Gerald Ajam

Plural models before the right model

The contribution that stops an analysis betting everything on one picture of the situation. It builds several partial models, each wrong in a different way, and acts on what they agree about. Where they disagree, it treats the disagreement as information about where to look next.

All seven contributions
On the arc
3 of 7 · How we know
The shift
From one model to many partial ones
Carried by
Holding the frame lightly

What would other credible models say, and what survives across them?

Cilliers showed that complex systems are incompressible. Every model leaves something out, and you cannot know in advance whether what it left out matters. So the search for the right model is the wrong search. This contribution uses several partial models on purpose, built on different simplifications, and trusts the conclusions that survive across them. Levins called that “the intersection of independent lies”. Plurality is treated as a permanent condition, not a stage on the way to agreement. The method is strongest where single-model confidence is the usual cause of failure. It is weakest when the models are not really independent, or when nobody is willing to conclude anything at all.

WHAT SURVIVES ACROSS THEM
Every model leaves something out, so use several and trust what survives across them

Outside school

Three forecasts for Saturday

You are planning a long walk on Saturday. One weather app says rain from two o’clock. Another says dry. A third says scattered showers. You do not pick the app you trust most and ignore the others. If all three had shown rain, you would have packed a coat without thinking. Because they split, you choose a route that passes a café halfway, and you decide at the café.

That is the whole idea at domestic scale. Agreement across different models is worth more than the confidence of any one. Disagreement is worth something too: it tells you the day is genuinely uncertain, and that the plan should be easy to change. Forecasters do a formal version of this. They run their models many times with slightly different starting conditions and read the spread of results as a measure of how far to trust the forecast.

Levins made it a method for science in 1966. Every model of a living system has to sacrifice something, so he built several with different simplifications and trusted what they agreed on. In his phrase, “our truth is the intersection of independent lies”. The word doing the work is independent. Three apps that all repackage the same underlying forecast are one model shown three times, and their agreement tells you nothing new.

The idea is much older than Levins. The Jain doctrine of anekāntavāda holds that reality is many-sided, and that any single proposition captures one aspect of it. Its companion, syādvāda, qualifies every claim as true “in some respect”. This stops short of relativism, because each claim is true within its respect. The doctrine is a worked-out grammar for holding several partial models at once without collapsing them into one.

The term

Four models of the same learning

Every page follows the same Singapore secondary school through the same semester, Term 1 and Term 2. The school is changing how it assesses, both of learning and for it: fewer weighted assessments, more feedback, and ratings that are meant to say something. The five people and the events of the semester stay fixed. Only the contribution reading them changes.

All five, interconnected

One day 13 beats

The five threads interleaved across the twelve weeks, so the hand-offs between them are visible. Pick a person to follow their term on its own. The people are illustrative, and the same five appear on every contribution’s page.

Term 1, Week 3

Mrs Lim and Mr Ravi, after the first ratings

Parents read Developing as a fall, and the phones start. Mr Ravi says the scale is one account of what a Secondary 2 student knows, and his department holds another. Mrs Lim asks him to write it on one page, with what would show it wrong. Then she asks the tracking-system supplier to do the same for the scale, and gets a brochure.

Term 1, Week 4

Aisyah, comparing ratings

Aisyah is Developing in science and Secure in English, in the same fortnight. Science rates against the end of the year and English against the current unit, so one scale is quietly running two models. Her friends decide science is “harsh”, which is a third.

Term 1, Week 5

Mr Ravi, writing it down

He writes the science model in an hour. Learning shows first as fewer common mistakes, so watch the mistakes, not the comments in books, and it would be proved wrong if errors stayed flat under whole-class feedback. He starts whole-class feedback in Secondary 2 that week, outside the policy. Writing the model down is harder than complaining about the scale, because now his own idea can fail.

Term 1, Week 6

Mdm Rohani, at 3am on a break

The class parents’ chat group has its own model, and it is simple. A test score tells you where your child stands, the school has stopped giving them, so families must buy them back. Tuition centres with practice papers are full by Friday. Mdm Rohani opens a tuition centre’s website twice and does not sign Aisyah up, mainly because she cannot tell what it would change.

