Cross-Impact Analysis

Cross-impact analysis is the general name given to a family of techniques designed to evaluate changes in the probability of the occurrence of a given set of events consequent on the actual occurrence of one of them. The cross impact model was introduced as a means of accounting for the interactions between a set of forecasts, when those interactions may not have been taken into consideration when individual forecasts were produced.

The origin of cross-impact analysis was the problem that Delphi panellists were sometimes asked to make forecasts about individual events, when other events in the same Delphi could affect these events. Thus, it was recognised that there was a need take these cross impacts of one event on another into account.
While cross-impact analysis was initially associated with the Delphi method, its use is not restricted to Delphi forecasts. In fact, cross impact models can stand alone as a method of futures research, or can be integrated with other method(s) to form powerful forecasting tools. A typical output of cross-impact analysis is a list of possible future scenarios and their interpretation.

Cross-impact analysis is mainly used in prospective and technological forecasting studies rather than in Foresight exercises per se. In the past, this tool was used as a simulation method and in combination with the Delphi method.
More recently, cross-impact analysis was used on a stand-alone basis or in combination with other techniques to answer a number of research questions on different subjects such as the future of a particular industrial sector, world geopolitical evolution, the future of corporate activities and jobs. The target audience for this method typically comprises experts from industry, academia, research and government.


The steps described in this section are valid for different variations of cross-impact analysis. The steps needed to implement the SMIC method (developed in France in 1974 by Duperrin and Godet) which is supported by dedicated software, are described here.
Choice of the issue and selecting experts: The purpose of a cross-impact exercise is primarily to gain more insight into future developments of selected issues. The collection of information on the historical background of such issue is therefore important: during this step a preliminary list of events related to the issue could be formulated.

The survey is usually carried out by mail or over the Internet. The experts chosen should be familiar with the issue under study and they should have some capacity to envisage future developments. However, as for all other techniques that rely on eliciting expert opinion, there is the problem of avoiding bias in the group of experts.

It is not obvious how to define ‘relevant expertise’ when complex technological, social and political issues are involved. There are no clear guidelines, either on whether it is better to have a panel of experts which involves experts from various sub-disciplines of the subject considered, or if it is better to have experts that are highly specialised or generalists with a broad view. To some extent, a large multidisciplinary group of experts should narrow down the risk of a biased sample of experts.

Experts are normally asked to do the following:

• Appraise the simple probability of a hypothesis occurring by means of a scale from 1 (very low probability) to 5 (highly probable)

• Appraise the conditional probability of a hypothesis if the others occur or not.

Final selection and definition of the events: This step is crucial to the successful implementation of the method; in fact any influence not included in the events’ set will be completely excluded from the study. On the other hand, the inclusion of irrelevant events can complicate the final analysis of the results unnecessarily. The final list of events should be as clear as possible, definitions and wording must be carefully checked and defined. The selection of events to be included in the final list can cover both the occurrence and non-occurrence of events (i.e. ‘no price increase is taking place’ are non-occurrence events, whereas events such as ‘price increase is taking place’ is considered an occurrence event). Then, the events considered can be totally independent or connected in some way.

The final list of events can also be compiled with the support of experts on the selected issue, or can stem from other methods used to collect opinions, such as the Delphi method.


Design of the probability scale and definition of the time horizon: The definition of a probability scale is needed to translate qualitative appreciation from the experts on the degree of occurrence (e.g. most probable, very probable etc.) into probabilities. In general, the probability scale for cross-impact methods usually goes from 0 (impossible event) to 1 (almost certain event).

This step also involves determining the time horizon of the forecast. In the context of Foresight the main objective is to try to think ahead in the long term. Therefore, in Foresight the short term is considered to range from the present to five years from now; the medium term from five to ten years; and the long term from twenty to fifty years. In fact one of the main differences between Foresight and planning is the temporal dimension. The time horizon to be considered in a cross-impact analysis must be stated explicitly.


