Cross-Impact Analysis
Cross-Impact Analysis (CIA) is a futures research method used to examine how different events, trends, variables or developments may influence one another. Instead of analysing each future development independently, the method considers the wider system of interactions in which a change in one factor can strengthen, weaken or alter another.
The method is commonly represented through a cross-impact matrix, where the variables being studied appear along both axes and each cell represents the influence of one variable on another. Depending on the particular cross-impact approach, these relationships may be expressed qualitatively, through numerical influence scores, or through changes in conditional probabilities.
Cross-Impact Analysis is particularly useful when a future cannot reasonably be understood as a collection of independent developments. However, completing a matrix is not sufficient in itself. Researchers need to explain why particular relationships have been identified and why specific impact assessments have been assigned.
A cross-impact matrix is only as defensible as the reasoning behind its cells. The number assigned to an interaction should summarize an analytical judgement—not substitute for one.
On this page:
- Cross-Impact Analysis Explained Simply
- What Is Cross-Impact Analysis?
- Why Interactions Matter in Futures Research
- How a Cross-Impact Matrix Works
- Qualitative and Probabilistic Cross-Impact Analysis
- How to Conduct Cross-Impact Analysis
- Selecting Variables for the Matrix
- Assessing Relationships and Assigning Scores
- Dudovskiy Cross-Impact Relationship Evaluation Framework
- Interpreting a Cross-Impact Matrix
- Cross-Impact Analysis and Delphi Method
- Cross-Impact Analysis vs Futures Wheel
- Application of Cross-Impact Analysis: an Example
- Advantages and Limitations of Cross-Impact Analysis
- Common Mistakes When Using Cross-Impact Analysis
- Cross-Impact Analysis in Business Research
- Cross-Impact Analysis in the Age of AI and Digital Research
- When to Use Cross-Impact Analysis
- Dissertation Example
- Exam Tip
| Aspect | Cross-Impact Analysis |
|---|---|
| Main purpose | Analyse interactions among future events, trends or variables |
| Basic analytical question | How might a change in A influence B? |
| Typical representation | Cross-impact matrix |
| Inputs | Events, trends, drivers, variables or other relevant developments |
| Relationships | Positive, negative, neutral or expressed probabilistically |
| Common approaches | Qualitative/scoring and probabilistic approaches |
| Typical applications | Futures research, foresight, scenario development and strategic analysis |
| Major strength | Reveals interdependencies that independent-variable analysis may overlook |
| Major methodological risk | Assigning interaction scores without adequately justifying them |
Cross-Impact Analysis Explained Simply
Imagine researchers are exploring the future of grocery retail and identify four important developments:
A. Growth of online grocery shopping
B. Adoption of automated warehouses
C. Shortage of logistics workers
D. Demand for same-day delivery
Studying these developments separately provides useful information, but it misses their interactions. Greater demand for same-day delivery may accelerate investment in automated warehouses. A shortage of logistics workers could strengthen the business case for automation. Automation might, in turn, make faster delivery economically feasible and encourage further online shopping.
A simplified matrix could represent these relationships:
| Impact of ↓ on → | Online shopping | Automation | Labour shortage | Same-day delivery |
|---|---|---|---|---|
| Online shopping | — | +2 | +1 | +2 |
| Automation | +1 | — | -2 | +2 |
| Labour shortage | 0 | +2 | — | -1 |
| Same-day delivery | +1 | +2 | +1 | — |
Here, an illustrative scale might be:
+2 = strong positive influence
+1 = weak/moderate positive influence
0 = no meaningful influence
-1 = weak/moderate negative influence
-2 = strong negative influence
The important point is not the numbers themselves. Researchers must be able to explain why, for example, a logistics labour shortage is judged to exert a strong positive influence on warehouse automation.
That reasoning is the substance of the analysis. The matrix records it.
What Is Cross-Impact Analysis?
