Disclaimer: this is not a project from Alliance to Feed the Earth in Disasters (ALLFED).

# Summary

- I estimated the future benefits of mitigating food shocks caused by abrupt sunlight reduction scenarios (ASRSs). These are scenarios in which a catastrophe causes a significant reduction in the amount of sunlight reaching the Earth’s surface, such as a
__nuclear winter__,__volcanic winter__, or__impact winter__. - The future benefits of globally mitigating the food shocks caused by an ASRS, conditional on it happening, are in the table below
^{[1]}.- Relative to the future benefits suggested by the guesses of
__Denkenberger 2022__for the reduction in far future potential, my estimates for an ASRS of:- 5 Tg
^{[2]}are 1.80 % as large as those for a 10 % agricultural shortfall^{[3]}in its survey model, and 8.10 times as large as those in Anders Sandberg’s model. - 150 Tg are 22.9 % as large as those for a full scale nuclear war in its survey model, and 76.7 % as large as those in Anders Sandberg’s model.

- 5 Tg
- In other words, my estimates for the future benefits are:
- For mild ASRSs, much smaller than those from the survey, and larger than those from Anders Sandberg.
- For severe ASRSs, smaller than those from the survey, and similar to those from the survey and Anders Sandberg.

- Relative to the future benefits suggested by the guesses of

- The future benefits of locally mitigating the food shocks caused by ASRSs vary significantly by country. Those of the 1st country, i.e. the one whose local mitigation leads to the largest future benefits, are:
- For 5 Tg, 7.70 and 135 times as high as those of the 10th and mean countries.
- For 150 Tg, 3.66 and 19.0 times as high as those of the 10th and mean countries.

- I think one should target democratic countries with large real GDP significantly affected by ASRSs, or ones which could plausibly influence them.

- All results should be taken with a big grain of salt, as they rely on quite speculative assumptions.

Soot ejected into the stratosphere which caused the ASRS (Tg) | Future benefits of globally mitigating food shocks as a fraction of the current value of the future (%) | |||
---|---|---|---|---|

Mean | 5th percentile | 95th percentile | Probability of being negative/harmful | |

5 | 0.216 | -2.44 | 3.01 | 41.2 |

27 | 1.67 | -3.75 | 9.54 | 31.8 |

150 | 5.54 | -9.74 | 22.7 | 26.2 |

## Acknowledgements

Thanks to Anders Sandberg, Anonymous Person, ChatGPT, Christian Ruhl, João Cortes, Lili Xia, Nuño Sempere, and Zvi.

# Introduction

In __this__ episode of The 80,000 Hours Podcast, William MacAskill said that:

It’s quite plausible, actually, when we look to the very long-term future, that that’s [whether artificial general intelligence is developed in “liberal democracies” or “in some dictatorship or authoritarian state”] the biggest deal when it comes to a nuclear war: the impact of nuclear war and the distribution of values for the civilisation that returns from that, rather than on the chance of extinction.

The distribution of values after a nuclear war depends on how the food shocks caused by the ensuing __nuclear winter__ are handled, among other factors (e.g. degree of infrastructure destruction). This analysis quantifies the future benefits of mitigating food shocks caused by ASRSs. These are scenarios in which a catastrophe causes a significant reduction in the amount of sunlight reaching the Earth’s surface, such as a __nuclear winter__, __volcanic winter__, or __impact winter__.

Quantifying the future benefits of mitigating food shocks is relevant to more accurately assess the __cost-effectiveness__ of interventions which aim to mitigate them. __Denkenberger 2022__ estimated the cost-effectiveness of planning, and research and development (R&D) for __resilient food solutions__ in terms of increasing the value of the future. However:

- The models of
__Denkenberger 2022__rely on directly guessing the relative variation in the value of the future due to “full scale nuclear war” and “10% agricultural shortfall”. In contrast, my approach explicitly looks into the changes in values which supposedly lead to a worse future, which I believe is more informative. - I present results by country and as a function of the amount of soot ejected into the stratosphere, which is less vague than the above terms.

My approach can also inform which countries should be targeted to develop preparedness and response plans for ASRSs. It allows one to estimate the future benefits of locally mitigating the food shocks in any given country.

