“Estimates”: five factors, seven assessments and temple calculation

In plain language: Therefore measure it by five factors, compare by assessment, and so seek out the true situation: the first is the Way, the second Heaven, the third Earth, the fourth the general, the fifth method. … Therefore compare by assessment and seek out the true situation, asking: Which ruler has the Way? Which general has ability? Which side has Heaven and Earth? Whose laws and orders are carried out? Whose troops are stronger? Whose officers and soldiers are better trained? Whose rewards and punishments are clearer? By these I know victory and defeat. Now, one who before battle wins in the temple calculation has obtained many suan; one who before battle does not win in the temple calculation has obtained few. Many suan win, few do not, still less none at all! Looking at it in this way, victory and defeat are plain to see.

First, the original sense. Ji here is estimation and comparison before war, and the body of the chapter consists of the “five factors” and the “seven assessments”: all seven questions take the form “which side…?”, that is, an item-by-item comparison of which side holds the advantage. “Temple calculation”, in the usual explanation of later commentators and modern scholars, is the planning and reckoning of the two sides’ conditions in the ancestral temple or at court before an army set out; that before a campaign rites were held and state affairs deliberated in the ancestral temple is its historical setting.

Two common claims need the text separated from its interpretation. First, does suan mean counting rods? The character can denote the tallies used for counting, and some modern translators read the passage as “reckoning with counting rods at court, and whoever obtains more rods wins”; the Denma translation, for example, renders “obtains many suan” as obtaining many counting rods, and, on the basis of a quotation in the encyclopaedia Beitang shuchao and the space on a fragmentary Yinqueshan bamboo slip, follows the reading “many counting rods are victorious over few” for the sentence “many suan win, few do not” (Denma Translation Group 2001). Other readings take suan as calculation and planning in a general sense. The text itself does not say whether tallies were actually used; this is interpretation, not text. Second, were the “five factors and seven assessments” weighted and scored item by item? The text has only “measure by the five factors, compare by assessment” and the seven “which side…?” questions; it assigns no weights and gives no rule for adding them up. Describing it as a weighted scoring model is a later elaboration.

On that understanding, what can be set beside modern research is a structure: before acting, break the judgement into items and compare them one by one, instead of deciding on an overall impression. This has something in common with the superforecasters’ “breaking the question into parts that can be estimated” (Chapter 1) and with reference-class forecasting’s “first the class, then the case” (Chapter 5). Decision research has also found that in many prediction tasks a simple rule that adds several relevant factors with equal weights often does no worse than a model with carefully estimated weights, and beats experts’ holistic intuition (Dawes 1979). If “obtaining many suan” is read as counting the favourable items, it resembles this equal-weight tallying in form.

But the differences are just as fundamental. Sunzi’s “win” and “not win” are categorical pronouncements, “victory and defeat are plain to see”, not “a 70 % chance of winning”; he distinguishes neither calibration nor resolution, and has no mechanism for scoring the temple calculation afterwards to see whether it was right. Probabilistic judgement in the modern sense is precisely the rewriting of “plain to see” as a number that outcomes can test.

“Assessing”: what is weighing power?

In plain language: Those of old who were good at managing the world always weighed the power of the world and assessed the dispositions of the feudal lords. If power is not weighed carefully, one does not know how strength and weakness, heavy and light, compare; if dispositions are not assessed carefully, one does not know the hidden changes and movements. What is weighing power? It is to measure great and small, and to reckon many and few; to weigh how much wealth there is and is not, to estimate how many the people are, whether rich or poor, and how much is in surplus or short; to distinguish where the terrain is difficult or easy, where advantage lies and where harm; whose plans are long-sighted and whose short; to examine the closeness of ruler and ministers, who is worthy and who is not; among the retainers, whose wisdom is less and whose more; to observe the fortunes of the season, what is auspicious and what ominous; in relations among the lords, who can be used and who cannot; in the hearts of the people, their changing allegiance, where there is security and where danger, who is loved and who hated; who can tell the fickle. One who can know all this is said to weigh power.

