THE GOLD STANDARD OF JUDGEMENT · SPECIALIST STUDY
Represent what evidence supports without pretending ignorance is probability
Dempster–Shafer evidence theory can assign support to sets of possibilities rather than forcing every unit of uncertainty onto a single hypothesis. Belief and plausibility then bound how strongly the evidence commits to a proposition. The framework is powerful when evidence is coarse or sources are combined, but only when the frame, mass assignments, dependence and conflict policy are explicit.
This guide belongs to the Judgement subject guide, the Gold Standard of Education, and the How X Works learning library. Choose a reading route, work the examples, then use the transfer checks to test whether the method survives a changed context.
Choose a reading route
Build the foundations · chapters 1–2
Apply the core method · chapters 3–5
Test evidence and alternatives · chapters 6–7
Handle limits and disagreement · chapters 8–9
Transfer and govern · chapters 10
The whole problem at a glance
| Object | Question | Meaning |
|---|---|---|
| Frame of discernment | Which mutually exclusive possibilities are considered? | The universe over which masses are assigned |
| Basic belief assignment | Which subsets receive direct support? | Mass committed exactly to each focal set |
| Belief | How much support is fully committed inside a set? | Sum of masses of its subsets |
| Plausibility | How much support does not rule the set out? | Sum of masses intersecting the set |
| Conflict | How much combined support meets on the empty intersection? | A diagnostic of source and model incompatibility |
Belief and plausibility are not automatically lower and upper frequencies. Their interpretation depends on the evidence model that generated the masses.
CHAPTER 1 OF 10 · Build the foundations
1. Define the frame of discernment
Core idea. The frame of discernment is the set of mutually exclusive and collectively relevant possibilities used by the model. Every focal set and later calculation depends on its boundaries. The important discipline is to name the object being assessed, the boundary around it and the kind of conclusion the evidence can support. Without those three choices, technical vocabulary creates confidence without creating a checkable claim.
Method. Name the decision, time and resolution; test exclusivity; include an open-world or other category when needed; and document hypotheses deliberately excluded. Write the procedure before looking at the preferred result, retain intermediate evidence and record who can challenge each assumption. A method becomes reusable when another reader can repeat the steps, locate disagreements and understand why a different answer emerged.
Worked example. A diagnostic frame contains red, amber and green system states. If simultaneous states are possible, the frame must be redesigned rather than hidden in later masses. The example is deliberately small enough to inspect. Its purpose is not to imitate every real case but to expose the decision rule, the evidence it consumes and the point at which judgement enters.
Changed-context transfer. For a document source question, the frame might list candidate production processes rather than authors if the evidence speaks to processes. Keep the underlying principle while changing the actors, incentives or data. If the conclusion survives only because the original labels were familiar, the learner has memorised a case rather than acquired a transferable method.
Limits. Frames can be coarse, incomplete or change over time. Refining a frame is not a harmless relabelling because masses must be translated. A responsible conclusion therefore states what remains unknown, what evidence could reverse it and when the analysis must be repeated. Precision about limits is part of the result, not a disclaimer added after it.
Misconception to avoid. The frame is simply a list of every imaginable outcome. It is a decision-relevant modelling boundary, not the universe. Test the tempting shortcut against a counterexample and ask which stakeholder bears the cost when it fails. The correction should alter the workflow, not merely add cautious wording.
Practical evidence check
- Give the frame to a domain expert and ask for overlapping states, missing states and distinctions no available evidence can support.
- Return to chapter contents
CHAPTER 2 OF 10 · Build the foundations
2. Assign mass to focal sets
Core idea. A basic belief assignment gives mass to subsets of the frame. Mass on a multi-element set records support that does not distinguish among its members, rather than distributing that mass arbitrarily. The important discipline is to name the object being assessed, the boundary around it and the kind of conclusion the evidence can support. Without those three choices, technical vocabulary creates confidence without creating a checkable claim.