# Methods

## Model and definitions

The diagram below illustrates how my model works. Note:

- I am only trying to quantify the future benefits of mitigating the food shocks caused by ASRSs. However, these have multiple other adverse consequences. For example, if caused by a nuclear war, ASRSs may involve loss of electricity and industry.
- The model is quite simplified, not including all pathways which will affect the value of the future. For instance, a change in calorie supply may well change factors besides total and per capita real GDP which influence Varieties of Democracy’s main index.

The Future Expected Value Index (FEVI) is the mean of 14 indices, __rescaled__ to range from 0 to 1^{[4]}, which look like decent proxies for future value (assessed for the baseline conditions in the last year for which I found data):

__Bertelsmann Transformation Index__(2021), which “captures the extent of democratic features — political participation, rule of law, stable democratic institutions, political and social integration, and a capable state”.__Economist Intelligence Unit's democracy index__(2021), which “captures the extent to which citizens can choose their political leaders in free and fair elections, enjoy civil liberties, prefer democracy over other political systems, can and do participate in politics, and have a functioning government that acts on their behalf”.__Environmental Performance Index__(2022), which “provides a quantitative basis for comparing, analyzing, and understanding environmental performance”.- Minus
__Global Peace Index__(2022), which “is the world’s leading measure of global peacefulness”. __Happy Planet Index__(2019),__which__“is a measure of sustainable wellbeing, ranking countries by how efficiently they deliver long, happy lives using our limited environmental resources”.__Human Development Index__(2021), which “is a summary measure of achievements in three key dimensions of human development: A long and healthy life, access to knowledge and a decent standard of living”.__Intergenerational Solidarity Index__(2019), which “is a measure of how much different nations provide for the wellbeing of future generations”.__Polity's democracy index__(2018), which “combines information on the extent to which open, multi-party, and competitive elections choose a chief executive who faces comprehensive institutional constraints, and political participation is competitive”.__Social Capital Index__(2022),__which__“measures competitiveness of countries based on 189 measurable, quantitative indicators” “grouped into 6 sub-indexes: Natural Capital, Resource Efficiency & Intensity, Social Cohesion, Intellectual Capital, Economic Sustainability, and Governance Efficiency”.__Social Progress Index__(2022), which is “based on tiered levels of scoring that include measures in health, safety, education, technology, rights, and more”.__Varieties of Democracy's main index__(2021), which “denotes the best estimate of the extent to which political leaders are elected under comprehensive suffrage in free and fair elections, and freedoms of association and expression are guaranteed”.__World Energy Council's (WEC’s) Trilemma score__(2022), which “ranks countries on their ability to provide sustainable energy through 3 dimensions: Energy security, Energy equity (accessibility and affordability), Environmental sustainability”.__World Happiness Report's (WHR’s) happiness score__(2019 to 2021), whose “measure of SWB (Subjective Well-being) is from the Gallup World Poll (GWP)”.__World Giving Index__(2022), which aims to “establish a rounded measure of giving behaviour across the world” accounting for “helping a stranger”, “donating money”, and “volunteering time”.

I came up with 6 of these, and OpenAI’s __ChatGPT__ suggested the other 8.

The Global Future Expected Value Index (GFEVI) is the FEVI across countries weighted by __real gross domestic product__ (real GDP), which I suppose is a good proxy for (good or bad) influence in the value of the future.

I explain the model in the sections below, going from the start to the end of the causal chain. The calculations are in __this__ Sheet (see tab “TOC”) and __this__ Colab. I modelled all variables as independent distributions, and ran a __Monte Carlo simulation__ to get the results^{[5]}. Additionally, I also estimated the key results from the table in the Summary using point estimates equal to the means of the distributions.

## Calorie production without adaptation

I considered the ASRSs caused by nuclear wars of various levels of severity described in Table 1 of __Xia 2022__, which is reproduced below. The direct fatalities and people without food at the end of the 2nd year of the ASRS without adaptation increase linearly with the soot ejected into the stratosphere. The coefficients of determination of the respective __linear regressions__ are 98.0 % and 96.7 % (see tab “Nuclear war fatalities”).