First, a common quotation must be corrected. The received Guiguzi has no chapter called “Weighing Power”; “weighing power” (liang quan) is a concept at the opening of the chapter “Assessing”, paired with “assessing dispositions” (chuai qing). The often-quoted sentence “weighing power is the means to measure great and small and to plan for strong and weak” is not in the received text, which reads “What is weighing power? It is to measure great and small, and to reckon many and few…”. Editions differ slightly in wording; this book follows the received text.

“Weighing power” lists a long checklist: territory, population, wealth, terrain, strategy, ruler and ministers, retainers, the season, diplomacy, the people’s hearts. What it shares with the “outside view” of Chapter 5 is the demand to gather comparable facts before judging, rather than relying on one’s impression of a particular ruler. But what the chapter goes on to call “assessing dispositions” is visiting the other party “when he is most pleased” or “when he is most afraid” so that emotion prevents him from hiding his true intentions; that belongs to the techniques of persuasion and intrigue and has nothing to do with the calibration and statistical inference discussed in this book, so this book does not take it up.

“Eminent Teachings”: to be certain without cross-checking is folly

In plain language: Confucius and Mozi both praised Yao and Shun, yet they accepted and rejected different things, and each claimed to present the true Yao and Shun. Yao and Shun will not live again; whom shall we have decide which of the Confucians and Mohists is genuine? The Yin and Zhou lie more than seven hundred years back, the Yu and Xia more than two thousand, and still no one can decide which of the Confucians and Mohists is true; now people wish to examine the way of Yao and Shun from three thousand years ago. Surely it cannot be made certain? To be certain of something without cross-checking it is folly; to rely on what one cannot be certain of is deceit. So those who openly appeal to the former kings and insist on what Yao and Shun were like are either fools or deceivers.

“Cross-checking” (canyan) is an important method in Han Fei’s thought: setting words against facts, names against realities, and comparing and testing them. The passage can be set beside two points of this book. First, “being certain without cross-checking” is the extreme form of the overconfidence of Chapter 2: reporting an untested judgement as 100 %. Second, “relying on what one cannot be certain of” amounts to making decisions on claims that are neither clear nor checkable. The forecasting tournaments’ demand that questions be unambiguously resolvable afterwards, and that forecasts be written as numbers, shares the spirit of “cross-checking”: a claim that cannot be tested does not count.

But the boundaries must be stated just as clearly. First, Han Fei’s “cross-checking” served the Legalist politics of a ruler checking his ministers and stripping away empty talk, and this passage’s immediate aim is to discredit the Confucian and Mohist interpretations of the former kings; it is strongly polemical. Second, “cross-checking” is qualitative comparison, not probabilistic calibration, still less anything with the modern statistical notions of sample and error. Third, the testing spirit of modern science has its own sources and institutions (reproducible experiments, pre-registered hypotheses, open data), and it cannot be said that Han Fei “had already proposed” them.

The limits of reading them together

Reading these three texts beside modern research has three limits. First, the classical texts concern war, diplomacy and royal rule; modern research concerns uncertain events in general and individual judgement, and their aims and values differ. Second, the classical texts make categorical pronouncements (“plain to see”, “fools or deceivers”), whereas the core of modern research is to express uncertainty as probability and to test probabilities against outcomes; that step is absent from the classical texts. Third, the plain-language readings in this chapter are the author’s; whether suan means counting rods, and how the “five factors and seven assessments” were applied, are understood differently in the commentarial tradition and among modern scholars.

Chapter summary

The Sunzi’s chapter “Estimates” requires an item-by-item comparison of the two sides by the “five factors and seven assessments” before war, and judges victory by “obtaining many or few suan” in the temple calculation; whether suan means counting rods, and whether the items were weighted, are later interpretations on which the text is silent. The Guiguzi’s “weighing power” appears in the chapter “Assessing” and is not a chapter title; the text reads “What is weighing power? It is to measure great and small, and to reckon many and few…”. The Han Feizi’s “to be certain without cross-checking is folly; to rely on what one cannot be certain of is deceit” shares the spirit of calibration and testability, but serves Legalist politics and is qualitative comparison, not statistical testing. All three stress comparison beforehand and checking afterwards, but none writes a judgement as a probability that can be scored. The next chapter offers a checklist and a trial protocol.