An independent study reference written by Dr Phuc V. Nguyen. It is not official subject material — for assessment requirements always follow your subject outline and vUWS.

Decisions and Modelsintermediate

Models as deliberate abstraction

Q: Two models of the same supply chain disagree about whether to open a second warehouse. The most useful first step is

identify the assumption the two models disagree on and whether it can be tested. Two models disagree because they abstracted differently. Finding the assumption that drives the gap converts an argument about models into a question about the business, which can often be settled with one small piece of evidence. Averaging hides the disagreement, and preferring detail assumes complexity equals accuracy.

Q: A demand model fits historical sales almost perfectly but performs poorly on the following quarter. The most likely explanation is that

the model traced patterns specific to the period it was built on rather than durable structure. A near-perfect fit to the past is usually a warning rather than a result. Extra flexibility lets a model follow noise as though it were signal, so it describes one particular period beautifully and generalises badly. Adding more variables typically makes this worse, since it gives the model more ways to trace the noise.

A model is a simplified representation of something real, built to answer a specific question. The simplification is the point. A model that kept every detail would be as hard to work with as the world it describes, so modelling is the craft of deciding what to throw away. What you keep depends on the question, which is why the same business can be modelled a dozen ways with none of them wrong. Every model also rests on assumptions it cannot test from the inside, and stating those plainly is what separates an honest model from a merely confident one.

Why it matters

A street map leaves out the trees, the traffic and the colour of the buildings. That is not a defect. It is why the map fits in your pocket and gets you to the station. A different question, such as where to plant shade trees, needs a different map of the same street. So ask what a model is for before you ask whether it is right.

Before you read on — recall

Two models of the same supply chain disagree about whether to open a second warehouse. The most useful first step is

Formulas

What a model separates

y = f(x_1, x_2, \dots, x_k) + \varepsilon

The outcome

y

splits into a part the model explains from inputs

x_1

through

x_k

and an error term

\varepsilon

, which is a theoretical quantity nobody observes. What a fitted model actually reports is an estimated residual, and that mixes together the influences the modeller chose to leave out, measurement error, ordinary noise, estimation error and any misspecification of

f

. So a large residual says something is missing without saying what. It is also not a clean score of the abstraction, because an omitted influence that moves with the inputs biases the coefficients instead of sitting quietly in the residual.

A deliberately thin demand model

Q = 1200 - 15P

Unit sales

Q

over seven days at a price

P

in dollars. At

P = 40

it predicts 600 units and revenue of A$24,000. At

P = 44

it predicts 540 units and A$23,760, so the rise reduces revenue by A$240. Whether it reduces profit is unknown, because the model carries no costs and 60 fewer units also cost less to supply. It ignores competitors, weather and brand entirely. That is the trade you accepted in return for an answer you can compute during a meeting.

Worked examples

Scenario

A logistics firm wants to know whether to add a third van. The analytics team is asked to build a full simulation of the depot.

Solution

A full simulation would represent every parcel, route and driver break, and would take months. The decision only needs to know how often demand exceeds what two vans can carry inside the delivery window. A model with three inputs, parcels per day, average drop time and hours available, answers that in an afternoon and shows how often the ceiling is breached. If the answer sits close to the boundary, then invest in something richer. Building fidelity nobody needed is the most common and most expensive modelling error.

Scenario

A pricing model built on two years of data recommends a rise. A senior manager objects that it does not include the competitor who opened last month.

Solution

The manager is right about the abstraction and wrong about what to do next. The model cannot see the competitor because no period in its data contained one, so its standing assumption is that demand behaves as it did before. Say that out loud, then decide whether it still helps. It may still be useful as a bound, showing what the rise would have earned without competition, which brackets the real answer from one side. Discarding a model for leaving something out is as unhelpful as trusting it for producing a number.

Common mistakes

✗A better model is a more detailed model. Detail costs data, time and transparency, and past a point it makes results harder to check and to defend. The right level of detail is the least that still answers the question being asked.
✗A model that does not match reality exactly is wrong and should be discarded. Every model differs from reality by design. The only question that matters is whether the differences matter for the decision at hand.
✗The model produced the number, so the number is objective. Someone chose the inputs, the shape of the relationship, the period of data and the outcome to predict. Those are judgements, and they travel invisibly inside the output.
✗Assumptions are technical detail for an appendix. Assumptions are where models break. Naming the two or three that would most change the answer if violated is worth more to a decision maker than another decimal place.

Revision bullets

•A model is a purposeful simplification, not a miniature of reality
•What gets left out is chosen by the question being answered
•The error term is theoretical; a fitted residual mixes omissions with noise
•Fidelity trades against speed, transparency and data cost
•State the assumptions whose failure would most change the answer
•Usefulness for a decision is the test, not resemblance to reality

Quick check

Two models of the same supply chain disagree about whether to open a second warehouse. The most useful first step is

A demand model fits historical sales almost perfectly but performs poorly on the following quarter. The most likely explanation is that

Connected topics

Three Analytics Types Correlation vs Cause Decision Support Supervised vs Unsup.Into Production

More in Decisions and Models

What Is a Decision Decision Process A/B Testing KPI Design

Sources

Box (1976)
Box, G. E. P. "Science and Statistics." Journal of the American Statistical Association, 71(356), 1976.
Source of the working principle that all models are wrong while some are useful, and of the warning against elaborating a model in the hope of making it correct.
Rosenblueth & Wiener (1945)
Rosenblueth, A., & Wiener, N. "The Role of Models in Science." Philosophy of Science, 12(4), 1945.
Argues that a model useful for reasoning must be simpler than what it represents, because a perfect copy would be no easier to study than the original.
Ackoff (1979)
Ackoff, R. L. "The Future of Operational Research is Past." Journal of the Operational Research Society, 30(2), 1979.
Warns that real problems arrive as interacting messes rather than tidy units, so a model of one neatly carved-out piece can solve the wrong thing very well.

How to cite this page

Dr. Phil's Quant Lab. (2026). Models as deliberate abstraction. Derivatives Atlas. https://phucnguyenvan.com/concept/ba-models-abstraction