Cross-impact methods emerged within futures research as a response to a fundamental limitation of treating future events independently. Early work by Theodore Gordon and Olaf Helmer demonstrated how judgements about future events could be extended by considering whether the occurrence of one event would change the likelihood of another.
Since then, a variety of cross-impact approaches have developed. Consequently, Cross-Impact Analysis should not be treated as one completely standardized procedure. Some approaches focus primarily on qualitative or ordinal assessments of influence, whereas others use conditional probabilities and mathematical procedures to investigate how interacting events alter possible future configurations.
Despite these variations, the central logic remains consistent:
Future developments can interact, and analysing those interactions may produce a more realistic understanding of possible futures than analysing each development independently.
The method therefore shifts attention from individual variables to the relationships among them.
Why Interactions Matter in Futures Research
A common weakness in futures analysis is to identify several important trends and discuss them one after another. A researcher might examine artificial intelligence, demographic ageing, environmental regulation and changing consumer behaviour as four separate developments. Yet the future produced by those developments depends partly on how they interact.
For example, demographic ageing might increase demand for automation because organizations face labour shortages. Greater automation could alter employment structures and influence political attitudes toward technological regulation. Regulation might then accelerate or constrain further technological adoption. The resulting system contains feedback and interdependence rather than four independent trends.
Cross-Impact Analysis makes these relationships explicit by asking a directional question:
If A changes or occurs, what effect might that have on B?
Importantly, the reverse relationship is a separate question:
If B changes or occurs, what effect might that have on A?
The two answers do not have to be identical. A strong influence of A on B does not imply an equally strong influence of B on A.
How a Cross-Impact Matrix Works
A conventional cross-impact matrix places the same set of variables along the rows and columns. Each cell then represents the influence of the row variable on the column variable.
Suppose a study examines four developments:
| Impact of ↓ on → | A | B | C | D |
|---|---|---|---|---|
| A | — | +2 | 0 | -1 |
| B | +1 | — | +2 | 0 |
| C | -1 | +1 | — | +2 |
| D | 0 | -2 | +1 | — |
The diagonal cells are normally excluded because they would represent the influence of a variable on itself. The remaining cells require separate consideration.
The cell A → B = +2, for example, means that A is judged to have a strong positive influence on B according to the scoring system adopted for that particular study. The cell B → A = +1 represents a different judgement. The relationship is therefore directional rather than automatically reciprocal.
A matrix with five variables already requires consideration of 20 directional relationships if self-effects are excluded. Ten variables produce 90 such relationships. Variable selection therefore has major consequences for analytical feasibility as well as conceptual quality.
Qualitative and Probabilistic Cross-Impact Analysis
Cross-impact methods can take different forms, and researchers should identify the particular approach they are using rather than assuming that every cross-impact study follows the same procedure.
In a qualitative or influence-scoring approach, researchers assess whether one variable promotes, constrains or has little effect on another. Numerical scales such as -2 to +2 or other ordinal systems may be used to summarize these judgements. The numbers function primarily as structured representations of assessed influence rather than precise empirical measurements.
In probabilistic cross-impact approaches, the question changes. Researchers may begin with an estimate of the probability of event B and then consider how occurrence of event A would change that probability. The analysis therefore concerns conditional relationships such as:
P(B | A)
rather than merely assigning an influence score to A → B.
Probabilistic variants can involve considerably more demanding mathematical and consistency requirements. A dissertation should not adopt a probabilistic procedure merely because it appears more sophisticated. The selected approach needs to match the research question, available evidence, expertise of participants and intended analytical output.
How to Conduct Cross-Impact Analysis
The process begins by defining the system or futures problem being investigated. Researchers need a clear boundary around the analysis: what future, sector, organization, geographical context or strategic problem is actually being explored?
Relevant variables are then identified. These may emerge from literature review, Environmental Scanning, expert interviews, Delphi research, workshops, existing datasets or other forms of preliminary analysis. The variables should represent developments important enough to influence the system while remaining sufficiently distinct to make relationships interpretable.
