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Sustainability and the Infinite Future: A Case Study of a False Modeling Assumption in Environmental Economics

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Abstract

This essay examines the issue of false assumptions in models via a case study of a prominent economic model of sustainable development, wherein the assumption of an infinite future plays a central role. Two proposals are found to be helpful for this case, one based on the concept of derivational robustness and the other on understanding. Both suggest that the assumption of an infinite future, while arguably legitimate in some applications of the model, is problematic with respect to what I call “Parfitian” welfare functions. This result is relevant to debates about discounting the future in economics and environmental ethics.

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Notes

  1. Undiscounted utilitarianism weights the utility of each generation equally (see Heal 1998, pp. 12–13).

  2. Note that the ⇐ direction in both definitions is always trivially satisfied. For instance, in the definition of dictatorship of the present, γ K can be identical to α K and σ K identical to β K , and similarly in the definition of dictatorship of the future.

  3. The two additional technical assumptions are continuity and independence (see Chichilnisky 1996, pp. 246, 251–252). Continuity is also assumed in Koopmans (1960) and Diamond (1965), and is criticized by Broome (1992) as not being a genuine normative constraint on welfare functions. Chichilnisky’s result also relies on the axiom of choice, and as a result her sustainable welfare functions are not always explicitly describable. Note, however, that if utility streams converge to limits, then W e+la (α) = W e (α) + W la (α), where W e (α) is exponentially discounted and W la (α) the limit of the average, is a sustainable welfare function.

  4. In the literature, time impartiality is sometimes also referred to as “anonymity” (Vallentyne 1995).

  5. Sensitivity is sometimes also divided into strong (sensitive to utility improvements of a finite number of generations) and weak (sensitive to utility improvements in infinite number of generations) variants. Strong sensitivity is the version of the concept used by Chichilnisky and throughout this paper.

  6. In addition, some authors seek to find welfare functions that satisfy intergenerational impartiality and which come as close as possible to being sensitive when inputs are infinite utility streams (cf. Zuber and Asheim 2012). Basu and Mitra (2007) pursue a related approach. Instead of welfare functions, Basu and Mitra recommend, “social welfare relations (SWRs) which are pre-orders that allow (consistent) comparisons between only some pairs of infinite utility streams but not others” (2007, 351; italics in original). They then show that there are social welfare relations that satisfy both sensitivity and impartiality.

  7. For simplicity, I assume that infinite utility streams converge to limits. As remarked in footnote 3, some restriction on utility streams is needed to ensure that sustainable welfare functions in Chichilnisky’s sense are explicitly describable.

  8. To see this, note that both α and β have the same lower bound (i.e., .5), so W n (α) = W n (β).

  9. I know of only one article in this literature, by Luc Van Liederkerke, that calls into question the assumption of an infinite future (Van Liederkerke 1995). However, Van Liederkerke does not discuss the possible grounds for adopting or rejecting this assumption and only remarks that utilitarians “should be cautious about an infinite future” (1995, p. 407).

  10. See Bahr et al. (2015) for an accessible introduction to some of the leading theories on this topic.

  11. In fact, Zuber and Asheim (2012) consider degrees of insensitivity.

  12. Thus, this case is distinct from those treated by “turnpike” theorems mentioned in Sect. 3.2. Turnpike theorems focus on goals, such as capital accumulation, where it is assumed that more is better than less. But even given a concept of sensitivity that admits of degrees, there seems no plausible reason why the most highly sensitive welfare functions should be preferred.

  13. This raises an interesting question about what the normative basis for sensitivity is. To see the concern, note that theories of justice do not always accept sensitivity as a general rule, since benefits that accrue only to the already advantaged will amplify inequalities. For example, such an increase of inequality would not be permitted by Rawls’ difference principle (Rawls 1971). Perhaps the most plausible argument for sensitivity is that it is a consequence of utilitarianism in finite populations.

  14. Other authors have also explored the distinction between abstraction and idealization (see Cartwright 1989; Jones 2005).

  15. Of course, assuming an infinite future enables some distinctions that could not be drawn otherwise, such as the difference between weak and strong sensitivity (see footnote 5). But the point here is to question the relevance of such distinctions for understanding decisions that concern a finite timeframe.

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Acknowledgements

I would like to thank Paul Bartha, Kareem Khalifa, Eric Schliesser, David Silver, Sean Valles, as well as audience members at the 2016 Philosophy of Social Science Roundtable and the 2016 Descartes Lectures at Tilburg University for helpful commentary and suggestions on earlier versions of this paper.

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    Daniel Steel

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Steel, D. Sustainability and the Infinite Future: A Case Study of a False Modeling Assumption in Environmental Economics. Erkenn 82, 1065–1084 (2017). https://doi.org/10.1007/s10670-016-9859-x

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