Help for the Italian Flag demo page
Start by looking at the demo page and then return to this page for interpretation and guidance.
Note that to start the demo you must move/click your cursor over the rectangular space below the title.
The rectangular space has three main areas which I will describe separately.
First on the left you see three boxes containing Italian Flags with grey boxes with sliders between them.
Second and top right is a graph showing the relationship between the sufficiency and necessity values – this needs some explanation – see below.
Third and bottom right are two Venn diagrams separately showing the results for the green and red evidence. Instead of circles I have used rectangles because they are easier to programme.
In the first area the top box for Process 1 contains the results from manipulating the green and red bounds of the lower processes 2 and 3. If you read the notes at the very top of the page then you can see that you can move the flags around by dragging their outside corners. You can change the green and red bounds on the two lower flags for Processes 2 and 3 by dragging their inside corners. You will see the corresponding results for the IF of Process 1.
Don’t worry at this stage if the flag turns blue – it shows you have a logical inconsistency and the choice is not acceptable. More on this further down this page.
The grey boxes contain sliders for you to change the bounds on the dependance between Process 2 and Process 3 and on the left the sufficiency and the necessity values between Processes 2 and 1 and between Processes 3 and 1. In each case the lighter slider bar is the lower bound. The initial values for dependency are [0, 1] and for sufficiency and necessity are [1, 1]. Try moving the values around and seeing what happens.
The second area at the top right is a graph which important in interpreting how the sufficiency and necessity values are influencing the weightings of the lower flags as they contribute to the upper flag. On the graph I have replaced R in Fred and Vera’s example with H for Hypothesis and A and B with E for Evidence.
As you move the sliders you will see lines or boxes appearing on the graph to show you the range of the choices you have made. Their influence is described qualitatively on the graph.
So for instance if you choose sufficiency = necessity =1 then the lower process E (on the page Process 2 or 3) is logically equivalent to the top process H (on the page Process 1). In other words the success of E is logically necessary and sufficient for the success of H.
If you choose sufficiency = necessity = 0 then the lower process has the exact opposite effect i.e. of H succeeds if E fails.
Note that values of necessity = 0 and sufficiency = 1 always result in an all green flag i.e. H succeeds whatever the evidence. The values on the diagonal are such that E is irrelevent to H.
So in summary when you choose sufficiency and necessity values you should recognise a) that values above the diagonal give weight to the evidence as providing increasing support and b) values below the diagonal give weight to the evidence as providing decreasing support and oppositeness.
Finally the third area at the bottom right of the page show Venn diagrams as rectangles for green and white areas and separately for the red and white areas. You will see them change as you change the green and red bounds on the IFs. The reason for the separation of the green and red areas is simply for clarity – one should really superimpose them on each other. I have included them as they may be useful in understanding what is happening to the various areas that we have discussed previously.
Why does a flag or an area of the Venn diagram go blue?
You will see blue when there is a logical inconsistency.
The simplest case is when the red and green areas overlap – you can make this happen yourself by dragging the bounds on Processes 2 and 3.
Of course those cases are easily changed. However if you get blue in the IF for Process 1 then the values for the IFs or the sufficiencies and necessities you have chosen should not be used because they are logically inconsistent.
Try this in a rather blatent way by choosing and all green flag for Process 2 and all red flag for Process 3 and a dependency between Process 2 and 3 which is total i.e. [1, 1]. The IF for Process 1 should be all blue. Now move the lower bound necessity on the all red flag to 0 and see the blue disappear and become green. Restore the values then change the lower bound sufficiency on the all green flag and see that Process 1 becomes all red.