Safe vs. Fair: A Formidable Trade-Off in Tackling Climate Change

Global warming requires a response characterized by forward-looking management of atmospheric carbon and respect for ethical principles. Both safety and fairness must be pursued, and there are severe trade-offs as these are intertwined by the limited headroom for additional atmospheric CO2 emissions. This paper provides a simple numerical mapping at the aggregated level of developed vs. developing countries in which safety and fairness are formulated in terms of cumulative emissions and cumulative per capita emissions respectively. It becomes evident that safety and fairness cannot be achieved simultaneously for strict definitions of both. The paper further posits potential global trading in future cumulative emissions budgets in a world where financial transactions compensate for physical emissions: the safe vs. fair trade-off is less severe but remains formidable. Finally, we explore very large deployments of engineered carbon sinks and show that roughly 1000 GtCO2 of cumulative negative emissions over the century are required to have a significant effect, a remarkable scale of deployment. We also identify the unexplored issue of how such sinks might be treated in sub-global carbon accounting.


Introduction
Climate change is recognized as one of the most challenging problems that the world faces today. At the same time, only limited progress has been achieved at the national and international level to address it. Nations have found it difficult to manage the atmosphere as a common property resource. They have been unable to distribute responsibilities among themselves for mitigation actions, and they have been reluctant to adopt unilateral policies, which they view as ineffective or even counterproductive. As a result, the stock of greenhouse gases in the atmosphere continues to rise. Since the Kyoto protocol of 1997, the atmospheric concentration of CO 2 alone has increased by about 25 parts per million, to more than 390 ppm. The coming decades will test the world's ability to decide how much needs to be done and who has to do what.
We assume that avoiding dangerous climate change and addressing the issue of responsibility and equity in CO 2 emissions are the two fundamental pillars on which comprehensive climate change legislation will be based (Stern 2009). Henceforth, we refer to these two as "safety" and "fairness". The extent to which 2 safety and fairness are mutually realizable and can be attained simultaneously will depend on future policies, institutions and technology, as well as the extent to which fossil fuels remain attractive. At the moment, this challenge appears immense (Pacala and Socolow 2004).
Equity and responsibility are repeatedly invoked to convey the obligations of the developed world in terms of mitigation action. Yet, researchers and policy makers discuss these objectives largely without reference to their interactions with the stringency of climate policy. This paper seeks to remedy this omission by demonstrating how fairness in its various guises is intertwined with safety. The strategy adopted is use the same physical concept, "cumulative emissions," to express both fairness and safety. Fairness is explored at the aggregated level of developed vs. developing countries. We focus on CO 2 emissions and ignore emissions of other greenhouse gases and aerosols. 2 We consider both energy (CAIT 2010) and land-use change emissions ( Houghton 2008) .
Cumulative emissions of CO 2 connect to safety through the concept of CO 2 "headroom." Headroom is defined as the difference between the maximum amount of CO 2 in the atmosphere judged to be safe (the "safety cap") and the amount already in the atmosphere. The safety cap can be linked to equilibrium temperature rise, and, consequently, expected damage. Headroom becomes smaller when climate stabilization targets become more stringent. The lower stabilization targets that have been emphasized in the past few years produce less headroom and thereby tighten the entanglement of safety and fairness.
Cumulative emissions connect to fairness when the atmosphere is viewed as a common property resource shared by all humans: In one version of fairness, all individuals have an equal right to CO 2 emissions in the atmosphere. This definition derives from 1) the right to economic growth and a better standard of living, and 2) the strong observed correlation between economic growth and CO 2 emissions. This fairness principle amounts to equating economic well being with cumulative CO 2 emissions. To be sure, this version needs to be supplemented with a decision about which people, past and future, should be included. In this paper we show the consequences quantitatively of specific inclusion rules. We do not explore quantitatively modifications that take into account how efficiency improvements and dematerialization of the economy weaken the connection between CO 2 emissions and standard of living.

