Plate vi in print

The Bound

Simon's bounded rationality; the chooser who searches until good enough, not until best.

The capacity of the mind for solving complex problems is small beside the size of the problems whose solution real choosing would require. No one can lay out every option, foresee every consequence, and compute the best of them; the world is too large and the reckoning too long. So the reasonable chooser does not maximize but satisfices — fixes a standard of what will do, searches until something meets it, and takes that, the looking itself being the dearest part of the choosing.

— the limit of this plate, after Herbert Simon, 1955

Five plates have pressed on the preference, and found it softer than advertised: not reliably there before the choosing, not faithful to transitivity, not definable apart from its setting, and not, past a modest abundance, even welcome. But the assumption this volume examines has two halves, not one. The standfirst named them together — a preference complete and consistent, and a choosing that merely maximizes it — and the plates so far have worried only the first. Grant, for the length of this plate, everything the others took away. Suppose a person equipped with a preference flawless and full: complete over every option, perfectly transitive, fixed regardless of menu or framing, undismayed by abundance. One question remains, and it is the question the whole apparatus was built to answer in the affirmative without ever quite asking it. Can such a person actually do the thing the theory says choosing is — survey the options, weigh each against the flawless preference, and select the maximum? The plate's wager, and Herbert Simon's, is that they cannot, and that the failure is not a flaw in them but a fact about the task.

To maximize is to perform a particular and surprisingly heavy computation. It requires that the chooser have before her the whole set of available options — not a sample but the entirety — and that for each she trace out its consequences, often far into an uncertain future, and that she then rank the whole field and seize its top. State the requirement plainly against any choice that matters and it collapses of its own weight. The options are rarely a tidy list: the moves available in a game of chess outrun the atoms of the visible universe; the houses one might buy, the careers one might enter, the people one might marry are not enumerated anywhere, but must be sought out one by one, at cost. The consequences are not given but guessed, and guessed across a future that branches faster than any mind can follow. And the ranking, even were the options and outcomes somehow in hand, is a labor that grows beyond tractability as the field widens. The optimum, in short, is not a mark the chooser aims at and, through frailty, misses; it is a mark that for any finite intelligence was never computable to begin with. This is the turn that separates Simon's claim from the easy and absorbable observation that people err. A theory of ideal choosing can shrug off mistakes as noise scattered about a true best. It cannot shrug off the discovery that the true best was a quantity no one could have computed — that the optimization it places at the center of choice is, for the problems choosing actually faces, not a hard task but an impossible one.1

1. To maximize is to hold the whole option set, trace each option's consequences across an uncertain future, rank the field, and take the top. Against any real choice it collapses: the options are not enumerated but sought out at cost; the consequences are guessed across a branching future; the ranking grows intractable as the field widens. So the optimum is not a mark missed through frailty but one uncomputable for any finite mind. This is what separates Simon's claim from the absorbable observation that people err: the true best was never a quantity anyone could have found.

What, then, does a chooser do instead, since choose she plainly does? Simon's answer is that she satisfices: she replaces the demand for the best with a demand for the good enough, and stops when she has met it. In place of the optimum she sets an aspiration level — a threshold, a standard of acceptability — and she searches the options not exhaustively but sequentially, examining them one at a time and taking the first that clears the bar. The shopper does not survey every loaf in the city and buy the ideal one; she walks to the nearest acceptable bakery and buys a good-enough loaf. The firm does not compute the profit-maximizing price; it adjusts last year's price until complaints and stock both fall to a tolerable level, and leaves it there. The job-seeker does not interview with every employer on earth; she accepts the first offer that meets her standard, and stops looking. In each case the search itself is the costly thing — every option examined takes time and effort and forgone alternatives — and so the rule that ends the search early, at the first sufficient option rather than the best possible one, is not laziness but economy. Stopping is the whole art. The optimizer never stops, because there is always, in principle, a better option unexamined; the satisficer stops the moment the good enough appears, and is thereby able to choose at all.2

2. A chooser satisfices: she replaces the best with the good enough and stops on meeting it. In place of the optimum she sets an aspiration level — a threshold of acceptability — and searches sequentially, taking the first option that clears the bar. The shopper buys at the nearest acceptable bakery; the firm adjusts last year's price until complaints fall to a tolerable level; the job-seeker takes the first offer meeting her standard. Search is the costly thing, so stopping early at the sufficient rather than the best is economy, not sloth. Stopping is the whole art.
⁂

