**Three Examples of quantitaive use of Italian Flags based on the**** demo page**

Try these examples and see how they work for you.

**1. Owning a dam and running it successfully**

Parent (top) Process 1: *Owning a dam*

Child (bottom left) Process 2: *Assessing the stability of the dam*

Child (bottom right) Process 3: *Operating the dam*

Starting flag for Process 2 = [0.45, 0.9]

Starting Flag for Process 3= [0.2, 0.5]

Starting Dependency between process 2 and 3 (bottom slider) = [1, 1]

Starting Sufficiency of Process 2 for Process 1 (top left slider) = [1, 1]

Starting Necessity of Process 2 for Process 1 (bottom left slider) = [1, 1]

Starting Sufficiency of Process 3 for Process 1 (top right slider) = [1, 1]

Starting Necessity of Process 3 for Process 1 (bottom right slider) = [1, 1]

**Comments**

The result for Process 1 = [0.45, 0.5] because lower and upper bounds are the maxima of the equivalent child processes. 0.45 is biggest green and 0.5 is biggest red because we are using the simple union of totally dependent child processes.

Try

1) varying the dependency values – you can change the lower bound and you’ll see some inconsistent blue below about 0.75 and if you reduce the upper bound you get inconsistency in the Venn diagram almost straightaway;

2) moving both dependencies bounds back to [1, 1] and then varying the bounds on Processes 2 and 3 and you’ll see big changes in Process 1;

3) checking out the Venn diagrams at bottom right – notice how the rectangles for each process separate as you reduce the dependency from 1 (total dependency) to 0 (mutual exclusion);

4) playing with necessity and sufficiency values and observing where you are on the top right diagram. You can move around to each corner – for example to see you get all red when both are [1, 0] and all green at [0, 1] and when at exact opposite [0, 0] with dependency at [1, 1] you get [0.5, 0.55] i.e. [1-upper bound of largest red = 1 – 0.5 = 0.5 and 1 – largest lower bound of green = 1 – 0.45 = 0.55.

**Conclusion** Interpreting the results is tricky but strictly logical according to the assumptions of the theory.

**2. Creating a good design for a structure**

Parent (top) Process 1: *Making the structure good*

Child (bottom left) Process 2: *Making the structure safe*

Child (bottom right) Process 3:* Making the structure sustainable*

Starting flag for Process 2 = [1, 1]

Starting Flag for Process 3= [0, 1]

Starting Dependency between process 2 and 3 (bottom slider) = [1, 1] because a sustainable structure must be safe

Starting Sufficiency of Process 2 for Process 1 (top left slider) = [1, 1]

Starting Necessity of Process 2 for Process 1 (bottom left slider) = [1, 1]

Starting Sufficiency of Process 3 for Process 1 (top right slider) = [0.3, 1]

Starting Necessity of Process 3 for Process 1 (bottom right slider) = [1, 1]

**Comments**

The result for Process 1 = [1, 1] because we have made safety sufficient for a good design and there is no negative evidence of lack of sustainability. However if we introduce some by lowering the upper bound on Process 3 (increasing red) then we get inconsistency (blue) in Process 1. If we reduce either or both bounds on necessity between Process 3 to Process 1 to [0, 0] we remove the inconsistency but now the failure of Process 3 (by increasing the red or lowering the upper bound) has no effect on Process 1 because safety in Process 2 is sufficient and sustainability is not necessary. As soon as we lower the sufficiency on safety in Process 2 to Process 1 then we see the green reducing and the red creeping in on Process 1.

**3. Is there life elsewhere in the Universe?**

Parent (top) Process 1: *Finding out if there is life elsewhere in the Universe.*

Child (bottom left) Process 2: *Finding any living organism of any type*

Child (bottom right) Process 3: *Deducing statistically that by sheer numbers the likelihood is high.*

Starting flag for Process 2 = [0, 1]

Starting Flag for Process 3= [1, 1]

Starting Dependency between process 2 and 3 (bottom slider) = [1, 1]

Starting Sufficiency of Process 2 for Process 1 (top left slider) = [1, 1]

Starting Necessity of Process 2 for Process 1 (bottom left slider) = [1, 1]

Starting Sufficiency of Process 3 for Process 1 (top right slider) = [0.8, 1]

Starting Necessity of Process 3 for Process 1 (bottom right slider) = [0.8, 1]

**Comments**

The result for Process 1 = [0.8, 1] is entirely dependent on the value of sufficiency for Process 3. Vary the lower bound on the sufficiency of Process 3 for Process 1 and the lower bound (green) on Process 1 varies with it. Vary the upper bound and some red creeps in. In other words in the absence of any real specific evidence in Process 2 then our belief in life in the Universe depends on how much credibility we give to the statistical argument.