Quantifying safety using global cumulative emissions
Our definition of climate safety is parameterized by a target expressed as a maximum rise in the earth's average global surface temperature. Recent work suggests that a relatively well-defined probabilistic linear relationship connects cumulative emissions and the rise in this temperature. Each 1000 GtCO 2 of cumulative emissions since pre-industrial times (here, year 1850) and extending indefinitely into the future produces, as the central value of the temperature distribution, roughly a half degree Celsius rise 3 (more precisely, 0.48 o C). Moreover, the temperature rise associated with 1000 GtCO 2 of emissions has a 90% probability of being in the interval between 0.27 o C and 0.68 o C (Solomon et al., 2010). 3 In IPCC parlance, values falling in this 90% confidence interval are called "very likely." This linear relationship allows us to use cumulative emissions as a quantitative metric for safety. Because the "very likely" range is quite wide, the desired level of risk aversion for a given temperature target (like "2 o C") strongly affects the cumulative emission target 4 .
We consider four global cumulative emissions budgets: 1000, 2000, 3000 and 4000 GtCO 2 of "future" cumulative emissions, where the year 2005 divides past from future. Table 1 reports the central value of the temperature distribution and the "very likely" range for these four emission budgets, obtained from the rules above and accounting for the 1800 GtCO 2 that was emitted in the atmosphere prior to 2005 5 . Values of temperature increase in Table 1 range from 0.8 o C to 4.0 o C. The 1000 GtCO2 is the only budget that achieves the 2 o C signpost with 'very likely' probability.
3 Solomon et al. recommends a multiplicative coefficient 1000 GtC of cumulative emissions per 1.75 o C of maximum temperature rise. It also provides a "very likely' range (centered range containing 90% of the distribution), where 1000 GtC of cumulative emissions produce a temperature rise between 1.0 o C and to 2.5 o C.
One GtC contains the same amount of carbon as 11/3 GtCO 2 .
4 The approach adopted here, moving directly between cumulative emissions and temperatures and thereby finessing concentrations, recognizes that temperature, rather than concentration, ultimately determines the impacts of climate change. Climate models enable the tracking of concentration and temperature trajectories associated with any emissions trajectory and the inclusion of other greenhouse gases. When we use MAGICC, with an emissions trajectory restricted to the 21 st century, we find that cumulative CO 2 emissions produce a temperature response in 2100 near the top-5% boundary.
5 The carbon budgets in Table 1 appear to be more permissive than budgets analyzed with integrated assessment models. Budgets meeting a 450ppm-equivalent concentration target have traditionally been associated with the 2°C objective. The IPCC Representative Concentration Pathway RCP 3-PD(2.6) generated by the IMAGE model (Van Vuuren et. al. 2007), for example, foresees a future cumulative CO2 budget of about 1500GtCO2. (The data are publicly available at http://www.iiasa.ac.at/webapps/tnt/RcpDb/dsd?Action=htmlpage&page=compare.) The models involved in the EMF22 international scenarios have, on average, only 1100GtCO 2 of future cumulative emissions . To compare integrated assessment models directly with the models whose outputs produced the simplified assumptions leading to Table 2, however, one must run the integrated assessment models beyond 2100, after which time cumulative emissions will continue to increase and surface temperature will continue to rise, As a result, a direct comparison is not possible. Moreover, all these models feature simplified carbon cycle modules, and each is simplified in its own way.  The relation between cumulative carbon emission and climate change measured by temperature increase is shown graphically in Figure 1. The twelve entries in Table 1 are shown as dots superimposed on a color-coded scale for global mean temperature change.

Quantifying fairness using per capita cumulative emissions
To include "fairness" in this formalism, we now move to a regional analysis at the highly aggregated level of developed versus developing countries, or, in this instance, the two UNFCCC categories of Annex I and Non-Annex I countries in the United Nations Framework Convention on Climate Change 6 . A global future cumulative emissions budget is the fixed sum of Annex I and Non-Annex 1 future cumulative emissions (A I and N-A 1, respectively). The sum is a simple straight line -the "safety line" in a chart like Figure 2, which plots the Annex I carbon budget on the horizontal axis and the Non Annex I budget on the vertical axis.

Global Future Cumulative Emission Budget = A I + N-A I
The ( Table 1. With this mapping the reader can consider safety and fairness simultaneously.
Once the reader has expressed a preference for a given safety line, the remaining choice is how to distribute the global carbon budget between Annex I and Non-Annex I.