Method. For each source, define the evidence-generation model, map observations to compatible subsets and verify non-negativity and the total-mass convention. Record whether the empty set can receive mass under the chosen framework. Write the procedure before looking at the preferred result, retain intermediate evidence and record who can challenge each assumption. A method becomes reusable when another reader can repeat the steps, locate disagreements and understand why a different answer emerged.
Worked example. A sensor supports {red} with 0.6 and cannot distinguish red from amber for 0.3, so the latter mass stays on {red, amber}. The example is deliberately small enough to inspect. Its purpose is not to imitate every real case but to expose the decision rule, the evidence it consumes and the point at which judgement enters.
Changed-context transfer. A witness places an event in either of two adjacent time windows. The direct support belongs to the pair unless another model justifies a split. Keep the underlying principle while changing the actors, incentives or data. If the conclusion survives only because the original labels were familiar, the learner has memorised a case rather than acquired a transferable method.
Limits. Mass assignments are often elicited subjectively and can look precise without calibration. Different schools allow different treatment of conflict and the empty set. A responsible conclusion therefore states what remains unknown, what evidence could reverse it and when the analysis must be repeated. Precision about limits is part of the result, not a disclaimer added after it.
Misconception to avoid. A mass of 0.3 on {red, amber} means red and amber each have probability 0.15. Set-valued support deliberately avoids that forced allocation. Test the tempting shortcut against a counterexample and ask which stakeholder bears the cost when it fails. The correction should alter the workflow, not merely add cautious wording.
Practical evidence check
- Trace every nonzero mass back to an observation, mapping rule, reliability adjustment and responsible owner.
- Return to chapter contents
CHAPTER 3 OF 10 · Apply the core method
3. Compute belief and plausibility
Core idea. Belief in a proposition sums mass committed entirely within it. Plausibility sums mass that intersects it and therefore has not ruled it out. The gap represents unresolved support under the model. The important discipline is to name the object being assessed, the boundary around it and the kind of conclusion the evidence can support. Without those three choices, technical vocabulary creates confidence without creating a checkable claim.
Method. Enumerate the proposition’s subsets for belief and intersecting focal sets for plausibility. Check the complement identity and compute results with exact sets before simplifying. Write the procedure before looking at the preferred result, retain intermediate evidence and record who can challenge each assumption. A method becomes reusable when another reader can repeat the steps, locate disagreements and understand why a different answer emerged.
Worked example. If masses are 0.6 on {red}, 0.1 on {amber} and 0.3 on {red, amber}, belief in red is 0.6 and plausibility is 0.9. The example is deliberately small enough to inspect. Its purpose is not to imitate every real case but to expose the decision rule, the evidence it consumes and the point at which judgement enters.
Changed-context transfer. For a two-route investigation, the interval shows what evidence directly supports one route and what remains compatible with it. Keep the underlying principle while changing the actors, incentives or data. If the conclusion survives only because the original labels were familiar, the learner has memorised a case rather than acquired a transferable method.
Limits. The interval is not automatically a confidence interval, Bayesian credible interval or calibrated frequency range. A responsible conclusion therefore states what remains unknown, what evidence could reverse it and when the analysis must be repeated. Precision about limits is part of the result, not a disclaimer added after it.
Misconception to avoid. Plausibility is the probability that the proposition is true. It is an upper compatibility measure under the stated belief model. Test the tempting shortcut against a counterexample and ask which stakeholder bears the cost when it fails. The correction should alter the workflow, not merely add cautious wording.
Practical evidence check
- Calculate belief and plausibility for every singleton and confirm that each belief is no greater than its plausibility.
- Return to chapter contents
CHAPTER 4 OF 10 · Apply the core method
4. Use commonality and related transforms carefully
Core idea. Belief functions have equivalent representations, including plausibility, commonality and Möbius transforms. Each can make different operations or diagnostics easier without changing the underlying mass assignment. The important discipline is to name the object being assessed, the boundary around it and the kind of conclusion the evidence can support. Without those three choices, technical vocabulary creates confidence without creating a checkable claim.
