Italian Flags

Why do we need to consider using an Italian Flag of uncertainty?
Because we are collectively realising that the world is more complex than we previously thought.

The Italian Flag can help in at least four ways:-

  • to make better decisions
  • to manage uncertainty
  • to allow us individually and collectivelyto admit we don’t know when we genuinely don’t know
  • provide a means by which we can embark on a ‘learning journey’ through complexity together

What is an Italian Flag of uncertainty?

We have characterised uncertainty in the FIR space (Fuzziness, Incompleteness and Randomness).

Our purpose now is to have a relatively simple and practical measure of evidence that can be used on open complex problems. We propose a mapping (i. e. a functional relationship) from the FIR space to an interval probability measure that we colour in and call an Italian Flag (IF).

The mapping is essentially a judgement of the strength of evidence assessed on a scale [0, 1]. We appraise quite separately the evidence in favour of and the evidence against a proposition. In particular we are concerned with the proposition, at a point in time, that a process is heading for success or failure.

The mapping is a judgement but we have found that a useful way to think about it is as a vote (see further down this page).

Evidence in favour is coloured green, as shown here.  



Evidence against is assessed on a scale [0, 1] and is coloured red, starting from 1 and working back to zero. The difference in the middle is white and makes an Italian flag.

If the evidence is, for example, [0.4, 0.9] there is 40% green, 10% red and 50% white.

There are three interesting special cases.
Evidence=[1, 1], which is all green, and means that there is complete evidence for and no evidence against (no red).
Evidence=[0, 0], which is all red, and means that there is complete evidence against and no evidence for (no green).
Evidence=[0, 1], which is all white, and means there is no green evidence for and no red evidence against, and so we really ‘do not know’.

Italian Flags are not physical measures

Note that judgements of the strength of evidence are not easily testable in the same way as the measurements we are used to relying on in physical science.

Italian flags are not physical measures like mass, length and time but, as we have said, are measures of judgements about the strength of evidence concerning a particular proposition such as reaching our objectives in a process.

The propositions are of two basic types which are typically described as objective and subjective but which perhaps are better described as testable and non-testable.

Testable propositions can be checked by repeatable experiments performed by anyone with the requisite skills and equipment. Non-testable propositions cannot be easily tested except by constant critical discussion by the players involved in a decision.

If we have measures over large samples then they may be statistically testable but when they represent individual judgements they can only be tested by making comparisons between players of similar expertise.

How might we use Italian Flags?

There are two basic ways – qualitatively (see below) and quantitatively. Each has advantages and disdavantages.

Using Italian Flags qualitatively

The following figure shows a simple model of a process with two subprocess holons, which together are necessary for the success of the top process.


The players who own each process associate an Italian flag with that process. The flag represents their view, based on evidence, that their process will be successful. Clearly, there is something wrong in the diagram as the flags are
inconsistent (in a rather blatant way for the purpose of an example). This means that the process owners when they realise this inconsistency can discuss the reasons for it and decide on adjustments or on what needs to be done to ensure success. This type of social process can enable the team members to admit what they ‘do not know’, and hence take action to
manage it and importantly to learn from it.

Below is a more practical example again simplified for illustration concerning owning, operating and assessing the stability of a dam. The text in the boxes with a green outline lists the reasons for the judgements of the evidence for the success of each process and the boxes outlined in red do the same for the judgements about the evidence against.

What are the advantages and disadvantages of using the Italian Flags qualitatively?

The advantages are

  • simplicity – no need for mathematics
  • intuitive
  • facilitates discussion amongst the players in a process

The disadvantages are

  • may not be rigorous
  • possibility of logical inconsistencies
  • inferences may not be repeatable

Let us now go on to examine the quantitative approach.  So far on this page we have been using the Italian Flag purely purely as a qualitative tool to facilitate learning. Now we want to explore being numerically more rigorous. However the issues are not straightforward and it is particularly important to understand the underpinning concepts of dependency, necessity and sufficency as explained on the next page on the quantitative approach. Indeed these ideas are important in all forms of numerical analysis.