Term 1, Week 8

Ms Tay, reading the four columns

Mrs Lim sends a single page with four columns: the rating scale, the science model, the parents’ chat, and the cluster superintendent’s office’s own, in which consistent feedback in books means students are learning. The first book check has just rated humanities “inconsistent”, and teachers are already writing longer comments for the next one. All four models can live with the compliance figure rising, because teachers can raise it without anyone learning more. So the figure, the only thing her office collects about feedback, cannot tell any of them apart.

Term 1, Week 10

The staff premortem

Mrs Lim asks staff to imagine it is June and the plan has failed, and to write why. The answers sort roughly by model: the scale tells parents nothing, the books fill with comments nobody reads, families buy the tests back, the checkpoint decides everything anyway. The three probes are chosen because each could separate two models. English signs up only for the quiz, the one probe that leaves nothing in a book.

Term 2, Week 2

Aisyah, in the fortnightly quiz

The quiz finds a Secondary 2 misconception about energy that the checkpoint would not have shown until the end of the semester. Aisyah gets nearly everything else right, again, and no rating on the app says so, because the quiz is never recorded. The science model has produced its first evidence. The other three models have no column to put it in.

Term 2, Week 2

Mrs Lim, reading the allied educator’s note

The allied educator for learning support notes that students still building their English are rated Emerging in nearly everything. It is a fifth model nobody had put on the page: the scale’s assumption that understanding shows up as written explanation. It was also the only one that reached parents automatically. Nobody had written it down, because nobody had seen it as a choice.

Term 2, Week 4

Aisyah and Mdm Rohani, the checkpoint

Aisyah freezes in the timed English paper and is rated Emerging. To the parents’ model this is the first honest number all semester, and to the science model it is one bad hour against eight good quizzes. Mdm Rohani complains through the app. A teacher quietly rates borderline students up, which turns the rating, for a week, into a model of who complains.

Term 2, Week 5

Ms Tay, reading the cluster newsletter

The newsletter cites the school as an exemplar of “feedback culture”, on the strength of 96 per cent of books compliant. Ms Tay has the four-column page in her drawer. Every model on it predicted that number, including the ones that say the plan is doing harm. Her office has praised a result that confirms nothing.

Term 2, Week 6

Mrs Lim, with the finance committee

The supplier offers a further discount to extend to five years and lock in the five-point scale. It is the best choice under one model, the scale’s own. Under each of the other three a five-year lock-in is the worst case, and one year at a higher price is acceptable under all four. The finance committee calls that paying extra for doubt, and she does not have a better answer than yes.

Term 2, Week 8

Mdm Rohani and Mr Ravi, at the Saturday Meet-the-Parents session

Mr Ravi shows Mdm Rohani Aisyah’s quiz record, and she sees learning the Emerging did not show. He hears his model confirmed, then stops. The parents’ model has an answer too: Aisyah knows the science, and will still be judged one day by a timed paper she cannot yet sit. Two models fit the same girl, and the semester has produced nothing that says which one the school should report.

Term 2, Week 10

Ms Tay, drafting a proposal

She proposes the cluster stop collecting twice-a-term ratings. Her case is plain. Of the four models, hers was the only one the semester could not test, because its only evidence was the figure every model expected to rise. She suggests asking schools what their quizzes are finding, in words, and her manager asks what will go in the termly report.

Laid side by side, the four models agreed on one thing worth acting on: ratings and book checks can rise with no change in what students know, so neither should be read alone. Their disagreements told the school which probes to run. What stayed open is the question that mattered most to Mdm Rohani: whether Aisyah is the student in the quiz record or the one in the checkpoint, and which of them the school should report. The semester ended with two good accounts and no test that could choose between them.

Implications

What this contribution adds, and how it goes hollow

The same five dimensions for all seven contributions. Read them across on the compare page.

The shift

From searching for the correct model to deliberately using several partial ones, and trusting the conclusions that survive across them. Cilliers gave the reason. A complex system cannot be compressed into a model without losing something, and what is lost may be the thing that matters. Adding detail does not solve that. A more detailed model is still one way of being wrong.

So plurality is the permanent working condition, and the models stay separate even after a decision is made. The shift also brings a finer vocabulary for not knowing. Stirling separates risk, uncertainty, ambiguity and ignorance, and each calls for a different response. Several models are the right answer to uncertainty. They are the wrong answer to a dispute about values, where more modelling only delays the argument.

Why no neighbouring way asks it

Critical thinking evaluates one argument at a time and asks whether it is warranted. Analytical traditions, and most planning, converge on the best available model and then work from it. Systems thinking usually produces one map, however many loops it contains. Each of them treats several competing accounts as a problem to resolve.

