# Driving with Eyes on the Rear-View Mirror—Why Weak Sustainability Is Not Enough

## Abstract

**:**

## 1. Introduction

#### 1.1. Context

#### 1.2. Objectives and Outline

_{t}and $\Delta $W

_{t}should be non-diminishing. W

_{t}should generate enough production to sustain itself and secure a surplus that maintains welfare.

_{t}and $\Delta $W

_{t}, $\forall t$, be non-diminishing: welfare should be sustained without reducing IW, i.e., without dis-saving.

## 2. Materials and Methods

w(t): | The time stream of welfare, for t in (0, …, ∞). |

${\widehat{w}}_{\tau}\left(\tau \right):$ | The time stream of expected welfare. The “hat” indicates expectations, which are revised over time, i.e., as $\tau $ becomes larger, for $\tau $ in (0, …, ∞). |

${W}_{0}^{\infty}:$ | The unobserved true value of IW evaluated at $\tau $ = 0. |

${\widehat{W}}_{\tau}^{\infty}$: | The expected IW evaluated at time $\tau $; when $\tau $ = 0, expected IW is ${\widehat{W}}_{0}^{\infty}$. Expected IW is revised over time, i.e., as $\tau $ becomes larger. |

${\widehat{W}}_{\tau}^{\infty}\left(\tau \right):$ | $\mathrm{The}\mathrm{time}\mathrm{path}\mathrm{of}\mathrm{expected}\mathrm{IW}.\mathrm{Although}{W}_{0}^{\infty}$ is, in concept, an integral with a fixed numerical value given the operative assumptions undergirding it, its expectation is revised at times $\tau $. |

${K}_{k0}^{\infty}$: | The value of a long-lived asset k at $t$ = 0, given perfect foresight. |

${\widehat{K}}_{k\tau}^{\infty}$: | The value of k given the expectations operative at time $\tau $. |

${\widehat{K}}_{k\tau}^{\infty}\left(\tau \right):$ | The time path of expected value of k, as revised at times τ. |

## 3. Welfare, Wealth, and Weak Sustainability

#### 3.1. Welfare and Wealth—The Promise of WS

#### 3.2. IW Is the Sum of Several Categories of Capital

#### 3.3. Accounting for Intangible Capitals—The Problem of Circular Reasoning

**Proposition**

**1:**

**Proposition**

**2:**

**Proposition**

**3:**

**Proposition**

**4:**

## 4. Asset Values in General Have a Circular Reasoning Problem

**Proposition**

**5:**

_{c}($t$), for t in (0, …,$\tau $−1) and vice versa. For example, the common expedient of capitalizing GDP to update ${\widehat{W}}_{\tau}^{\infty}$, in the large or for particulars (e.g., place-bound built and/or natural capital), assumes what it sets out to assess—the sustainability of current output and the welfare it generates—and therefore, fails to address the question of whether w(t) is being sustained by drawing-down wealth.

**Proposition**

**6:**

## 5. Tracking, Rather Than Projecting, Changes in IW

#### 5.1. Tracking $\Delta $IW

_{t}+ $\Delta $W

_{t}should be non-diminishing. W

_{t}should generate enough production to sustain itself and secure a harvest, literally in simple rural societies and metaphorically in all kinds of societies, which maintains welfare. Welfare can be maintained, at least for a while, by consuming capital. Thus, intergenerational equity requires that both w

_{t}and $\Delta $W

_{t}, $\forall t$, be non-diminishing: welfare should be sustained without reducing IW, i.e., without dis-saving. The present should not over-consume at the expense of the future nor over-save at the expense of its own wellbeing.

#### 5.2. Guardrails for WS:SS Suggests Three Kinds of Approaches

_{ij}SOS

_{i}is the downscaled SOS for pollutant i in jurisdiction j [36,37,38,39,40], that jurisdiction would be compliant if its footprint for i is no more than d

_{ij}SOS

_{i}. The literature downscaling various PBs for regions, cities, etc., is growing [41,42]; however, I am not aware of any jurisdiction that has committed to a d

_{ij}SOS

_{i}limit.

## 6. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Randall, A.
Driving with Eyes on the Rear-View Mirror—Why Weak Sustainability Is Not Enough. *Sustainability* **2022**, *14*, 10203.
https://doi.org/10.3390/su141610203

**AMA Style**

Randall A.
Driving with Eyes on the Rear-View Mirror—Why Weak Sustainability Is Not Enough. *Sustainability*. 2022; 14(16):10203.
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**Chicago/Turabian Style**

Randall, Alan.
2022. "Driving with Eyes on the Rear-View Mirror—Why Weak Sustainability Is Not Enough" *Sustainability* 14, no. 16: 10203.
https://doi.org/10.3390/su141610203