Soot ejected into the stratosphere which caused the ASRS (Tg) | Nuclear weapon detonations | Yield (kt) | Direct fatalities without adaptation (M) | People without food at the end of the 2nd year without adaptation ( |
---|---|---|---|---|

5 | 100 | 15 | 27 | 0.255 |

16 | 250 | 15 | 52 | 0.926 |

27 | 250 | 50 | 97 | 1.426 |

37 | 250 | 100 | 127 | 2.081 |

47 | 500 | 100 | 164 | 2.512 |

150 | 4400 | 100 | 360 | 5.341 |

There is no consensus regarding the relationship between the amount of soot and nuclear weapon detonations^{[6]}. However, there seemingly is greater agreement on the climate and agricultural impacts given a certain amount of soot, and I present my results as a function of the amount of soot.

The relative variation in the calorie production without adaptation of major food crops^{[7]} and marine fish, from baseline to the 2nd year after the onset of the ASRS, is in Table S2 of __Xia 2022__ (see __here__). The values for the mean, and 5th and 95th percentile countries among the 167 analysed by __Xia 2022__ are below. The full data by country are in tab “Calorie production without adaptation”^{[8]}.

Soot ejected into the stratosphere which caused the ASRS (Tg) | Relative variation in the calorie production without adaptation among the 167 countries analysed by | ||
---|---|---|---|

Mean country | 5th percentile country | 95th percentile country | |

5 | -1.63 | -22.4 | 24.0 |

16 | -4.01 | -58.9 | 59.3 |

27 | -12.5 | -74.1 | 42.9 |

37 | -19.0 | -96.1 | 71.7 |

47 | -23.7 | -97.1 | 64.8 |

150 | -61.3 | -100 | -3.28 |

I modelled the calorie production (for humans^{[9]}) without adaptation in the worst year of the ASRS as a fraction of its baseline value (CPWAf/CPWAi) as a __rectified normal distribution__^{[10]} with unrectified 5th and 95th percentiles equal to the minimum and maximum between (1 + RV)^2 and (1 - RV)*(1 + RV)^{[11]}, where RV is the relative variation in calorie production without adaptation estimated in __Xia 2022__.

- The mean of the unrectified distribution is 1 + RV, i.e. it corresponds to the point estimate of
__Xia 2022__. - The distribution ensures the uncertainty, as measured by the distance between the unrectified 5th and 95th percentiles, is null when RV is -1 or 0, and maximum for RV = -0.5
^{[12]}, which makes sense. - If
__Xia 2022__predicts no change (RV = 0) or total breakdown (RV = -1) in calorie production without adaptation, the distribution resumes to the point estimate CPWAf/CPWAi = 1 or CPWAf/CPWAi = 0. - If
__Xia 2022__predicts a 50 % drop in calorie production without adaptation (RV = -0.5), I am supposing there would be a 5 % chance of the unrectified CPWAf/CPWAi being:- Lower than 25 %.
- Higher than 75 %.

## Calorie production

I determined the calorie production in the worst year of the ASRS as a fraction of its baseline value from CPf/CPi = (CPWAf/CPWAi)^E_CP_CPWA^{[13]}, where:

- CPWAf/CPWAi is the calorie production without adaptation in the worst year of the ASRS as a fraction of its baseline value.
- E_CP_CPWA is the
__elasticity__^{[14]}of calorie supply with respect to calorie production without adaptation.- This elasticity decreases with the level of preparedness and quality of the response to the ASRS
^{[15]}, and would be null for complete mitigation. - I set it to a normal distribution with 5th and 95th percentile equal to 0 and 1. So, for a decrease in calorie production without adaptation, I am assuming a chance of 5 % of calorie supply:
- Increasing (E_CS_CPWA < 0).
- Decreasing more in relative terms than calorie production without adaptation (E_CS_CPWA > 1).

- For what is worth, ChatGPT’s best guesses for the 5th and 95th percentiles were -0.1 to 1, whose mean of 0.45 (= (-0.1 + 1)/2) is 10 % lower than mine of 0.5 (= (0 + 1)/2).
- I only chatted with ChatGPT after defining my 5th and 95th percentiles.
- You can see our chat
__here__(ChatGPT’s guesses are in bold).