Consider the simple case where the budget of future emissions is distributed according to population. We approximate the regional populations with values close to the United National population projections for 2050: 7.5 billion people in Non-Annex I and 1.5 Billion people for Annex I (UN World Population Prospects: The 2008 Revision). Thus, five-sixths of future emissions are assigned to Non-Annex 1; currently Annex I and Non-Annex I emissions are roughly equal. In Figure 2, emissions allocations for this case and our four specific targets appear as four black diamonds that fall on the line with a slope of 5, the population ratio. Note that by constraining cumulative emissions, this case gives more priority to equity than "Contraction and Convergence" schemes (Meyer 2000), which require the same per capita emissions for various parts of the world at some particular future date (typically 2050 or 2100). 7 The principle of equal per capita emissions is widely invoked, which is why it is at the core of this paper. Applications of per capita rules to climate have been criticized on the grounds that they are not linked to 6 the damages of global warming, for which a better focus would be compensation, not emissions. Moreover, per capita rules embody naïve assumptions about the capacity and willingness of governments to allocate on a per capita basis, rather than to sustain privilege (Posner and Sunstein 2008) 8 . Yet, the equity of rights applied at the national level remains a politically powerful ethical principle.

Accounting for Historical Emissions
A generalization of the simple example above takes into account historical emissions for the same two regions. 9 We equalize cumulative per capita emissions inclusive of historical emissions beginning at some date. We consider three different start dates: 1850, 1950, and 1990. These choices account, respectively, 9 Many commentators have supported the inclusion of historical emission rights in international climate agreements (Aslam 2002, Agarwal and Narain 1991, Baer et Al. 2000, Sagar 2000, Neumayer 2001, Grasso 2007. Similarly, Several versions of burden-sharing have been recently proposed that involve scoring both past and future national CO 2 emissions and that require equalized per capita emissions (Bode 2004, Pan 2008, Ding et al. 2009, He et al. 2009, Kanitkar et al. 2009, Kanitkar et al. 2010, WBGU 2009, Oberheitmann 2010).
for all historical emissions, for emissions only after the Second World War, and for emissions only after the reference year defined in the Rio Convention of 1992. We use the notation ECPC1850 to refer to an allocation of future emissions based on Equal Cumulative Per Capita emissions beginning in 1850, and similarly for other start times. The simple example shown in Figure 2 becomes an application of ECPC2005, which ignores historical emissions.
The required emissions data are shown in Table 2. Between 1850 and 2005, Annex I countries emitted almost 1000 GtCO 2 to the atmosphere, roughly one-third more than Non-Annex I countries 10 Figure 3 has the same coordinates as Figure 2, with future cumulative emissions from Non-Annex 1 vs. Annex-1 as its axes. To understand the lines plotted on Figure 3 algebraically, define N-A 1H and A 1H as the historical emissions between some start date (say, 1950) and 2005, for Non-Annex 1 and Annex-1, respectively. The ECPC principle becomes:

N-A I + N-A IH = 5 (A I + A 1H)
We saw in Figure 2 that the line we are now calling ECPC2005, on which the four diamonds fall, is a line through the point (0,0) with a slope of 5 (reflecting the population ratio). The corresponding line associated with one of the earlier start dates is obtained by shifting the starting point of the fairness line from (0,0) to the point in the lower-left quadrant whose coordinates are the negative values that, in magnitude, equal the pair of past emissions shown for the corresponding row in Table 2. For example, for 1950, the starting point is (-660 GtCO 2 , -530 GtCO 2 ). 11 There are 16 intersections in Figure 3, each shown as a black diamond at an intersection of one of the four ECPC fairness lines with one of the four safety lines discussed in the previous section. (The rightmost four points are the same as those highlighted in Figure 2.) Figure 3 also shows the uncertainty range in temperature rise -the color coded background under these points shows the average (labeled 50%) increase in temperature, while the color change in the two bars at the left show the temperatures that span the very likely (5%--95%) range.
The 16   The historical dimension of the ECPC principle addresses responsibility for future damage to some people by the past actions of others -in particular, future damage to people in developing nations caused by the past emissions of people in industrialized countries, mediated by global warming. However, for the redress of such damage to take the form of exactly equating future and past emissions is simplistic. To be sure, as developing countries pass through the early energy-intensive stages of industrialization in the pursuit of economic growth and a modern lifestyle (Grubb 1995, Shukla 1999), they will need to emit substantial quantities of carbon dioxide. But these countries will confront options that were not available to industrialized countries as they went through the same transitions at an earlier time. Notably, increased energy efficiency has been a steady feature of the past and shows every sign of continuing for the foreseeable future, enabling modern lifestyles to be achieved with less energy expenditure. Moreover, the energy system for most of the past century has become steadily less carbonintensive, and, to the extent that this trend continues (i.e., that fossil fuel technologies become less economically attractive than low-carbon technologies), fewer carbon emissions will accompany the same economic growth. A more formal analysis would take these trends into account.
