A departure has a direction only after a line has been drawn. The earlier Collected Bias opened with that fact and closed by turning it upon the mind that does the measuring. Between those ends lay the patterned failures of judgment: an irrelevant anchor, an owned object valued differently, an unrecoverable expenditure permitted to govern another one. The patterns matter because they make behavior intelligible where the simplest account of choosing would not predict it. Yet describing a departure and condemning it are different achievements. One must identify the rule, establish that its conditions apply, and say what is lost when it is broken. A model can be a useful description, a standard of consistency, a forecasting instrument or a guide to welfare. The same observation can challenge one of those purposes without deciding all the others.
Some standards make a narrow demand that requires no impossible intelligence. If two payments arrive at the same time under identical conditions, and only the amount matters to a chooser who prefers more money, ten is better than eight. Changing the label on those payments does not change that comparison. This is the force of a consistency requirement: hold the relevant objects fixed and ask whether the ranking survives an alteration that should be irrelevant. But the relevant objects must actually be fixed. If obtaining ten requires an effort valued at six, while obtaining eight requires an effort valued at three, the net values in this illustration are four and five. Choosing the smaller receipt now conforms to the stated objective. Adding the omitted cost repairs the description of the choice. It does not establish that a person faced with the original, costless payments would be right to mistake eight for ten.1
A forecasting rule faces a further test: how well does it predict what has not yet been observed? Gigerenzer and Gaissmaier's account of heuristic decision making directs attention to the relation between a strategy and its environment. The comparison is with other usable strategies, given the available observations, uncertainty and costs. An elaborate model can fit a small sample closely while learning its accidents; a simpler rule can sometimes predict new cases better. The word sometimes carries the result. Sparse information does not confer accuracy by itself, and abundant information does not oblige a careful method to misuse it. What must be compared is the performance of specified procedures under specified conditions. That turns an invocation of bounded rationality into a testable inquiry: which information is used, how is it used, and what happens when the environment changes?2
Even the word bias changes its job in this comparison. In statistical estimation it can mean the difference between an estimator's average answer and the quantity being estimated. Suppose an unknown quantity is ten. An illustrative procedure gives either six or fourteen with equal probability: its average is right, but its squared error is sixteen either way. A rigid rule that always says eight is biased by minus two, yet its squared error is only four. Under this scoring rule it performs better at that true value. Now let the unknown quantity be zero while the first procedure still errs by plus or minus four. Its mean squared error remains sixteen; the rule that always says eight now has an error of sixty-four. The comparison has reversed. The analyst supplied the true values to evaluate the procedures; the decision maker was not given an oracle. The example shows why a statistical bias can coexist with lower prediction error, not why a familiar mistake must be beneficial.3
The evidence must therefore keep the chooser, the rule and the setting in view. A group average can hide different methods used by different people. A pattern that persists across several settings may still weaken or reverse in another. A successful prediction does not establish that the proposed psychological process produced it, just as a failure does not by itself identify which shortcut was used. The ecological program's demand for formal, comparative tests is valuable here: a name such as availability or intuition should specify enough to risk being wrong. The same discipline applies to an optimizing model. Its objects, information and constraints must be stated before the behavior is scored. Neither description earns authority merely by sounding more exact, more humane or more realistic. The standard has to expose the difference it claims to measure.4
Welfare poses a question that predictive accuracy alone cannot answer. Correctly forecasting what someone will choose does not establish that the choice serves her; identifying an inconsistency does not establish which correction would. The preceding volume on choice made this separation unavoidable. Bernheim and Rangel's behavioral welfare framework offers one disciplined response: retain guidance from the coherent aspects of choice while admitting ambiguity where choices conflict. Its use requires decisions about what counts as the object chosen, which features of presentation are ancillary, and which choice situations belong in the welfare-relevant domain. Those decisions can be argued for and examined; they do not disappear into the act of observing. The result is neither a license for the observer to substitute any preferred outcome nor a demand that every decision certify its own benefit. It is a way to state what the evidence supports and what further judgment the intervention requires.5
The baseline gives the catalogue its force by making its accusations specific. A probability can be inconsistent with the stated events; a forecast can perform badly on new observations; a decision can defeat the end the chooser herself endorses. These are consequential findings, and they need not rise or fall together. The task is to preserve their precision when moving from experiment to explanation, and from explanation to action. This volume has followed a mind that must judge with limited time and evidence, and whose shortcuts can carry both competence and error. Its final question belongs equally to the model brought against that mind. What does the measure hold fixed, what does it leave out, and for what purpose is it being used? The numéraire supplies a unit in which values can be compared. When the object of comparison is reason itself, choosing the unit becomes part of the argument.