- This elasticity decreases with the level of preparedness and quality of the response to the ASRS

## Calorie supply

I computed the calorie supply in the worst year of the ASRS as a fraction of its baseline value from CSf/CSi = (1 - CLWf/CPf)/(1 - CLWi/CPi)*CPf/CPi, where CLWf/CPf and CLWi/CPf are the calorie loss and waste^{[16]} in the supply chain as a fraction of the calorie production in the worst year of the ASRS and baseline conditions.

- I defined CLWf/CPf as the minimum between 1
^{[17]}and a__rectified normal distribution__^{[18]}with unrectified 5th and 95th percentile equal to the minimum and maximum between (1 + RV)^2*CLWi/CPi and (1 - RV)*(1 + RV)*CLWi/CPi^{[11]}.- The mean of the unrectified distribution is (1 + RV)*CLWi/CPi, i.e. it dictates the relative variation in calorie loss and waste equals that of the calorie production without adaptation predicted in
__Xia 2022__. This is reasonable because less calorie availability will tend to result in less loss and waste. - The distribution ensures the uncertainty, as measured by the distance between the unrectified 5th and 95th percentiles, is null when RV is -1 or 0, and maximum for RV = -0.5
^{[19]}, which makes sense. - If
__Xia 2022__predicts no change (RV = 0) or total breakdown (RV = -1) in calorie production without adaptation, the distribution resumes to the point estimates CLWf/CPf = CLWi/CPi or CLWf/CPf = 0. - If
__Xia 2022__predicts a 50 % drop in calorie production without adaptation (RV = -0.5), I am supposing there would be a 5 % chance of the unrectified CPWAf/CPWAi being:- Lower than 25 % of CLWi/CPi.
- Higher than 75 % of CLWi/CPi.

- The mean of the unrectified distribution is (1 + RV)*CLWi/CPi, i.e. it dictates the relative variation in calorie loss and waste equals that of the calorie production without adaptation predicted in
- I set CLWi/CPi to the fraction of 30 % applying to cereals mentioned
__here__by the Food and Agriculture Organisation (FAO). This parameter would ideally be defined by country.

I thought about explicitly estimating for each country the elasticity of calorie supply with respect to calorie production^{[20]}, but data on this is not readily available, so I opted to follow the approach described above for simplicity.

## Real GDP

For the baseline conditions, I used the total and per capita real GDP and population of each country in 2021, which I took from __these__, __these__ and __these__ data from The World Bank.

For the worst year of the ASRS, I set the real GDP per capita of each country as a fraction of its baseline value to the minimum between 1 and RGDPC(CSf)/RGDPC(CSi), where:

- The real GDP per capita (RGDPC) is predicted with a linear regression of the daily calorie supply per capita on the reciprocal of the logarithm of real GDP per capita, fit to the available data of each of the 145 countries I analysed from 1960 to 2021.
- The 145 countries are the ones for which there is data on Varieties of Democracy’s main index
^{[21]}, which I use to estimate FEVI (see next section). - 1960 and 2021 are the earliest and latest years encompassed by
__these__data on real GDP per capita from The World Bank. For the daily calorie supply per capita, I used__these__data from Our World in Data (OWID).

- The 145 countries are the ones for which there is data on Varieties of Democracy’s main index
- CSi and CSf are the initial and final daily calorie supply per capita, i.e. the ones in the baseline conditions and worst year of the ASRS.

As shown in the table below, the fit of the regression on the reciprocal of the logarithm of the real GDP per capita to data of the UK from 1789 to 2016, and of 145 countries from 1960 to 2021 is similar to other types of regression. Nonetheless, the one I selected leads to daily calorie supply per capita not increasing indefinitely with real GDP per capita^{[22]}, which arguably makes sense. In any case, I assumed the real GDP per capita in the worst year of the ASRS could not exceed those in the baseline conditions^{[23]}.