In Figure 3, several of the points of intersection to which we are calling attention involve negative emissions from Annex I. Negative emissions have two possible meanings. A later section of this paper explores a world where technologies that actually remove CO 2 from the atmosphere, thereby tackling both safety and fairness, are widely deployed and "count" as negative emissions. But negative emissions can also be understood to be the result of trade in cumulative emissions, where, for example, money is paid by Annex I to Non-Annex I so that Annex I can emit more in the future and Non-Annex I can emit less. These trades produce movement down and to the right along a safety line. For example, the point at the intersection of ECPC1850 and 3000GtCO2, with roughly 200 GtCO 2 of negative cumulative emissions from Annex I, could represent actual emissions at the intersection of the same safety curve with ECPC1990, but the purchase of about 550 GtCO 2 by Annex I from Non-Annex I.
A market in cumulative emissions could increase economic efficiency, to the extent that it takes advantage of low-cost abatement opportunities wherever they occur. In particular, it could also hasten the arrival of low-cost green technology options in the developing world, if it results in an augmentation of the capital investments already expected to occur mostly there.
However, it is not at all obvious that a market in cumulative emissions can become a vehicle for justice (Eckersely 2009, Ott andSachs, 2002). With today's large disparities in wealth and quality of governance, such a market could lead to early transactions that were regretted later. Clearly, new, very strong institutions would be required. The experience of CDM has already revealed major problems concerning credit verification and quality certification of the projects involved (Wara and Victor 2008). Moreover, there is the issue of scale. CDM, the largest existing offset market and likely to continue in some version for years to come, is far smaller in scale than the trading that is envisioned here. It is hard to conceive of an exchange of many hundreds of GtCO 2 , which -as seen in Figure 3 -is needed to move from ECPC2005 to ECPC1850.

Minimum Cumulative Emissions after 2005
In Figures 2 and 3 Figure 4, Panel a, as a vertical and a horizontal line, respectively, drawn at locations that will be discussed below. The bands between the axes and these lines are forbidden outcomes, unless there is trading in cumulative emissions or (the subject of the next section and Panels b and c of Figure 4) negative-emission technology arrives.  Figure 3 for the corresponding color coded bands for the two bounds of "very likely" range.
Many considerations should be accounted for in determining the positions of the MCE lines of Figure 4, Panel a. First, consider minimum global cumulative emissions. One must include the 150 GtCO 2 of global emissions from fossil fuels and deforestation over the past five years (for Annex I and Non-Annex I, approximately 75 GtCO 2 each). Also, one must allow for societal inertia, which will constrain emissions reduction over the next few decades. Even with great effort, the world cannot reduce its future emissions to zero instantly. Mitigation over the next few decades will be dominated by available technology options (Pacala and Socolow 2004) and will be achieved in sectors of the economy that are known to resist change. The fossil fuel system now providing 85% of the world's primary energy will not be replaced suddenly. For example, it has been estimated that roughly 500 GtCO 2 will be emitted globally by the currently existing energy infrastructure over its lifetime (Davis et. al 2010).
A rough estimate of minimal future global cumulative emissions from 2005 through 2100 is provided by considering twelve energy-economy-climate models that have been evaluated in an international modelcomparison exercise, EMF22 ). For each model, a lower bound was produced for global cumulative emissions, consistent with achieving various climate stabilization targets under alternative policy architectures and assumptions about mitigation technologies and socio-economics pathways 12 . Averaging over the twelve models, minimum global cumulative emissions are 1700 GtCO 2 (2500 GtCO 2eq when counting also non-CO2 gases 13 ). For simplicity we set minimum cumulative global emissions after 2005 at 2000 GtCO 2 .
As for the separate lower bounds for Annex 1 and Non-Annex 1, in Figure 4, Panel a, we assign 500 to Annex I 14 and 1500 to Non-Annex 1 15 . This allocation is intended to take into account the difficulty Non-Annex I can expect to face in the short term, given the high value of fossil fuels for development at this time. Figure 4, Panel a, reveals that only two of the 16 safe-fair points are beyond the forbidden zone, and one more is on the boundary. Trading in cumulative emissions can move all the points on the safety lines for 13 4000 and 3000 GtCO 2 into the allowed region and it can move all the points on the safety line at 2000 GtCO 2 approximately to the corner where the two MCE lines intersect. But even with unlimited trading the points on the 1000 GtCO 2 safety line cannot be brought into the feasibility space, meaning that the most stringent of our four stabilization targets remains out of reach. In short, resolving the safetyfairness conundrum is more difficult for more ambitious targets than for less ambitious ones. It is hardly surprising that the trend towards stricter targets has lead to more alarm about the potential to achieve fairness.

