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Research Papers

Aggregation and Multilevel Design for Systems: Finding Guidelines

[+] Author and Article Information
Donald G. Saari

Institute for Mathematical Behavioral Sciences, University of California, Irvine, CA 92697-5100dsaari@uci.edu

A point that was strongly reinforced by a referee’s comments.

The Pareto condition can be replaced with the much weaker condition where at least each of two pairs of alternatives have at least two different societal outcomes (8).

If a divide-and-conquer method does not have compatibility requirements, it may be immune from the negative assertions developed here.

As an illustration, in an ongoing project with A. Chandra, the compatibility conditions are, as of now, unspecified conditions about a certain process that can cause cracks in the product. Part of the project is to use the information from this paper to identify the appropriate compatibility conditions.

This condition helps to capture my objective of understanding what causes incompatible outcomes, i.e., if a particular element always is in compatible outcomes, it probably does not cause the experienced difficulties, so ignore it. Anyway, engineering issues seldom are so accommodating.

As an illustration of how these kinds of problems are avoided in a special case, an integrated way is developed in Saari (14) to relate the total mass and rotational velocities of a galaxy.

In practice, when such an event occurs, an adjustment is made to create a compatible outcome. But, the path-dependency concern raises the issue whether the adjustment is an appropriate one. Also, the adjustment involves an extra step, which increases costs, and reflects the “inefficiency” message of theorem 2.

“Majority vote” is used only to illustrate; the same effect occurs with other paired comparison rules.

J. Mech. Des 132(8), 081006 (Jul 28, 2010) (9 pages) doi:10.1115/1.4002075 History: Received December 08, 2008; Revised May 14, 2010; Online July 28, 2010; Published August 10, 2010

All areas of engineering have a need to find appropriate aggregated outcomes for systems. Issues range from decision problems, “divide-and-conquer” approaches that include aspects of multidisciplinary design optimization and the effects of a division of labor for, perhaps, a design project, the inefficiencies that can accompany multidisciplinary projects involving, say, design, manufacturing, and sales, to the complexities of multiscale design, analysis, and even nanotechnology. But as shown, if the adopted approach (e.g., management choices, divide-and-conquer methodology, modeling of the biology/physics, decision rule, etc.) satisfies particular accepted practices, then certain complexities and inefficiencies must be anticipated. A disturbing corollary is that even should “success” appear to have been achieved with an approach that satisfies these conditions, it need not be as firm as expected. Ways to improve methodologies must avoid the specified conditions.

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