The threshold is not fixed, and watching it move shows satisficing to be less a crude shortcut than an adaptive method in its own right. The aspiration level rises and falls with experience. Where options keep clearing the bar with ease, the chooser raises it, growing pickier as good outcomes prove plentiful; where nothing clears it for a long and discouraging stretch, she lowers it, learning to accept what the world is actually offering rather than holding out for a standard it will not supply. The level floats, in other words, toward the neighborhood of the attainable — high enough to refuse the poor, low enough to be met by the available — and in doing so it performs, without any optimizing, a rough and serviceable calibration of demand to reality. This is why satisficing is not merely the optimizer's behavior degraded by error. It is a different procedure with a logic of its own: set a standard, search until it is met, adjust the standard as the search teaches what is on offer, and stop. A chooser following it need never compute a maximum, never enumerate the options, never trace the branching future — and yet she will, in most ordinary environments, end with an outcome that is decent, arrived at in finite time, by a mind of finite power. She trades the unreachable best for the reachable good, and the trade is the only one a bounded creature was ever in a position to make.3

3. The aspiration level is not fixed: it rises where options clear it easily (the chooser grows pickier) and falls where nothing clears it (she settles for what the world offers), floating toward the attainable — high enough to refuse the poor, low enough to be met. So satisficing calibrates demand to reality without optimizing. It is not the optimizer degraded by error but a procedure of its own: set a standard, search until met, adjust as the search teaches what is on offer, stop. No maximum computed, no options enumerated, yet a decent outcome in finite time.

Behind the method lies a redrawing of what rationality is, and it is the deepest thing the plate has to offer the volume. The theory the other plates examined holds an implicit and demanding picture: a choice is rational if it is the objectively best available, given the chooser's situation and preferences — rationality as a property of the outcome selected, the optimizer's standard. Simon's bounded rationality proposes another: a choice is rational if it issues from a sensible procedure, a reasonable way of searching and deciding given the chooser's real limits of knowledge and computation — rationality as a property of the process, not the result. The distinction is between being right and going about things reasonably, and once the optimum is conceded to be uncomputable, only the second standard remains available at all. A chooser cannot be faulted for failing to select a best that no one could identify; she can only be asked to have searched and stopped in a defensible way. So rationality migrates from the outcome to the method — from the impossible question, did you choose the best, to the answerable one, did you choose sensibly given what choosing actually costs. The boundedly rational agent is not the rational agent with a worse score. She is rational under a different and more honest definition, the only one a finite mind can satisfy.4

4. Bounded rationality redraws what rationality is. The other plates assumed substantive rationality: a choice is rational if it is the objectively best available — rationality as a property of the outcome. Simon proposes procedural rationality: a choice is rational if it issues from a sensible process given real limits of knowledge and computation — a property of the method. Once the optimum is conceded uncomputable, only the second remains. Rationality migrates from whether you chose the best to whether you chose sensibly given what choosing costs. The bounded agent is not the rational agent with a worse score, but rational under the only definition a finite mind can meet.

This is the seam, and it lies beneath the other five. They showed the preference to be less solid than the theory needs — not there before the choice, not transitive, not free of its frame, not improved by plenty. This plate grants the preference entire and shows that the second half of the assumption fails on its own: that even a flawless ranking cannot be maximized by any creature that must actually do the choosing, so the optimization the model installs at the center of the act was never within reach, and what sits there in fact is search with a stopping rule. The two halves of the floor give way together, and from opposite sides.5 The chooser the axioms drew — ranging over the complete field, ranking it whole, lifting out the maximum — was not a description of a person at all but a portrait of a god, for whom alone the survey is free and the computation instant. The person, the actual finite person the whole edifice rests upon, does something humbler and entirely different: she fixes a standard of enough, looks until she finds it, and stops. The best was never what she chose, because the best was never something she could find; what she chose was the good enough, and to have called that choosing the maximization of a preference was to mistake a limited creature's reasonable search for a calculation no creature could perform.

5. This seam lies beneath the other five. They showed the preference less solid than the theory needs; this plate grants the preference entire and shows the second half of the assumption fails on its own — even a flawless ranking cannot be maximized by a creature that must do the choosing, so what sits at the center of the act is not optimization but search with a stopping rule. The chooser the axioms drew, ranging over the whole field and lifting out the maximum, was a portrait of a god; the finite person fixes a standard of enough, looks until she finds it, and stops.