An inspectable investigation

Who gets the credit?

An inspectable constructed model of Shapley allocation, with all six orders, assumptions and exact calculations.

Collective output can exceed what each person could produce alone. That leaves a question: how much of the result should be attributed to each contributor?

One answer is to average a person's marginal contribution across every possible order of arrival. This is the Shapley value. With three contributors, there are six orders; the entire calculation fits on the page.

The values below are constructed. They make the rule visible without pretending to measure a real team.

YOUR TASK / CONSTRUCTED EXAMPLE

Inspect how the shared result is attributed

You’re reviewing a constructed collaboration between A, B and C. Name what an allocation should recognize, then inspect how one person’s contribution changes across arrival orders.

A first judgment.
An evidence trail.
Your decision.

Begin with a provisional judgment

Loading the supplied example…

What would you ask an allocation to recognize?Equal shares of the shared resultWhat each person produces aloneWhat each person adds across combinations

Keep a private first thought (optional)

Your first reasoning

Private writing stays out of links and default downloads. A reopened link does not restore it.

This records a provisional judgment and the starting configuration. It does not change a mathematical setting or save automatically.

Keep a model beside your next experiment.

Coalition values

Eight coalitions; one order traced.

Selected order

The complete order is shown.

Scrub the six possible orders A → B → C

Reduced motion: use the step controls and order slider.

Marginal contributions by order

Each row shows the additional value each contributor brings in that order.

All possible orders. Select an order to trace it in the diagram.
A	B	C	Total
12	16	14	42
12	20	10	42
20	8	14	42
24	8	10	42
18	20	4	42
24	14	4	42

Resulting allocation (Shapley value)

φ_A =

φ_B =

φ_C =

φ_A + φ_B + φ_C = 42

Constructed example · allocation under the selected ruleAssumptions & limits ↗Method: Shapley value

The rule cannot choose the evidence

To use this method in the world, someone must first assign a value to every coalition. That can require counterfactual judgments: what would two people have produced without the third? The precision of the fraction does not remove uncertainty in that judgment.

The rule also treats every ordering equally. It recognizes marginal contribution to the chosen output measure. Needs, risks, ownership and obligations require additional arguments.

Derivation and original source →