | Aggregation Compatibility | Interpretive Load | Boundary Conditions |
|---|---|---|---|---|---|---|---|---|---|
| Second | Fundamental | Continuous, additive, linear, unbounded | Absolute (physical standard) | Differences, ratios, scaling | Time-indexed, instantaneous or cumulative | Instrument resolution, recording error | Fully aggregatable | Minimal (purely quantitative) | Breaks at relativistic / non-operational scales |
| Millisecond | Fundamental | Continuous, additive, linear, bounded by instrument | Absolute (physical standard) | Differences, ratios, scaling | Time-indexed, instantaneous | Resolution limits, clock precision | Fully aggregatable | Minimal | Invalid below measurement resolution |
| Currency Unit (e.g., dollar) | Fundamental | Continuous, additive, linear | Institutional absolute (legal definition) | Differences, ratios, inflation-adjusted conversions | Time-indexed, stock or flow | Reporting error, denomination changes | Aggregatable within same currency regime | Moderate (institutional meaning) | Invalid across regimes or redenomination |
| Currency Subunit (e.g., cent) | Fundamental | Discrete, additive, linear | Institutional absolute | Differences, ratios | Time-indexed | Rounding, discretization error | Aggregatable within same currency | Moderate | Breaks under rounding or currency reform |
| Probability (0–1) | Fundamental | Continuous, bounded, nonlinear at extremes | Axiomatic absolute | Differences, ratios (not additive) | Timeless per presentation | Elicitation error, misunderstanding | Aggregatable only under identical definitions | Moderate (interpretive risk) | Invalid if probabilities are subjective or inconsistent |
| Percentage | Fundamental | Continuous, bounded, normalized | Relative (representation of probability) | Differences, ratios | Timeless | Representation and scaling error | Same as probability | Moderate | Invalid if baseline shifts |
| Physical Quantity Unit (when explicit) | Fundamental | Continuous, additive | Absolute physical reference | Differences, ratios | Context-dependent | Instrument and unit conversion error | Aggregatable within same unit | Minimal–moderate | Invalid outside defined physical context |
| Delay (time until outcome) | Derived | Continuous, additive, linear | Absolute (time standard) | Differences, ratios | Time-indexed, cumulative | Timing and recording error | Aggregatable under identical conditions | Low | Invalid if outcome timing is undefined |
| Waiting Time | Derived | Continuous, additive, linear | Absolute (time standard) | Differences, ratios | Time-indexed, cumulative | Measurement and censoring error | Aggregatable with consistent definitions | Low | Breaks under truncated observation |
| Response Latency | Derived | Continuous, additive, linear | Absolute (time standard) | Differences, ratios | Instantaneous per decision | Instrument resolution, reaction noise | Aggregatable across comparable tasks | Low | Invalid if decision onset unclear |
| Price Difference | Derived | Continuous, additive, linear | Relative (currency unit) | Differences, ratios | Timeless per comparison | Reporting and denomination error | Aggregatable within same currency regime | Moderate | Invalid across currencies or regimes |
| Payoff Difference | Derived | Continuous, additive, linear | Relative (currency unit) | Differences, ratios | Timeless per option set | Outcome recording error | Aggregatable under consistent payoff definitions | Moderate | Breaks if payoff definitions change |
| Cost Difference | Derived | Continuous, additive, linear | Relative (currency unit) | Differences, ratios | Timeless | Accounting and classification error | Aggregatable within consistent cost definitions | Moderate | Invalid if costs are reclassified |
| Net Payoff | Derived | Continuous, additive, linear | Relative (payoff minus cost) | Differences, ratios | Timeless | Propagated component error | Aggregatable under stable components | Moderate | Invalid if components are incomparable |
| Opportunity Cost | Derived | Continuous, additive, linear | Relative (forgone payoff baseline) | Differences only | Context-dependent | Counterfactual specification error | Not directly aggregatable across agents | High | Invalid if counterfactual is ill-defined |
| Expected Value | Derived | Continuous, additive, linear | Relative (probability-weighted outcomes) | Differences, ratios | Timeless per option | Probability & payoff specification error | Aggregatable under identical definitions | Moderate | Invalid if probabilities or outcomes are ill-defined |
| Expected Payoff | Derived | Continuous, additive, linear | Relative (probability × payoff) | Differences, ratios | Timeless per option | Elicitation & outcome error | Aggregatable with consistent payoff spaces | Moderate | Breaks if payoff domain shifts |