Method. Choose the representation suited to the calculation, retain numerical precision, transform back for interpretation and test on a small frame with a known answer. Write the procedure before looking at the preferred result, retain intermediate evidence and record who can challenge each assumption. A method becomes reusable when another reader can repeat the steps, locate disagreements and understand why a different answer emerged.
Worked example. Commonality values simplify aspects of conjunctive combination. The analyst still reports the resulting belief and plausibility in terms decision makers understand. The example is deliberately small enough to inspect. Its purpose is not to imitate every real case but to expose the decision rule, the evidence it consumes and the point at which judgement enters.
Changed-context transfer. A software implementation stores a Möbius transform for speed but preserves the original focal-set labels in the audit record. Keep the underlying principle while changing the actors, incentives or data. If the conclusion survives only because the original labels were familiar, the learner has memorised a case rather than acquired a transferable method.
Limits. Transforms can amplify rounding error, and sparse algorithms may silently drop small focal sets. A responsible conclusion therefore states what remains unknown, what evidence could reverse it and when the analysis must be repeated. Precision about limits is part of the result, not a disclaimer added after it.
Misconception to avoid. Equivalent mathematics guarantees equivalent implementation. Representation conversions need tests and tolerance rules. Test the tempting shortcut against a counterexample and ask which stakeholder bears the cost when it fails. The correction should alter the workflow, not merely add cautious wording.
Practical evidence check
- Round-trip one mass assignment through two transforms and quantify all residual error and discarded support.
- Return to chapter contents
CHAPTER 5 OF 10 · Apply the core method
5. Combine evidence only under a source model
Core idea. Dempster’s rule combines mass assignments by intersecting focal sets and normalising away conflicting mass. The calculation carries strong assumptions about how sources and evidence-generation processes relate. The important discipline is to name the object being assessed, the boundary around it and the kind of conclusion the evidence can support. Without those three choices, technical vocabulary creates confidence without creating a checkable claim.
Method. Specify why sources are distinct, compute the unnormalised conjunctive result and conflict first, inspect dependence and shared upstream information, then justify any normalisation. Write the procedure before looking at the preferred result, retain intermediate evidence and record who can challenge each assumption. A method becomes reusable when another reader can repeat the steps, locate disagreements and understand why a different answer emerged.
Worked example. Two sensors with separate failure mechanisms provide masses on the same frame. Their conjunctive table reveals agreements and empty intersections before a combined belief is reported. The example is deliberately small enough to inspect. Its purpose is not to imitate every real case but to expose the decision rule, the evidence it consumes and the point at which judgement enters.
Changed-context transfer. Two news reports repeating one press release are not two independent sources. Their shared origin must remain visible instead of being multiplied. Keep the underlying principle while changing the actors, incentives or data. If the conclusion survives only because the original labels were familiar, the learner has memorised a case rather than acquired a transferable method.
Limits. Conditional independence is difficult to establish, and normalisation can produce extreme answers under high conflict. A responsible conclusion therefore states what remains unknown, what evidence could reverse it and when the analysis must be repeated. Precision about limits is part of the result, not a disclaimer added after it.
Misconception to avoid. Dempster’s rule is the default whenever two opinions exist. Combination is a modelling choice, not an automatic averaging command. Test the tempting shortcut against a counterexample and ask which stakeholder bears the cost when it fails. The correction should alter the workflow, not merely add cautious wording.
Practical evidence check
- Draw a source-dependence graph and explain why every combined pair contributes new evidence rather than duplicated provenance.
- Return to chapter contents
Worked diagnostic example
| Focal set | Sensor A mass | Sensor B mass | Interpretation |
|---|---|---|---|
| {red} | 0.60 | 0.20 | Direct support for red |
| {amber} | 0.10 | 0.50 | Direct support for amber |
| {red, amber} | 0.30 | 0.30 | Uncommitted between the two |
| Bel({red}) | 0.60 | 0.20 | Support fully inside red |
| Pl({red}) | 0.90 | 0.50 | Support not excluding red |
Combination is not justified merely because two columns exist. Test whether the sensors supply sufficiently distinct evidence and whether the same frame fits both.