Regression |
| |
---|---|---|

UK from 1789 to 2016 | Mean weighted by 2021 real GDP of 145 countries from 1960 to 2021 (unweighted 5th to 95th percentile) | |

Linear regression of calorie supply per capita on real GDP per capita | 68.8 | 77.1 (0.667 to 93.8) |

Linear regression of calorie supply per capita on logarithm of real GDP per capita | 82.4 | 77.1 (0.667 to 93.8) |

Linear regression of calorie supply per capita on reciprocal of real GDP per capita | 82.5 | 76.0 (0.711 to 93.9) |

Linear regression of calorie supply per capita on reciprocal of logarithm of real GDP per capita | 84.3 | 77.7 (0.730 to 94.6) |

Best fit of the above | 84.3 | 79.2 (1.02 to 95.6) |

I presumed the population of each country as a fraction of its baseline value to be equal to the real GDP per capita of each country as a fraction of its baseline value (Pf/Pi = RGDPCf/RGDPCi). Consequently, I got the real GDP of each country as a fraction of its baseline value from RGDPf/RGDPi = (RGDPCf/RGDPCi)^2.

### Note on real GDP per capita and cereal production

A unitary elasticity of real GDP per capita with respect to calorie production could naively be inferred from historical data. As is represented below, real GDP per capita increased linearly with global cereal production between 1990 and 2020 (coefficient of determination of 95.9 %; see tab “Global cereal production and real GDP”).

However, the aforementioned relationships are not necessarily causal:

- They are arguably explained by population growth causing real GDP per capita as well as cereal production to increase. In addition, higher real GDP per capita usually leads to higher consumption of animals (see
__this__graph from OWID), which requires a greater calorie production. - The relative variation in real GDP per capita and relative variation in cereal production are only very weakly correlated (coefficient of determination of 0.421 %; see tab “Global cereal production and real GDP”), as is illustrated below. This suggests a low elasticity of real GDP per capita on calorie production.

For these reasons, I did not assume real GDP per capita to be directly proportional to the calorie production.

## Varieties of Democracy’s main index

For each country, I computed Varieties of Democracy's main index (VoDMI) in the worst year of the ASRS as a fraction of its baseline value from VoDMI(RGDPCf)/VoDMI(RGDPCi), where:

- VoDMI is predicted with a
__logistic regression__of it on the logarithm of real GDP per capita, fit to the available data of each country from 1960 to 2021^{[26]}. - RGDPCi and RGDPCf are the real GDP per capita in the baseline conditions and worst year of the ASRS. Further details are in the previous section.

This method is quite rough, but less resources per person (i.e. lower real GDP per capita) arguably lead to worse values. I used a logistic regression to predict VoDMI in the worst year of the ASRS because it corresponds to a __S-curve__ with VoDMI tending to 0 and 1 (the minimum and maximum possible values) as the real GDP per capita tends to 0 and infinity. This valid asymptotic behaviour is good given the possibility of extreme variations of the real GDP per capita following ASRSs.

__Sandberg 2021__ argues “the future fit [of S-curves] tends to be poor unless the data covers the entire range from before to after the inflection point”. I do not think this is a major issue for my dataset. The mean weighted by 2021 real GDP of the number of data points per country with VoDMI lower and higher than 0.5 is 25.1 and 33.1^{[27]}, so it looks like I have a good balance of points before and after the inflection point.

As shown in the table below, the fit of the logistic regression to data of the UK from 1789 to 2016, and of 145 countries from 1960 to 2021^{[28]} is similar to other types of regression^{[29]}. Nevertheless, I suspect the logistic regression will be a better predictor for large shocks for the reasons described just above.

Regression | Coefficient of determination | |
---|---|---|

UK from 1789 to 2016 | Mean weighted by 2021 real GDP of 145 countries from 1960 to 2021 (unweighted 5th to 95th percentile) | |

Linear regression of Varieties of Democracy's main index on real GDP per capita | 61.9 | 36.0 (0.195 to 81.3) |

Linear regression of Varieties of Democracy's main index on logarithm of real GDP per capita | 83.8 | 41.2 (0.716 to 81.4) |

Linear regression of Varieties of Democracy's main index on reciprocal of real GDP per capita | 86.0 | 47.1 (0.932 to 81.9) |

Linear regression of Varieties of Democracy's main index on reciprocal of logarithm of real GDP per capita | 86.5 | 43.0 (0.815 to 80.6) |