| Expected Loss | Derived | Continuous, additive, linear | Relative (probability × loss) | Differences, ratios | Timeless per option | Loss framing & probability error | Aggregatable under consistent loss definitions | Moderate | Invalid if loss reference changes |
| Variance of Outcomes | Derived | Continuous, non-additive, nonlinear | Relative (mean-referenced) | Differences only (no ratios) | Timeless per option | Estimation & sample error | Limited aggregation (requires homogeneity) | Moderate | Invalid under nonstationarity |
| Standard Deviation of Outcomes | Derived | Continuous, non-additive, nonlinear | Relative (variance-based) | Differences only | Timeless per option | Propagated variance error | Limited aggregation | Moderate | Invalid if distribution assumptions fail |
| Discounted Payoff | Derived | Continuous, additive, nonlinear | Relative (discount factor & time) | Differences, ratios | Time-indexed | Discount factor misspecification | Aggregatable under same discounting rule | Moderate–high | Invalid if discounting regime changes |
| Present Value | Derived | Continuous, additive, nonlinear | Relative (time-zero baseline) | Differences, ratios | Time-indexed (collapsed to present) | Discounting & timing error | Aggregatable with identical discount rules | Moderate–high | Invalid across discount regimes |
| Future Value | Derived | Continuous, additive, nonlinear | Relative (future baseline) | Differences, ratios | Time-indexed (projected) | Projection & rate error | Aggregatable under same growth rules | Moderate–high | Invalid if growth assumptions change |
| Expected Discounted Value | Derived | Continuous, additive, nonlinear | Relative (probabilities + discount factor + time) | Differences, ratios | Time-indexed | Compounded specification error | Aggregatable only under identical rules | High | Invalid if probability/discount regime differs |
| Price Ratio | Derived | Continuous, dimensionless, nonlinear | Relative (currency cancels) | Ratios only | Timeless | Denominator sensitivity, reporting error | Aggregatable under comparable contexts | Moderate | Invalid if denominators approach zero or regimes differ |
| Payoff Ratio | Derived | Continuous, dimensionless, nonlinear | Relative (payoff cancels) | Ratios only | Timeless | Denominator sensitivity, payoff definition error | Limited aggregation across heterogeneous payoffs | Moderate | Invalid if payoff definitions differ |
| Cost–Benefit Ratio | Derived | Continuous, dimensionless, nonlinear | Relative (cost vs benefit definitions) | Ratios only | Timeless or time-indexed | Definition and classification error | Limited aggregation | High | Invalid if costs/benefits are not commensurate |
| Discount Rate | Derived | Continuous, nonlinear | Relative (time base + discounting convention) | Differences, ratios | Time-indexed | Estimation and convention error | Aggregatable only under same compounding basis | High | Invalid if time base or compounding changes |
| Implied Discount Rate | Derived | Continuous, nonlinear | Relative (inferred from observed indifference) | Differences, ratios | Time-indexed | Inference error, noise sensitivity | Not directly aggregatable across agents | High | Invalid if indifference condition is unstable |
| Payoff per Unit Time | Derived | Continuous, nonlinear | Relative (payoff ÷ time) | Differences, ratios | Time-indexed (rate) | Propagated payoff/time error | Aggregatable under consistent units | Moderate | Invalid if time measurement is inconsistent |
| Number of Decision Events | Count | Discrete, additive | Contextual (event definition) | Addition only | Time-indexed | Event classification error | Fully aggregatable | Minimal | Invalid if event definition changes |
| Number of Decision Trials | Count | Discrete, additive | Contextual (trial protocol) | Addition only | Time-indexed | Protocol inconsistency | Fully aggregatable | Minimal | Breaks if trial structure changes |
| Number of Observations | Count | Discrete, additive | Contextual (observation rule) | Addition only | Time-indexed | Recording error | Fully aggregatable | Minimal | Invalid under missing data |
| Number of Agents | Count | Discrete, additive | Contextual (agent definition) | Addition only | Timeless per dataset | Identification error | Aggregatable across datasets | Minimal | Invalid if agent identity changes |
| Observations per Agent | Count | Discrete, additive | Relative (agent-level grouping) | Addition only | Time-indexed | Assignment error | Aggregatable under stable grouping | Low | Invalid if agent grouping shifts |
| Number of Times Option A Is Chosen | Count | Discrete, additive | Contextual (option definition) | Addition only | Time-indexed | Option coding error | Fully aggregatable | Low | Invalid if option set changes |
| Number of Times Option B Is Chosen | Count | Discrete, additive | Contextual (option definition) | Addition only | Time-indexed | Option coding error | Fully aggregatable | Low | Invalid if option set changes |