Next, researchers define how interactions will be assessed. A qualitative study may adopt an ordinal scale representing strong negative, moderate negative, neutral, moderate positive and strong positive effects. Whatever scale is selected should be defined before the matrix is populated so that participants share a reasonably consistent interpretation of its categories.
Each directional relationship is then evaluated. Researchers consider whether A influences B, the direction and strength of the influence, and the basis for that judgement. The completed matrix can subsequently be analysed to identify variables that exert substantial influence, variables that are highly affected by others, clusters of interaction and relationships requiring further investigation.
The final stage is interpretation. Cross-Impact Analysis should help researchers understand the system rather than merely produce a matrix filled with numbers.
Selecting Variables for the Matrix
Variable selection is one of the most consequential design decisions because the matrix can analyse only relationships among factors that have been included.
Variables that are excessively broad create ambiguous relationships. For example, “technology” is unlikely to be analytically useful because different technologies may have completely different effects. At the opposite extreme, dozens of narrowly specified variables can make the matrix unmanageable.
Researchers should also avoid including multiple labels for essentially the same phenomenon. If “AI adoption,” “increased use of AI” and “organizational AI implementation” appear as separate variables, apparent interactions may partly reflect conceptual duplication rather than genuine system relationships.
A useful set of variables therefore needs to balance coverage, distinctiveness and manageability. Researchers should be able to define each variable clearly and explain why it belongs within the system under investigation.
The number of relationships grows rapidly as variables are added. For n variables, excluding self-interactions, the number of directional relationships is:
n × (n − 1)
Thus:
5 variables → 20 relationships
10 variables → 90 relationships
15 variables → 210 relationships
20 variables → 380 relationships
Adding a variable is therefore not a trivial decision. It adds an entire row and column of relationships requiring evaluation.
Assessing Relationships and Assigning Scores
The matrix should not be populated by intuition alone simply because a numerical scale is available. For every meaningful interaction, researchers should consider what the score represents and what supports it.
Suppose a researcher assigns:
A → B = +2
The methodological question immediately becomes:
Why +2?
Perhaps published evidence suggests that A consistently increases B. Perhaps experts independently identify the relationship as strong. Perhaps historical cases show a recurring pattern. Alternatively, the judgement may depend heavily on assumptions that hold only under certain conditions.
These differences matter.
A numerical score can create an impression of precision that exceeds the evidence behind it. Researchers should therefore treat the number as a compressed representation of a reasoned judgement, particularly where ordinal scoring systems are used.
Where feasible, important interaction assessments should be accompanied by short rationales, supporting evidence or documented expert reasoning. This creates an auditable connection between the underlying judgement and the matrix value.
Dudovskiy Cross-Impact Relationship Evaluation Framework
The Dudovskiy Cross-Impact Relationship Evaluation Framework is a practical decision aid for evaluating a proposed interaction before reducing it to a matrix score or other assessment. It synthesizes established methodological concerns surrounding cross-impact relationships rather than introducing a new form of Cross-Impact Analysis.
The framework asks researchers to examine seven aspects of a proposed relationship.
Direction asks whether A increases, decreases or has no meaningful influence on B. The researcher should distinguish genuine influence from simple correlation or thematic association.
Strength considers how substantial the influence could reasonably be. Strong scores should require stronger justification than weak ones rather than being assigned simply because a relationship appears intuitively important.
Evidence asks what supports the proposed relationship. Depending on the study, this may include academic literature, empirical evidence, historical analogies, expert judgement or other documented reasoning.
Time lag considers when the effect might occur. A relationship may be genuine while operating only after months or years, which can be important when interpreting dynamic futures.
Conditionality asks whether A influences B generally or only when particular circumstances exist. Regulation, market conditions, technological maturity or stakeholder behaviour may determine whether a relationship becomes active.
