The Mathematics of Hiview and Equity

Keywords The Mathematics of Hiview and Equity Implementation in Hiview Equity
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Hiview allows a hierarchical representation of objectives and criteria.
Criteria are clustered under ‘parent’ nodes. All options are scored on all
the criteria under the parent. The criteria are weighted. Whatever
weighting system is used, Hiview assumes that the ratios of those weights
are sacrosanct, and it normalises them by dividing the weight on each
criterion by the sum of the weights on all the criteria under that node.
This preserves the ratios, and yields a set of weights that sum to 1.
Those weights are used in the above equation to give a single, weighted
average scale for the parent node. A Hiview matrix from the ‘Shampoo’
model shows how equation (1) is implemented. (Note that the weights
are shown here normalised. They were assessed as 60 and 120,
respectively for Size and Share.)

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The two computer programs Hiview and Equity are both based on multicriteria decision analysis, the subject of Keeney and Raiffa’s 1976 classic book. In that book, the authors extended the axioms of decision theory, which lead to the expected utility model, to provide for consequences characterised by multiple criteria. They pointed out, and Keeney (1992) subsequently elaborated, that decisions are made to realise objectives, but that objectives often conflict. How to deal with that conflict is the subject of multi-criteria decision analysis. Their approach is particularly attractive because it accommodates consequences that are both uncertain and appraised differently depending on the criteria considered.

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