THE QUESTION OF INTEGRATION
The question as to how one might effectively integrate measures/descriptions of impacts associated with water projects has long been of concern to analysts. Problems of integration stem primarily from the fact that impacts associated with the various objectives are, and we have argued should be, presented in different units. In this appendix, we explore this issue. Our purpose is to draw attention to the past debates regarding integration and alert the reader of some of the problems of a broad benefit-cost analysis.
F.2 AN EXAMPLE OF INTEGRATION PROBLEMS
Impacts on income-related items (included in the benefit- cost measure) are summed and are expressed in dollars. Distributive impacts are typically given by an (unsummed) array such as the percentage distribution of households in various income groups in the areas affected by different water reclamation projects. Environmental and or ecological impacts may be described by such measures as income or acres of wildlife habitat preserved, an affected biological species, and/or numbers of encounters (relevant for "congestion" in a wilderness experience).
The impacts associated with two projects under consideration might be represented as follows:
PROJECT A PROJECT B ______________________ ________________________ Benefit/ (a) .89 (a) 1.2 Cost Measure: Benefits: $20.2 mill. Benefits: $27.8 mill. Costs: $22.7 mill. Costs: $23.2 mill. (b) benefits and (b) a good part of costs are certain. Project benefits are uncertain. Distribution: 75% of affected 15% of affected Population "poor"; population "poor"; 90% of project incomes 10% of project incomes (benefits) accrue to (benefits) accrue to the poor. the poor. Environmental No wilderness areas Half of the lands Impacts: are affected in a 10 million acre
The trade-offs involved with these two projects are obvious: the greater, but uncertain, economic efficiency of Project B, as seen in the benefit/cost ratio of 1.2, may be traded off with the more certain, smaller income related benefits, greater effects of improving income distributions, and the protection of established wilderness areas affected by Project B. Alternatively, if Project A was being considered in isolation, the relevant trade-off to be considered is that between the objective of improving the incomes and social well-being of low income households in the state, with investing in "efficient" projects.
Thus, integration may involve nothing more than a presentation of the array of project-related impacts as exemplified above for projects A and B. Indeed, this mode of "integration" is the one implied by the arguments of Bromley and others described above. However, "integration" implies to many the need to bring together the diverse impacts of a project in one common unit (i.e., dollars) such that the impacts can be summed, and the net beneficial effects of the project can then be expressed as single integer. Then that integer can be compared with those derived for other projects to the end of comparing the relative desirability of projects. As an example, if we were to be told that each dollar of income had a "social weight" of 1 (for the purpose of this example, we ignore uncertainties), each dollar of income which accrues to low income families had a social weight of 1.25, and that each acre preserved in wilderness areas had a social value/weight of 1.5, the impacts of projects A and B could be expressed as an integer reflecting "social values" as follows:
Project A: (1) ($20.2 million - $22.7 million) + (1.25) (90% of $20.2 million, or $18.2 million) = - $2.5 million + $22.8 million = $20.3 million Project B: (1) ($27.8 million - $23.2 million) + (1.25) (10% of $27.8 million, or $2.8 million) + (1.5) (- $5 million) = $4.6 million + $3.5 million - $7.5 million = $0.6 million
Here, Wyoming's concern with the problems of the poor, environmental concerns, etc., are viewed as being adequately expressed in the weights 1.25 and 1.5, respectively. Intra- project trade-offs disappear, and the comparison of interest is $20.3 million with $.6 million and Project A is obviously superior. The obvious problem with this approach, of course, is with: where does one find these crucial weights? The answer to this question is equally obvious: you don't; at least, to date we know of no one's success in this regard.
F.3 THE PAST DEBATE AND OUR THOUGHTS
During the late 1960s and early 1970s, a great deal of effort was expended by economists and systems engineers with this approach (as examples, see Major  and the critique by Freeman and Haveman, ; Flack and Summers ; Miller and Byers ; and Seneca ). Of course, while analysts could provide any number of numeric algorithms for "integrating" benefits and costs of multi-objective projects, applications of these models were persistently stymied by the lack of information as to appropriate weights which might be assigned to non-monetary objectives:
Unless weights (values) can be specified or there is a political process for choosing among projects, the social optimum cannot be defined, and nothing further can be said about the choice of projects (Freeman and Haveman , p. 1534).In his treatise of efficiency in government through systems analysis, McKean acknowledges that:
In order for such opportunities (to use operations research methods for project analyses) to exist, there must be . . . meaningful quantitative indicators (weights) of gains and losses (, p. 16).Of course, the search for weights runs counter to Bromley's earlier noted admonition that everything is subject to conversion to a single integer. At issue in the "weights" problem is the well-known Arrow Impossibilities Theorem, which in homey terms, demonstrates the impossibility of acquiring meaningful social weights for these diverse impacts (Arrow ). Our view is that this admonition is well made, and that "integration" must be taken to describe no more than, but certainly no less than, the process of bringing together, in a comprehensive manner, the full array of relevant beneficial and adverse effects of a project.
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