Estimating probabilities: In this step the initial probability of the occurrence of each event is estimated. Then, conditional probabilities in a cross impact matrix are estimated in response to the following question: ‘If event x occurs, what is the new probability of event j’s occurring?’ The entire cross-impact matrix is completed by asking this question for each combination of occurring event and impacted event. The SMIC is designed to enable experts’ estimates to be checked for consistency. The SMIC method invites the experts to answer a grid the following questions:

• the probability of occurrence of each single event at a given time-horizon
• the conditional probabilities of the separate event taken in pairs at a given time-horizon:
• P (i/j) probability of i if j occurs
• P (i/not j) probability of i if j does not occur

Once the results are collected, they are entered on the computer and the program is run.


Generation of scenarios: The outcome of applying a cross-impact model is a production of scenarios.
Regardless of how the issue of assigning probabilities is resolved in specific cross-impact models, the usual procedure is to carry out a Monte Carlo simulation (Martino and Chen, 1978). Each run of the model produces a synthetic future history, or scenario, which includes the occurrence of some events and the non-occurrence of others.
The model is thus run enough times (i.e. approximately 100 in the SMIC version), so that the collection of output scenarios represents a statistically valid sample of the possible scenarios which the model might produce.

In a model with n events, “2 to the power of n” possible scenarios are generated, each differs from all the others in the occurrence of at least one event. For example, if there are 10 events to be considered, there are 1024 possible scenarios to estimate.
On the basis of the specific cross-impact model applied, the output scenarios attempt to generate either the best scenario – in the sense of likelihood of occurrence; or a set of statistically consistent scenarios; or one or more plausible scenarios from the total set. The SMIC method generates a cardinal sequence of possible scenarios (from the most probable to the least probable). This allows you to circumscribe the area of plausible future developments by retaining only those which have a high-average probability of occurrence. The list of scenarios generated by the software needs to be interpreted and described by referring back to the original set of events.

Once the cross-impact matrices are calculated, it is possible to carry out a sensitivity analysis. Sensitivity analysis consists of selecting an initial probability estimate or a conditional probability estimate, about which uncertainty exists. This judgment is changed and the matrix is run again. If significance differences appear between this run and the original one, then it is apparent that the judgment that was changed plays an important role. It may be worthwhile to reconsider that particular judgment.


The implementation of this method requires a minimum of two to eight months for the generation of the set of events and the running of the inquiry, and the interpretation of results. This time can vary and can be longer, if other tools and/or methods are used to define the set of the events (i.e. structural analysis, Delphi). Depending on the specific cross-impact tool applied by supporting software is needed.
In the case of the SMIC method, the special-purpose software can be downloaded free on request over the Internet []. Cross-impact analysis requires some (limited) skills in order to analyse the results. It requires specific modelling knowledge if the user wants to understand how the data are processed by the software.

Pros and cons

The main benefits are:

• It is relatively easy to implement a SMIC questionnaire
• Cross-impact methods forces attention into chains of causality; a affects b; b affects c.
• Estimate dependency and interdependency among events
• It can be used to clarify and increase knowledge on future developments

The following limitations need to be highlighted:

• Limitation in the number of events to be included in the inquiry (this is also a software limitation). In fact, with a set of ten events an expert should provide 90 conditional probability judgments. The task is somewhat tedious and a high number of drop-outs should be expected.
• It is very difficult to explore the future of a complex system with limited number of hypotheses. Interactions between pairs of events: does this reflect reality?
• Difficult to understand the consistency and validity of the technique.
• As any other techniques based on eliciting experts’ knowledge, the method relies on the level of expertise of respondents.


Many different cross-impact techniques were developed especially in the 1970s:

• KSIM, a simulation technique developed by J. Kane (1972) was based on expected interactions between time-series variables rather than events;

• EXPLOR-SIM developed by Duval, Fontela and Gabus is a cross-impact scenario approach;

• In 1975 the Futures Group developed a probabilistic system dynamics that was a joining of system dynamics and time-dependent version of cross-impact.

• INTERAX is a method developed in 1980 by Enzer that incorporates cross-impacts concepts.

Complementary methods

Cross-impact analysis can be used in combination with the Delphi method to check cross impacts between events. The method is also used in combination with other techniques as a tool to build scenario.
Some variations of cross-impact analysis are used as expert’s inquiry in combination with structural analysis, analysis of actors’ strategies. Since the method makes it possible to consider only a limited number of hypotheses, it is therefore important to use techniques (i.e. structural analyses-type methods) which allow for a better identification of key variables of a system, and consequently better formulation of basic hypotheses.