Indirect effects require researchers to ask whether the apparent A → B relationship actually operates through another variable. If A influences C and C influences B, researchers should consider carefully whether a separate direct A → B score would clarify the system or inadvertently double-count the same mechanism.
Finally, confidence expresses how secure the judgement is given the available evidence and uncertainty.
The sequence is:
Proposed A → B Relationship → Direction → Strength → Evidence → Time Lag → Conditionality → Indirect Effects → Confidence → Defensible Cross-Impact Assessment
The central principle is:
A cross-impact matrix is only as defensible as the reasoning behind its cells. The number assigned to an interaction should summarize an analytical judgement—not substitute for one.
Interpreting a Cross-Impact Matrix
Once the matrix has been completed, researchers can move beyond individual cells and examine broader patterns.
One useful distinction concerns influence and dependence. A variable that strongly affects many other variables may function as an important driver within the system. A variable that is strongly affected by many others may be particularly dependent on system conditions.
A variable can also be both influential and highly dependent. Such variables may deserve special attention because they participate actively in feedback structures rather than simply driving or receiving change.
Interpretation should nevertheless remain tied to the design of the study. Summing ordinal scores can help reveal patterns, but mathematical aggregation does not transform subjective or expert assessments into objective measurements. Researchers need to retain the substantive reasoning behind the scores when drawing conclusions.
Unexpected cells may sometimes be more informative than the largest totals. A relationship initially considered unimportant may reveal a pathway that changes how researchers understand the wider system.
Cross-Impact Analysis and Delphi Method
Cross-Impact Analysis and the Delphi Method can complement each other because they address different aspects of expert judgement.
A Delphi study provides a structured, usually iterative process for collecting and refining judgements from a panel of experts. Cross-Impact Analysis provides a structure for examining interactions among developments.
For example, researchers could use Delphi to identify important future developments and obtain expert assessments of their likelihood or importance. Selected developments could then populate a cross-impact matrix, with experts evaluating how each development might affect the others.
Alternatively, interaction assessments themselves could be subjected to iterative expert review.
The methods should not be treated as interchangeable. Delphi primarily structures expert judgement, whereas Cross-Impact Analysis structures interdependencies among variables or events.
Cross-Impact Analysis vs Futures Wheel
Both methods examine relationships among future developments, but their analytical structures differ.
| Cross-Impact Analysis | Futures Wheel |
|---|---|
| Examines interactions among multiple selected variables | Begins with one central change or development |
| Usually represented as a matrix | Usually represented as a radial consequence map |
| Asks how A affects B, C, D and vice versa | Asks what consequences follow from the focal development |
| Can identify reciprocal influences | Primarily traces outward consequence pathways |
| Suitable for system interdependencies | Particularly suitable for direct and higher-order consequences |
| Can incorporate scoring or conditional probabilities | Usually exploratory rather than probabilistic |
The methods can also be used sequentially. A Futures Wheel may identify consequences that later become variables in a Cross-Impact Analysis, while Cross-Impact Analysis can reveal interactions among developments that a single-centre Futures Wheel does not capture easily.
Application of Cross-Impact Analysis: an Example
Consider a study exploring the future competitiveness of European commercial aviation by 2040. Preliminary Environmental Scanning identifies five potentially important developments: sustainable aviation fuel adoption, carbon regulation, battery-electric aircraft development, changing business-travel demand and expansion of high-speed rail.
The researcher constructs a cross-impact matrix containing these five developments. Each directional relationship is evaluated using an ordinal influence scale.
For example, stronger carbon regulation might receive a strong positive influence score on sustainable aviation fuel adoption because tighter emissions requirements could increase incentives for airlines to use lower-carbon fuels. However, the relationship may depend on fuel availability, price differentials and regulatory design. The researcher therefore records these conditions alongside the matrix assessment.