Negative Emissions via Technology
The pursuit of the twin goals of safety and fairness would benefit from new technologies that enable moving down and left in Figures 2, 3 and 4 in this paper. Such technologies include not only those that provide very low emissions but also those that remove CO 2 from the atmosphere. Other words for CO 2 removal technologies are negative-emission technologies and engineered CO 2 sinks. They require manipulation of the global carbon cycle -for example, the deliberate transfer of CO 2 from the atmosphere to plants, soil, ocean, or deep underground in porous rock formations.
Among the proposed technological approaches are 1) biological sequestration of carbon in forests and soils, 2) CO 2 capture while processing biomass for power and fuels, followed by CO 2 sequestration below ground, 3) biological CO 2 removal from the atmosphere at the ocean surface (e.g., using plankton), and 4) direct air capture of CO 2 using chemical absorbers. There is no assurance that technologies of this kind can be deployed in this century at the scale required, nor that the concomitant, nearly complete decarbonization of the economy can be achieved. Costs are key and hard to predict, since none of these technologies has been commercialized. There are also major uncertainties regarding the effectiveness, costs, and environmental impacts of CO 2 removal technologies (The Royal Society 2009; American Physical Society 2011).
The figures in this paper suggest that a useful scale for "globally significant" removal of CO 2 from the atmosphere is the removal of 1000 GtCO 2 . In Figure 4, Panels b and c, we consider two arbitrary assignments of 1000 GtCO 2 of negative emissions. In Panel b the shares are equal: 500 GtCO 2 to Annex I and 500 GtCO 2 to Non-Annex I. By contrast, in Panel c all negative emissions are assigned to Annex 1. The 500:500 allowance exactly compensates Annex I for its minimum cumulative emissions, bringing the vertical MCE line back to the vertical axis and resulting in eight safe-fair pairs becoming "allowed"--all those with positive net cumulative emission allowances for Annex I. (Two 1000 GtCO 2 points are excluded --just barely.) The alternative allowance, which assigns industrialized countries the whole carbon dioxide removal program, produces twelve safe-fair pairs (there are four more allowed points in Panel c than in Panel b), largely because that allocation scheme assigns the effort to a smaller share of population.
How to assign any specific negative emissions undertaking to any specific country, or even to Annex I vs. Non-Annex I, is not at all clear. Should the allocation depend on who pays or where the program is hosted, for example? At present, deforestation and afforestation are credited in carbon accounting to the country whose land is affected. However, another accounting scheme is under development, as financial transfers from industrialized countries to developing countries are considered that would fund carbonmotivated forest management in developing countries while crediting emissions reductions to industrialized countries. As for CO 2 removal efforts that occur within the global commons rather than within national boundaries, such as CO 2 transfer from the atmosphere to the ocean, it would seem that only an allocation based on who pays could make sense.
The sequestration of 1000 GtCO 2 from the atmosphere would require huge investments and innovation. In many versions, associated land or ocean impacts would be central concerns. The 1000 GtCO 2 absorption task, if assigned to the second half of this century, translates into a removal rate of 20 GtCO 2 per year, which is two-thirds of the emissions rate today 16 .

Conclusions
In this paper we have provided a framework for thinking quantitatively about the trade-off between climate safety and fairness. Both matter, since goal setting and equity are intertwined in international climate change negotiations (Heyward 2007, den Elzen and Hohne, 2008, Ding et al. 2010. We associate levels of safety with cumulative global emissions. The starting point of our fairness principle is a view of the atmosphere as a common-property resource belonging equally to everyone in the world. The result is that an extra five tons of CO 2 of emissions are allowed in Non-Annex I for each extra ton of CO 2 emissions allowed in Annex I. This definition can also be extended back into the past, thereby combining the concepts of a right to emit and historical responsibility. This is in line with some recent analyses and policy proposals, but it is hardly unique. Many alternative definitions of fairness can be devised, expressing many alternative formulations of global justice and its application to climate change (Bodanski 2004).