CHAPTER 6 OF 10 · Test evidence and alternatives
6. Interpret conflict before normalising it
Core idea. Conflict is mass assigned to empty intersections in the conjunctive combination. It can indicate source disagreement, frame mismatch, unreliable mapping or genuinely incompatible observations. The important discipline is to name the object being assessed, the boundary around it and the kind of conclusion the evidence can support. Without those three choices, technical vocabulary creates confidence without creating a checkable claim.
Method. Report conflict separately, inspect which focal-set pairs create it, run sensitivity to source reliability and compare alternative combination or open-world treatments. Write the procedure before looking at the preferred result, retain intermediate evidence and record who can challenge each assumption. A method becomes reusable when another reader can repeat the steps, locate disagreements and understand why a different answer emerged.
Worked example. Sensor A strongly supports red while sensor B strongly supports amber. High conflict prompts a hardware and frame review before a sharp normalised conclusion. The example is deliberately small enough to inspect. Its purpose is not to imitate every real case but to expose the decision rule, the evidence it consumes and the point at which judgement enters.
Changed-context transfer. Two expert panels use the same labels but different operational definitions. The conflict is partly semantic and should be repaired upstream. Keep the underlying principle while changing the actors, incentives or data. If the conclusion survives only because the original labels were familiar, the learner has memorised a case rather than acquired a transferable method.
Limits. A low scalar conflict can hide local contradictions, and a high value does not reveal the cause by itself. A responsible conclusion therefore states what remains unknown, what evidence could reverse it and when the analysis must be repeated. Precision about limits is part of the result, not a disclaimer added after it.
Misconception to avoid. Normalisation solves conflict by redistributing it. It performs a defined calculation but may conceal the diagnostic meaning of disagreement. Test the tempting shortcut against a counterexample and ask which stakeholder bears the cost when it fails. The correction should alter the workflow, not merely add cautious wording.
Practical evidence check
- Produce a conflict matrix and identify the three largest incompatible focal-set products and their real-world causes.
- Return to chapter contents
CHAPTER 7 OF 10 · Test evidence and alternatives
7. Discount unreliable sources transparently
Core idea. Reliability discounting moves some committed mass toward the full frame, representing weaker trust in a source while preserving ignorance. The discount factor needs evidence and a clear interpretation. The important discipline is to name the object being assessed, the boundary around it and the kind of conclusion the evidence can support. Without those three choices, technical vocabulary creates confidence without creating a checkable claim.
Method. Estimate reliability from validation data or a documented elicitation, distinguish reliability from relevance, apply the rule before combination and test alternative factors. Write the procedure before looking at the preferred result, retain intermediate evidence and record who can challenge each assumption. A method becomes reusable when another reader can repeat the steps, locate disagreements and understand why a different answer emerged.
Worked example. A sensor validated at lower reliability has part of each focal mass transferred to the full frame. The output becomes less committed rather than favouring a rival state. The example is deliberately small enough to inspect. Its purpose is not to imitate every real case but to expose the decision rule, the evidence it consumes and the point at which judgement enters.
Changed-context transfer. An expert may be reliable in one domain but irrelevant to another. Separate source competence from whether the present evidence bears on the frame. Keep the underlying principle while changing the actors, incentives or data. If the conclusion survives only because the original labels were familiar, the learner has memorised a case rather than acquired a transferable method.
Limits. Reliability can vary by condition, and one scalar may hide mode-specific failure. A responsible conclusion therefore states what remains unknown, what evidence could reverse it and when the analysis must be repeated. Precision about limits is part of the result, not a disclaimer added after it.