High-speed rail expansion might negatively influence short-haul air-travel demand, but the magnitude could vary substantially between routes. Dense intercity corridors with competitive rail journey times may experience stronger effects than geographically dispersed markets. The interaction should therefore not be interpreted as a universal relationship applying equally across European aviation.
The completed matrix could reveal that carbon regulation exerts substantial influence across several developments while aviation demand is highly affected by multiple external factors. These findings could then inform scenario construction or identify relationships requiring further expert investigation.
Advantages and Limitations of Cross-Impact Analysis
The major advantage of Cross-Impact Analysis is that it challenges the assumption that important future developments can be understood independently. By forcing researchers to examine directional relationships explicitly, the method can expose reinforcing processes, constraints, dependencies and potential feedback structures that would otherwise remain implicit.
The matrix also creates analytical discipline. Participants cannot simply state that “everything is connected”; they must consider specific relationships such as A → B and B → A separately. When the reasoning behind those judgements is documented, the method can make complex expert assessments more transparent.
However, complexity increases rapidly with the number of variables. Large matrices impose substantial cognitive demands on participants and can create hundreds of relationships requiring judgement. This can produce fatigue and superficial scoring.
Cross-impact approaches also face methodological challenges surrounding subjectivity, consistency and time. Relationships may depend on assumptions or conditions that a single score cannot fully represent. An influence may emerge only after a substantial time lag, while static matrices can make the system appear more simultaneous than it actually is.
Quantification creates an additional risk. Numerical scores can give qualitative judgements an appearance of measurement precision they do not possess. Researchers therefore need to communicate clearly what their numbers represent and avoid interpreting ordinal assessments as though they were directly observed interval-scale data.
Common Mistakes When Using Cross-Impact Analysis
One common mistake is selecting too many variables. Researchers may assume that a larger matrix produces a more comprehensive analysis, while in practice the rapidly increasing number of relationships can reduce the quality of individual judgements.
Another is treating the relationship between A and B as automatically symmetrical. A → B and B → A are separate analytical questions and may have different directions and strengths.
Arbitrary scoring is particularly problematic. Filling cells because every cell appears to require a number can create false precision. A score should reflect a defensible judgement, and researchers should permit a neutral or negligible relationship where appropriate.
Researchers may also overlook time and conditionality. A relationship that becomes strong only after ten years or only under strict regulation is analytically different from an immediate and broadly applicable relationship.
Finally, direct and indirect effects can become confused. If A influences B through C, assigning strong scores to A → C, C → B and A → B without examining the underlying mechanism may exaggerate the apparent influence within the system.
Cross-Impact Analysis in Business Research
Cross-Impact Analysis is particularly relevant to business problems characterized by interconnected external and organizational changes. Strategic decisions rarely depend on a single trend operating independently.
A company considering future manufacturing investment, for example, might analyse interactions among energy prices, automation, labour availability, carbon regulation, geopolitical supply-chain risk and customer sustainability expectations. Cross-impact analysis can reveal that a development appearing moderate in isolation becomes strategically important because it influences several other variables.
The method can also support industry foresight, technology strategy, market-entry research, supply-chain analysis and scenario development. Its value lies less in predicting one business future than in helping researchers understand the system of interacting forces from which different futures may emerge.
Cross-Impact Analysis in the Age of AI and Digital Research
AI can reduce some of the practical burden associated with Cross-Impact Analysis. It can help researchers organize large sets of candidate variables, detect duplicate concepts, retrieve evidence relevant to proposed relationships, summarize expert rationales and identify matrix cells that may require closer examination.
Generative AI can also propose possible relationships extremely quickly. That capability should be treated cautiously. A language model can produce a convincing explanation for why A influences B even when the relationship is weak, highly conditional or unsupported. Automatically filling an entire matrix therefore risks replacing structured expert judgement with scalable speculation.
AI may be more valuable as a critical challenger than as an autonomous scorer. Researchers can ask it to identify alternative explanations, possible time lags, mediating variables, contradictory evidence or conditions under which an assumed relationship might fail. Those suggestions can then be evaluated against appropriate sources and expert knowledge.