Logistic regression of Varieties of Democracy's main index on logarithm of real GDP per capita | 86.6 | 41.6 (0.616 to 81.1) |

Best fit of the above | 86.6 | 51.6 (1.51 to 84.2) |

In any case, the figure below with data from the UK for 1789 to 2016 shows the logistic regression does not tell the whole story. Notably:

- From 1918 to 1919 (just after the end of
__World War I__), real GDP per capita decreased 7.44 %, but VoDMI increased 50.6 % from 0.464 to 0.699. - From 1920 to 1921, real GDP per capita decreased 10.5 %, but VoDMI remained constant.
- There were 4 transitions for which the real GDP increased significantly (8.73 % to 9.91 %), but VoDMI remained constant or barely increased (0.711 %).

In addition, as can be seen in the figure below^{[31]}, the correlation between the relative variation in real GDP per capita and relative variation in VoDMI is negative, although it is pretty weak (coefficient of determination of 2.98 %).

Moreover, the logistic regression to estimate FEVI relied on the shorter period from 1960 to 2021, for which the fit is worse in agreement with the last row of the table above (51.6 % < 86.5 %).

## Future Expected Value Index

For each country, I estimated FEVI in the worst year of the ASRS as a fraction of its baseline value from FEVI(VoDMIf)/FEVI(VoDMIi), where:

- FEVI is predicted with a
__linear regression__on VoDMI, fit to the available data of 156 countries^{[32]}in the baseline conditions (see tab “Predicted FEVI”). The respective coefficient of determination is 79.9 %. - VoDMIi and VoDMIf are the VoDMI in the baseline conditions and worst year of the ASRS (see previous section).

I did not directly estimate FEVI with a regression on the real GDP per capita due to:

- 12 of the 14 indices from which FEVI is calculated being quite recent.
- Data for Polity’s democracy index and VoDMI goes back to 1776 and 1789, but only as early as 1990 for the others (see tab “Indices time frame”).
- Data for the real GDP per capita is available from 1960, so there would be 30 (= 1990 - 1960) fewer years of such data for the other indices.
- In turn, that would lead to significantly less data points before the inflection point of the logistic curve, and therefore poorer predictions (see
__Sandberg 2021__).

- As illustrated in the table below, strong correlation for the baseline conditions between FEVI and VoDMI, for which data by country is readily provided by OWID
__here__.

Correlation for the baseline conditions between FEVI and… | Correlation coefficient |
---|---|

Real GDP per capita (2021) | 0.718 |

Logarithm of real GDP per capita (2021) | 0.767 |

Rescaled Bertelsmann Transformation Index (2021) | 0.895 |

Rescaled Economist Intelligence Unit's democracy index (2021) | 0.929 |

Rescaled Environmental Performance Index (2022) | 0.774 |

Rescaled minus Global Peace Index (2022) | 0.715 |

Rescaled Happy Planet Index (2019) | 0.373 |

Rescaled Human Development Index (2021) | 0.801 |

Rescaled Intergenerational Solidarity Index (2019) | 0.764 |

Rescaled Polity's democracy index (2018) | 0.735 |

Rescaled Social Capital Index (2022) | 0.731 |

Rescaled Social Progress Index (2022) | 0.905 |

Rescaled Varieties of Democracy's main index (2021) | 0.894 |

Rescaled World Energy Trilemma Index (2022) | 0.811 |

Rescaled WHR's happiness score (2019 to 2021) | 0.805 |

Rescaled World Giving Index (2022) | 0.232 |

The 4 indices which correlate more strongly with FEVI for the baseline conditions are the Economist Intelligence Unit's democracy index (0.929), Social Progress Index (0.905), Rescaled Bertelsmann Transformation Index (0.895), and VoDMI^{[33]} (0.894). I relied on this to estimate FEVI in the worst year of the ASRS because the others are available for much shorter periods (in comparison to 1789 to 2021 for VoDMI):

- Economist Intelligence Unit's democracy index, 2006 to 2021.
- Social Progress Index, 2014 to 2022.
- Bertelsmann Transformation Index, 2005 to 2021.