| Number of Times Each Option Is Chosen | Count | Discrete, additive | Contextual (menu definition) | Addition only | Time-indexed | Menu classification error | Aggregatable within menu | Low | Invalid if menu changes |
| Number of Acceptances | Count | Discrete, additive | Contextual (accept/reject rule) | Addition only | Time-indexed | Classification error | Fully aggregatable | Low | Invalid if rule definition changes |
| Number of Rejections | Count | Discrete, additive | Contextual (accept/reject rule) | Addition only | Time-indexed | Classification error | Fully aggregatable | Low | Invalid if rule definition changes |
| Number of Participations | Count | Discrete, additive | Contextual (participation rule) | Addition only | Time-indexed | Participation coding error | Fully aggregatable | Low | Invalid if eligibility changes |
| Number of Non-Participations | Count | Discrete, additive | Contextual (participation rule) | Addition only | Time-indexed | Participation coding error | Fully aggregatable | Low | Invalid if eligibility changes |
| Number of Switches | Count | Discrete, additive | Contextual (switch definition) | Addition only | Time-indexed | Sequence coding error | Aggregatable under same protocol | Low | Invalid if baseline choice undefined |
| Number of Non-Switches | Count | Discrete, additive | Contextual (switch definition) | Addition only | Time-indexed | Sequence coding error | Aggregatable under same protocol | Low | Invalid if baseline choice undefined |
| Number of Delayed Choices | Count | Discrete, additive | Contextual (delay definition) | Addition only | Time-indexed | Timing classification error | Aggregatable under same threshold | Low | Invalid if delay threshold shifts |
| Number of Immediate Choices | Count | Discrete, additive | Contextual (delay definition) | Addition only | Time-indexed | Timing classification error | Aggregatable under same threshold | Low | Invalid if delay threshold shifts |
| Number of Errors (Protocol-Defined) | Count | Discrete, additive | Contextual (error rule) | Addition only | Time-indexed | Definition and coding error | Aggregatable under identical rules | Moderate | Invalid if error definition changes |
| Rank order of options within a single choice set | Ordinal | Discrete, ordered, non-metrical | Contextual (defined menu) | Order-preserving relabeling only | Timeless per elicitation | Ordering/recording error | Not aggregatable beyond counts of ranks | Low | Invalid if menu changes |
| Rank position of chosen option within the menu | Ordinal | Discrete, ordered, non-metrical | Contextual (menu + ordering) | Order-preserving relabeling only | Timeless per choice | Misordering/mapping error | Aggregatable only as counts by position | Low | Invalid if ordering rule changes |
| First-choice / second-choice / nth-choice designation | Ordinal | Discrete, ordered, non-metrical | Contextual (elicitation protocol) | Order-preserving relabeling only | Timeless per elicitation | Elicitation/labeling error | Aggregatable only as counts by designation | Low | Invalid if elicitation protocol changes |
| Choice share indexed to a designated baseline option | Index | Continuous, normalized, dimensionless | Explicit baseline option (fixed reference) | Differences, ratios (baseline-preserving) | Timeless per measurement | Sampling error, baseline mis-specification | Aggregatable only with identical baseline | Moderate | Invalid if baseline option changes or is absent |
| Choice distribution indexed to a uniform baseline | Index | Continuous, normalized, composite | Explicit uniform-distribution baseline | Differences, ratios (baseline-preserving) | Timeless per measurement | Sampling error, normalization error | Aggregatable only under same uniform reference | Moderate | Invalid if option set changes or uniform baseline is redefined |
| Budget constraint satisfied / violated | Threshold | Binary, non-metrical | Explicit budget rule (price ≤ budget) | None beyond classification | Timeless per choice | Price/budget measurement error | Aggregatable as counts across identical rules | Low | Invalid if budget definition changes |
| Eligibility threshold met / not met | Threshold | Binary, non-metrical | Explicit eligibility criteria | None beyond classification | Timeless per decision | Classification and rule-application error | Aggregatable under identical criteria | Low | Invalid if eligibility rules change |
| Deadline met / missed | Threshold | Binary, non-metrical | Explicit time cutoff | None beyond classification | Time-indexed | Timing/recording error | Aggregatable under same deadline | Low | Invalid if deadline definition shifts |
| Time limit exceeded / not exceeded | Threshold | Binary, non-metrical | Explicit time-limit rule | None beyond classification | Time-indexed | Timing/measurement error | Aggregatable under same limit | Low | Invalid if time limit changes |