We have introduced a few simple concepts, along with rough estimates of their magnitudes, to promote quantitative discussion. Minimum Cumulative Emissions (MCE) capture the reality of long-lived energy infrastructure, current emissions-reduction commitments, and the lead long times required to develop alternatives to replace the current fossil-energy infrastructure. We estimate global Minimum Cumulative Emissions (MCE) at 2000 GtCO 2 and find that these emissions (in the absence of the deployment of negative emissions technology) already limit the chance of avoiding a 2 o C temperature rise to just above 50% (see Table 1). When we further assign these 2000 GtCO 2 of global emissions so that 500 GtCO 2 go to Annex I and 1500 GtCO 2 go to Non-Annex I, and restrict our attention to the 2000 GtCO 2 safety line, none of our four fairness conditions is satisfied (see Figure 4). For this case even ECPC2005 (which ignores all emissions prior to 2005 and is the most limited of the four visions of fairness) is inconsistent with an MCE for Annex 1 of 500 GtCO 2 , since it allows Annex 1 only one-sixth of future emissions, or 330 GtCO 2 in this case. To realize even ECPC2005, 170 GtCO 2 of Non-Annex I cumulative emissions would need to be purchased by Annex I.
Invoking the possibility of realizing 1000 GtCO 2 of negative emissions and changing no other assumptions, the chance of avoiding a 2 o C temperature rise exceeds 95%. A larger fraction of the targets are accessible and stricter ECPC rules are allowed under this technology scenario, though the exact consequences for fairness depend on how negative emissions are assigned. However, achieving 1000 GtCO 2 of negative emissions via engineered sinks will require a combination of monumental investment and extraordinary innovation. At present there is no reason to expect cheap, environmentally attractive, and scalable versions of these technologies to make a timely entrance into the space of options. As a consequence, counting on these technologies to provide the path to the simultaneous realization of safety and fairness is unwise.
Our mapping also considers future cumulative global emissions that exceed 2000 GtCO 2 , specifically 3000 and 4000 GtCO 2 . Higher emissions, of course, push the world into less safe territory. Figure 4, Panel a, confirms that, when no historical emissions are counted (ECPC2005), the 500-2500 split of 3000 GtCO 2 of global emissions allocates to Annex 1 exactly its estimated minimal cumulative emissions. Stronger fairness conditions are only realizable with trading -as much as 700 GtCO 2 of exchange for "full" historical responsibility (ECPC1850).
The recent trend towards stricter targets (more "safety"), associated with further developments in climate science and the rapid rise in global emissions in the recent past, has yet not taken cognizance of its impacts on various criteria of fairness. Our paper shows quantitatively, however, just how difficult meeting both objectives actually is, when a narrow definition of fairness in terms of equal per capita shares of global emissions is reconciled with stringent climate stabilization targets. Adding historical responsibility to the definition of fairness makes the reconciliation even more difficult -substantially more difficult. And all targets become harder to meet if emissions continue unabated for another 10 or 20 years. The challenges for both developed and developing countries, in this calculus, are immense.
We wish again to alert the reader to the shortcomings of a definition of fairness in terms of per capita access to the atmosphere for individual emissions. Associating equity with the right to emit CO 2 inadequately captures the more critical right of everyone to seek and achieve a higher standard of living. Once climate change is seriously addressed, priority will be given to reducing the CO 2 emissions associated with any given level of human welfare. Throughout the future global economy, less energy will be required to achieve the same amenity (mobility or comfort, for example) and lower carbon emissions will accompany the same energy expenditures. Such trends will not eliminate the difficult trade-offs between safety and equity, but they will weaken them.
The formalism presented here for dealing with historical emissions equates CO 2 emissions entitlements at all times -a convenient first step whose principal virtue is simplicity. Especially important for the further development of our approach would be a more sophisticated accounting for the steady lowering through time of the CO 2 emissions required for the satisfaction of human needs. We strongly encourage an exploration of alternative conceptualizations of the historical dimensions of equity that take the evolution of relevant features the global economy into account.
To summarize, our investigation shows the interplay of safety and fairness under different assumptions about historical emissions, trading in cumulative emissions, residual emissions, and negative emissions. It is meant to provide an instructive tool to treat safety and fairness simultaneously when exploring the problem of international burden-sharing. The Figures in our paper provide a reality check on the reader's preferences regarding safety and fairness. Our intention is to encourage iteration over such preferences.