Digital systems also make it easier to preserve the rationale behind individual matrix cells. Instead of storing only a numerical score, researchers can maintain evidence, comments, uncertainty assessments and revisions associated with each relationship. This improves transparency and becomes particularly important as cross-impact models become larger.
AI therefore makes matrix construction easier, but it does not remove the central methodological requirement: the researcher must still be able to defend why A is believed to influence B.
When to Use Cross-Impact Analysis
Cross-Impact Analysis may be appropriate when:
- the research problem involves several interacting future developments rather than one isolated trend;
- understanding interdependencies is important to the research question;
- researchers need to examine how occurrence or change in one variable could influence others;
- Environmental Scanning or another method has already identified a manageable set of important developments;
- expert judgement can contribute meaningfully to assessing relationships;
- scenario development requires a better understanding of compatible or interacting developments;
- researchers need to identify influential and dependent variables within a future system; or
- a Futures Wheel has identified important consequences whose interactions now require investigation.
The method is less appropriate when variables are poorly defined, there is no meaningful basis for assessing their interactions, or the research question concerns an isolated relationship better addressed through another research design.
Dissertation Example
Consider a dissertation titled “Exploring the Interactions Shaping the Adoption of Green Hydrogen in the European Steel Industry to 2040.” Cross-Impact Analysis could be justified because green-hydrogen adoption is influenced by several developments that may themselves interact, including renewable electricity costs, carbon pricing, hydrogen infrastructure, technological maturity and government subsidies.
In the methodology chapter, the researcher could explain that candidate developments were first identified through literature review and Environmental Scanning and then refined to produce a manageable set of clearly defined variables. A panel of industry and energy experts could assess each directional relationship using a predefined ordinal scale, with short written rationales collected for important interaction scores.
The researcher should explain that the resulting numerical values represent structured expert assessments of influence rather than directly measured causal effects. The analysis could then examine which variables exert influence across multiple parts of the system, which are highly dependent on other developments, and which relationships appear especially uncertain or conditional.
For example, experts might judge lower renewable-electricity costs to exert a strong positive influence on green-hydrogen competitiveness, while the reverse relationship is weaker. The methodology chapter should document the reasoning behind such asymmetric assessments and explain how disagreement between experts was handled. The matrix could subsequently inform scenario development by identifying combinations of developments that warrant deeper investigation.
Exam Tip
When explaining Cross-Impact Analysis, do not define it merely as “putting variables into a matrix.” The matrix is the representation, not the methodological purpose.
A stronger answer explains that Cross-Impact Analysis systematically examines how selected future events, trends or variables may influence one another. Each directional relationship should be considered separately, and qualitative scores or conditional probabilities may be used depending on the particular cross-impact approach.
Remember:
A → B does not necessarily equal B → A.
And if you assign a score to A → B, be prepared to answer the most important methodological question:
Why?
Need to analyse several interacting developments in your dissertation? Dudovskiy Research Assistant can help you determine whether Cross-Impact Analysis fits your research question, define appropriate variables, structure a cross-impact matrix and develop defensible reasoning for the relationships you assess.
References
Gordon, T.J. & Hayward, H. (1968). Initial experiments with the cross impact matrix method of forecasting. Futures, 1(2), 100–116.
Gordon, T.J. & Helmer, O. (1964). Report on a Long-Range Forecasting Study. RAND Corporation.
Glenn, J.C. & Gordon, T.J. (Eds.). (2009). Futures Research Methodology—Version 3.0. The Millennium Project.
Helmer, O. (1981). Reassessment of cross-impact analysis. Futures, 13(5), 389–400.
Weimer-Jehle, W. (2006). Cross-impact balances: A system-theoretical approach to cross-impact analysis. Technological Forecasting and Social Change, 73(4), 334–361.