Sunday, 28 December 2014

The Ocean Health Index - mathematics visited.

One Ocean, One Index – a 'Composite Essay' on Opportunities and Limits.

The scrutiny: Composite averaging and intermediate level of substitution
Rickles and co-workers [2] illustrate how limited substitution possibilities can be implemented for the ocean-health index using appropriate mathematics, i.e. specific functional forms ("functions of functions") [f]. The mathematical methods for calculating the index can get increasingly composite. They may combine nested approaches, generalized means, variable setting of substitution, constraints on the overall score for the less-performing assets, "hard" lower boundaries, etc.
Evidently, such kind of "composite averaging procedure" lacks the simplicity of the arithmetic average. The "composite averaging procedure" is an elaborate model of the substitution possibilities, which has to be analysed with care; not only for its non-linear behaviour. Notwithstanding its complexity, such a model could capture our best understanding of the functioning of the ocean-human intersections through appropriate mathematics. As such it may be a useful research tool.

However, for any index to be a useful management tool (e.g. how to value different resources or options) the method how the score of the index is calculated needs to be understandable. Therefore, the mathematical complexity of the composite model may be too high, and many users may prefer the method "weighted arithmetic average". Rickles and co-workers [2] show how the score of the index depends on the mathematical method.

[2], [f]: for references see "One Ocean, One Index – a 'Composite Essay' on Opportunities and Limits" 

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