4.3 Rank Ordering Objectives With Pairwise Comparison Charts Flashcards
What is a pairwise comparison chart (PCC) used for?
The pairwise comparison chart (PCC) is a simple matrix (a tool) for ordering the relative importance of objectives. It is based on the assumption that we can order any two objectives taken as a pair.
Pairwise comparison charts are based on what assumption?
Pairwise comparison charts are based on the assumption that we can order any two objectives taken as a pair.
What are the main three benefits of a pairwise comparison chart?
The main benefits of a pairwise comparison chart are that it allows us to:
- compare every objective with each remaining objective individually
- add total scores for each objective
- and if constructed correctly, preserve the important property of transitivity
What are the rules for constructing a pairwise comparison chart?
The rules for constructing a pairwise comparison chart are as follows
- Goals are ranked against each other in chart form
- Every entry is either a “1” or a “0”, where “1” indicates that the row objective is preferred over the column objective.
Consider an example of a pairwise comparison chart and rank the four objectives in order of decreasing value/importance?
Based on the example pairwise comparison chart, the order of importance of objectives are as follows:
- Portability (score of 3)
- Convenience (score of 2)
- Cost (score of 1)
- Durability (score of 0)
The sticking point of rank ordering objectives with pairwise comparison charts derives from what theorem of decision theory?
The sticking point of rank ordering objectives with pairwise comparison charts derives from the Arrow Impossibility Theorem of decision theory.
What is the main idea of the Arrow Impossibility Theorem of decision theory?
The main idea of the Arrow Impossibility Theorem of decision theory is that it is impossible to run a “fair” aggregation and preserve transitivity when there are more than two objectives to rank.
Provide an example that illustrates the Arrow Impossibility Theorem of decision theory concept that it is impossible to run a “fair” aggregation and preserve transitivity when there are more than two objectives to rank.
Suppose a team of 12 people is asked to rank order three objectives: A, B, and C. In doing so, the 12 individuals produce 12 individual orderings that, using the ranking symbol using the ranking symbol “>” to indicate that A > B means “A is preferred to B,” are:
Based on summing for the pairwise comparison chart example, what is the group consensus regarding relative importances?
Based on summing for the pairwise comparison chart example, C is most important, B second, and A least.
In what fashion should the pairwise comparison chart approach be applied?
The PCC (Pairwise Comparisons Charts) approach should be applied in a constrained, top-down fashion, such that:
- objectives are compared only when at the same level on the objectives tree, and
- the higher-level objectives are compared and ranked before those at lower, more detailed levels.
- more “global” objectives (i.e., those more abstract objectives that are higher up on the objectives tree) are properly understood and ranked before we fine-tune the details.
Why should PCC (Pairwise Comparisons Charts) be applied in a constrained, top-down fashion?
The PCC (Pairwise Comparisons Charts) approach should be applied in a constrained, top-down fashion because:
- For many design tasks, only top-level objectives need be so ranked.
- Rankings of objectives cannot be put on a scale or ruler.
- We cannot attach relative weights to objectives or make similar calculations.
When would it make sense to rank objectives below the top level?
It would make sense to rank objectives below the top level only for the design of complex subsystems, within large and complex systems.
Note another example of a pairwise comparison chart.