Misconception to avoid. Discounting a source by 20 percent means its claims are 20 percent false. Discounting modifies evidential commitment; it is not a direct error-rate statement. Test the tempting shortcut against a counterexample and ask which stakeholder bears the cost when it fails. The correction should alter the workflow, not merely add cautious wording.
Practical evidence check
- Recompute the decision over a plausible reliability range and report the point where the preferred action changes.
- Return to chapter contents
CHAPTER 8 OF 10 · Handle limits and disagreement
8. Condition and refine the frame with care
Core idea. New information may rule out possibilities or require a refined frame. Conditioning, coarsening and refinement move belief across representations, but the choice depends on how the new evidence was generated. The important discipline is to name the object being assessed, the boundary around it and the kind of conclusion the evidence can support. Without those three choices, technical vocabulary creates confidence without creating a checkable claim.
Method. State the conditioning rule, preserve any conflict created, define the mapping between frames and verify that refinement does not invent distinctions unsupported by evidence. Write the procedure before looking at the preferred result, retain intermediate evidence and record who can challenge each assumption. A method becomes reusable when another reader can repeat the steps, locate disagreements and understand why a different answer emerged.
Worked example. A later test rules out green. The analyst conditions the existing mass assignment under a named rule and compares it with rebuilding the model from raw observations. The example is deliberately small enough to inspect. Its purpose is not to imitate every real case but to expose the decision rule, the evidence it consumes and the point at which judgement enters.
Changed-context transfer. A policy frame splits “delay” into short and long delay. Old mass cannot be allocated between them without a refinement assumption. Keep the underlying principle while changing the actors, incentives or data. If the conclusion survives only because the original labels were familiar, the learner has memorised a case rather than acquired a transferable method.
Limits. Different conditioning rules can yield different results, especially under conflict or open-world models. A responsible conclusion therefore states what remains unknown, what evidence could reverse it and when the analysis must be repeated. Precision about limits is part of the result, not a disclaimer added after it.
Misconception to avoid. Frame refinement creates more precise evidence. It creates more detailed labels; evidence may remain coarse. Test the tempting shortcut against a counterexample and ask which stakeholder bears the cost when it fails. The correction should alter the workflow, not merely add cautious wording.
Practical evidence check
- Split one hypothesis and ask which old focal masses can be translated uniquely and which require explicit ignorance.
- Return to chapter contents
Evidence claim ladder
| Calculation | Supported statement | Unsupported leap |
|---|---|---|
| Masses sum to one | The assignment meets a basic formal requirement | The masses are empirically calibrated |
| Belief and plausibility computed | The stated evidence model yields an interval | The true probability lies in the interval |
| Dempster combination applied | Normalised conjunctive combination was performed | Sources were independent and conflict was harmless |
| Decision transform chosen | A decision rule maps evidence to action | The rule is uniquely rational or ethically neutral |
Report how masses were elicited, why sources can be combined and how conflict changes the decision.
CHAPTER 9 OF 10 · Handle limits and disagreement
9. Move from belief to a decision rule
Core idea. Belief functions represent evidence; decisions also need utilities, constraints and a rule for acting under interval-valued support. Pignistic, lower-expectation, dominance and robust rules make different commitments. The important discipline is to name the object being assessed, the boundary around it and the kind of conclusion the evidence can support. Without those three choices, technical vocabulary creates confidence without creating a checkable claim.
Method. Separate the evidence model from the decision layer, state utility ranges and risk posture, compare at least two rules and expose choices driven by unresolved mass. Write the procedure before looking at the preferred result, retain intermediate evidence and record who can challenge each assumption. A method becomes reusable when another reader can repeat the steps, locate disagreements and understand why a different answer emerged.
Worked example. A safety action is chosen under a conservative lower-expectation rule, while a ranking dashboard uses a pignistic transform for a different purpose. The example is deliberately small enough to inspect. Its purpose is not to imitate every real case but to expose the decision rule, the evidence it consumes and the point at which judgement enters.