The closest neighbour is integrative thinking, which holds two opposing models and builds a better one from both. But it assumes a small number of identifiable poles, and it aims to transcend them. Complexity thinking expects many partial models across several scales, keeps them apart, and treats their disagreement as a standing source of information.

What it adds to an analysis

Protection against single-model overconfidence, one of the most common causes of failure in strategy, finance and policy. The first robustness test is exactly this: do the conclusions survive different models built on different simplifications? A conclusion that survives is one you can act on with some confidence. One that rests on a single model is a bet on that model’s particular blind spots.

It also makes disagreement useful. Where two credible models split, the split marks the place where evidence would be most valuable, and so where a probe should go. A premortem extends the same habit to the future. Assume the plan failed, and ask each model to explain why. The question for a decision-maker moves from “is this analysis right?” to whether it is robust enough to act on and safe enough to be wrong about.

What it asks of a school

To write down the models it is already using. Every plan carries several: the tracking system’s, the department’s, the parents’, the cluster superintendent’s office’s. Most are never stated, so they cannot be compared or proved wrong. Each one needs a page, a prediction and a note of what would count against it. The parents’ model belongs on the list, because it acts on the school whether or not anyone writes it down.

It also asks for patience with narrow conclusions. What survives across four models is usually smaller than what any one of them claims. Teachers can build the habit into lessons, by asking students to explain one event through two models and say what both accept. Traditions such as anekāntavāda and Two-Eyed Seeing, which uses Indigenous and Western knowledge together without fusing them, show the habit can be a method rather than an attitude. In a society shaped by several heritages, some students will meet it at home first.

How it gets hollowed out

The models are averaged into one, and the disagreement is thrown away. A blended forecast is presented with a single confidence figure, and nobody can see that two of its inputs pointed in opposite directions. Or the models are not independent. Four versions of the same assumption, built by the same team, will agree, and their agreement means nothing.

The opposite failure is plurality as an excuse never to conclude. Every view is noted, every model is “partly right”, and the plan goes ahead unchanged. The guardrail is simple: commit to a working frame, hold it as partial, and write down what would make you revisit it.

Methods

What to use, and how far to trust it

The repertoire for this contribution, with an evidence rating for each method. Strong means tested in more than one field. Emerging means promising, and mostly case studies.

Many-model analysis

Moderate

Run the same problem through several models with different simplifications, then mark what survives across all of them. Page has turned it into a teachable practice.

Ensemble modelling

Strong

Many runs of one or more models, read as a spread instead of a single answer. Well established in weather and climate forecasting.

Agent-based modelling

Moderate

Simulates how individual actors following simple rules produce collective patterns. Useful for testing whether a proposed mechanism could produce what is observed.

Causal layered analysis

Moderate

Reads one issue at four levels, from surface events through systemic causes and worldviews to myths and metaphors. Each level is a different model of the same problem.

Red teaming

Moderate

A separate group builds the strongest case against the plan. It only works if the red team is genuinely independent and its findings can change the decision.

Pre-mortems

Strong

Assume the plan has already failed and ask everyone to write why. Cheap, quick, and good at surfacing doubts people would not otherwise voice.

Reading

Where it comes from

Start with the first on the list.

  • Cilliers, P. (1998). Complexity and postmodernism: Understanding complex systems. Routledge.

    The argument that complex systems are incompressible, so every model is partial and choosing one is a responsibility.

  • Levins, R. (1966). The strategy of model building in population biology. American Scientist, 54(4), 421–431.

    The origin of robustness analysis, and of “the intersection of independent lies”.

  • Page, S. E. (2018). The model thinker: What you need to know to make data work for you. Basic Books.

    Many-model thinking turned into a working practice, with a large set of models to draw on.

  • Stirling, A. (2010). Keep it complex. Nature, 468(7327), 1029–1031.

    The case for plural, conditional advice to policymakers, and the distinction between kinds of not knowing.

  • Klein, G. (2007). Performing a project premortem. Harvard Business Review, 85(9), 18–19.

    The short, practical source for the premortem, one of the two best-evidenced methods here.

  • Matilal, B. K. (1981). The central philosophy of Jainism (Anekānta-vāda). L. D. Institute of Indology.

    The Jain doctrine of many-sidedness, an older and formal grammar for holding several partial models at once.

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