Changed-context transfer. In resource allocation, a robust rule may protect against the worst compatible state while preserving options for more information. Keep the underlying principle while changing the actors, incentives or data. If the conclusion survives only because the original labels were familiar, the learner has memorised a case rather than acquired a transferable method.
Limits. No transform is neutral, and utility elicitation may dominate the evidential calculation. A responsible conclusion therefore states what remains unknown, what evidence could reverse it and when the analysis must be repeated. Precision about limits is part of the result, not a disclaimer added after it.
Misconception to avoid. Once masses are combined, the correct action follows automatically. Evidence never removes the need for values and consequences. Test the tempting shortcut against a counterexample and ask which stakeholder bears the cost when it fails. The correction should alter the workflow, not merely add cautious wording.
Practical evidence check
- Hold the mass assignment fixed, apply two decision rules and explain every action change in terms of values or ambiguity attitude.
- Return to chapter contents
CHAPTER 10 OF 10 · Transfer and govern
10. Validate the entire evidence pipeline
Core idea. A defensible Dempster–Shafer system validates frames, mappings, source dependence, reliability, numerical implementation, calibration and decision consequences—not only formulas. The important discipline is to name the object being assessed, the boundary around it and the kind of conclusion the evidence can support. Without those three choices, technical vocabulary creates confidence without creating a checkable claim.
Method. Use simulated and held-out cases, adversarial conflict tests, source ablations, transform round trips and outcome review. Publish model cards or audit notes suited to the stakes. Write the procedure before looking at the preferred result, retain intermediate evidence and record who can challenge each assumption. A method becomes reusable when another reader can repeat the steps, locate disagreements and understand why a different answer emerged.
Worked example. A fault-detection system is tested on shared-cause failures that violate independence. The review shows where combination becomes overconfident and changes deployment rules. The example is deliberately small enough to inspect. Its purpose is not to imitate every real case but to expose the decision rule, the evidence it consumes and the point at which judgement enters.
Changed-context transfer. A classroom exercise uses simple coloured cards to make focal sets and ignorance visible before any software is trusted. Keep the underlying principle while changing the actors, incentives or data. If the conclusion survives only because the original labels were familiar, the learner has memorised a case rather than acquired a transferable method.
Limits. Outcome frequencies may not map directly to belief intervals, and rare events limit validation. High-stakes use needs human review and remedy. A responsible conclusion therefore states what remains unknown, what evidence could reverse it and when the analysis must be repeated. Precision about limits is part of the result, not a disclaimer added after it.
Misconception to avoid. A mathematically correct library makes the application valid. Correct code cannot rescue an unjustified evidence model. Test the tempting shortcut against a counterexample and ask which stakeholder bears the cost when it fails. The correction should alter the workflow, not merely add cautious wording.
Practical evidence check
- Remove each source in turn, perturb every reliability factor and inspect whether conflict, belief, plausibility and action change plausibly.
- Return to chapter contents
Build a Dempster–Shafer evidence evidence worksheet
State the decision, unit of analysis, time horizon and affected people before collecting evidence. Separate observations from interpretations and interpretations from recommendations. Record data provenance, missingness and incentives that could distort reporting.
For every important claim, add a rival explanation and one observation that would favour it. Give uncertainty a visible place instead of hiding it inside a single score. Assign an owner and review date to assumptions that may change.
Run the worksheet with someone who did not design the analysis. Ask them to reconstruct the conclusion and identify where judgement entered. Revise any step that depends on private intuition or undefined terminology.
Finish with an action table: act now, monitor, investigate or stop. Link each action to evidence and a reversal condition so the method supports learning rather than defending the first answer.
Design a changed-context transfer check
Rewrite the case with a different scale, institution and distribution of power while preserving the underlying structure. Predict which parts of the method should remain stable and which require new evidence.
Remove one convenient data source and add one conflicting stakeholder account. Re-run the reasoning. If the answer changes, explain whether the change reflects better evidence, a different value choice or an unstable method.
Switch the time horizon. A decision that looks efficient this week may weaken resilience over years, while a long-run benefit may impose an unacceptable immediate burden. Report both rather than averaging them away.
Ask a reviewer to produce a counterexample. A transfer check passes when the method reveals why the new case differs, not when it mechanically produces the same conclusion.
Audit the reasoning and the record
Preserve source versions, transformations, thresholds, exclusions and decision notes. A final chart without its lineage cannot be independently checked and may conceal silent changes.
Trace one favourable and one unfavourable case from raw evidence to recommendation. Confirm that identical rules were applied and that exceptions were authorised, explained and reviewable.
Interview affected users about how the process works in practice. Formal policy may differ from operational reality, especially when time pressure, inaccessible interfaces or asymmetric power limit challenge.
Publish a proportionate account of method, limits, ownership and remedy. Protect sensitive data while ensuring that confidentiality is not used to block legitimate scrutiny.
Turn findings into accountable action
Assign every recommendation to a named role with authority, resources and a deadline. Distinguish mitigation from remedy: reducing future risk does not repair harm already caused.
Choose leading indicators that reveal drift early and outcome indicators that show whether people actually benefited. Disaggregate results where averages can hide concentrated burden.
Create an escalation rule for new evidence, missed thresholds and recurring complaints. Independent review should be available when the original decision maker has an incentive to defend the system.
Close the loop by publishing what changed, what did not and why. Re-open the analysis after material changes instead of treating one successful review as permanent certification.
Questions readers ask
Is a basic belief assignment an ordinary probability distribution?
- No. It can assign mass directly to sets of possibilities rather than only to singletons.
What is the difference between belief and plausibility?
- Belief is support committed wholly within a proposition; plausibility is support not ruling it out.
Does the gap represent error?
- Not necessarily. It represents unresolved evidential commitment under the chosen frame and mapping.
Can any two sources be combined with Dempster’s rule?
- No. Source dependence, shared provenance, frame alignment and conflict must be examined first.
What does high conflict mean?
- It signals substantial incompatible support, but the cause may be disagreement, dependence, frame error or faulty mappings.
How does evidence become a decision?
- Through a separately chosen decision rule and utilities or constraints; no unique action is built into the belief function.
Practise, verify and continue
Create a three-state frame and two source mass assignments with at least one non-singleton focal set. Compute belief, plausibility, the unnormalised conjunctive result, conflict and one normalised combination. Then vary reliability and compare two decision rules.
Move the example from sensors to documents or expert testimony. Preserve the formal steps while rebuilding the source model, dependence assumptions, reliability evidence and ethical review.
Related eduKate reading
Imprecise probabilities, credal sets, lower expectations and robust choice
Bayesian networks, conditional independence, diagnostic inference and sensitivity
Robust decisions and the assumption that reverses a choice
Bayesian model averaging, posterior model probabilities, predictive mixtures and model risk
Distributionally robust optimisation, Wasserstein balls, ambiguity and out-of-sample guarantees
Authoritative sources and scope
A. P. Dempster, Upper and Lower Probabilities Induced by a Multivalued Mapping
Glenn Shafer, A Mathematical Theory of Evidence
Sandia National Laboratories, Combination of Evidence in Dempster–Shafer Theory
Philippe Smets, What Is Dempster–Shafer’s Model?
Glenn Shafer, Probability Judgement in Artificial Intelligence
This article is an educational introduction to finite-frame Dempster–Shafer evidence theory. It does not prescribe a combination rule, software library, safety case or high-stakes automated decision. Examples and numbers are original teaching cases. Interpretations differ across belief-function frameworks, especially treatment of the empty set, open worlds, conditioning and decision transforms. Mass assignments require a defensible evidence-generation model and should not be presented as calibrated probabilities without validation. Source dependence and shared provenance must be checked before combination. Conflict should be diagnosed rather than hidden. High-stakes applications need domain testing, human oversight, privacy protection, appeal and proportionate remedy.