The 2 indices which correlate more weakly with FEVI are the Happy Planet Index (0.373), and World Giving Index (0.232). Additional correlation coefficients are in tab “Correlations among real GDP, rescaled indices and FEVI”.

## Value of the future

I estimated the value of the future after the ASRS as a fraction of its baseline value from VFf/VFi = (GFEVIf/GFEVIi)^(1 - RF), where:

- GFEVIi and GFEVIf are the GFEVI in the baseline conditions and worst year of the ASRS.
- RF is the recovery factor, which I set to a normal distribution with 25th and 75th percentiles equal to 0 and 1.
- A value of 0 would imply a relative variation in the value of the future matching that of GFEVI (unitary elasticity). So I am assuming a 25 % chance the future would be worse than suggested by a given drop in GFEVI.
- A value of 1 would imply no change in the value of the future (null elasticity), i.e. full recovery. So I am assuming a 25 % chance the future would be better for a drop in GFEVI.

1 - RF in the formula above is the elasticity of the value of the future with respect to GFEVI.

Finally, I determined the future benefits of mitigating a food shock caused by an ASRS as a fraction of the current value of the future from:

- If all countries completely eliminated the decrease in their real GDP and FEVI (global mitigation), (VFi - VFf)/VFi = 1 - (GFEVIf/GFEVIi)^(1 - RF).
- If a single country C completely eliminated the decrease in its real GDP and FEVI (local mitigation), (VFf*(C) - VFf)/VFi = (GFEVIf*(C)/GFEVIi)^(1 - RF) - (GFEVIf/GFEVIi)^(1 - RF), where GFEVIf*(C) is the GFEVI in the worst year of the ASRS if only country C completely eliminated the decrease in its real GDP and FEVI
^{[34]}.

These expressions indicate the scale of the risk of food shocks caused by ASRSs, but they are conditional on an ASRS happening. So they should be weighted by their probability to get a full picture of the risk. I plan to address this in a future post.

My formula for the future benefits of local mitigation calculates the counterfactual value, and therefore it does not account well for cooperation. Ideally, I should have used the Shapley value, as explained in __this__ (great!) post from Nuño Sempere.

## Parameters of the distributions

The distributions used in my Monte Carlo simulation are defined by many variables, but only 5 guessed constants (default values as mentioned in the previous sections):

- The 5th and 95th percentile elasticity of calorie production with respect to calorie production without adaptation (E_CP_CPWA_p5 = 0, and E_CP_CPWA_p95 = 1).
- Calorie loss and waste in the supply chain as a fraction of the calorie production in the baseline conditions (CLWi_CPi = 0.3).
- 25th and 75th percentile recovery factor (RF_p25 = 0, and RF_p75 = 1).

Feel free to make copies of the __Sheet__ and __Colab__ to use your own guesses (search for “Inputs” in the code). Copying the Sheet is needed because the Colab extracts data from there, and the copies must be in the same folder (unless you change the code).

# Results

The results are in the tables below. The full results by country are in the __Sheet__ (see tab “TOC”). For context, I also estimated the future benefits of mitigating food shocks caused by ASRSs based on the guesses of __Denkenberger 2022__.

## Daily calorie supply per capita

Soot ejected into the stratosphere which caused the ASRS (Tg) | Relative variation in daily calorie supply per capita due to the ASRS (%) - mean across countries | ||
---|---|---|---|

Mean | 5th percentile | 95th percentile | |

5 | -82.0 | -83.7 | -80.2 |

27 | -82.8 | -86.2 | -79.1 |

150 | -87.6 | -95.4 | -76.7 |

## Real GDP per capita and population

Soot ejected into the stratosphere which caused the ASRS (Tg) | Relative variation in | ||
---|---|---|---|

Mean | 5th percentile | 95th percentile | |

5 | -14.6 | -41.8 | -1.61 |

27 | -30.6 | -64.8 | -2.68 |

150 | -64.9 | -88.8 | -17.8 |

Soot ejected into the stratosphere which caused the ASRS (Tg) | Variation in | ||
---|---|---|---|

Mean | 5th percentile | 95th percentile | |

5 | -0.908 | -3.14 | 4.63 m |

27 | -2.40 | -4.72 | -0.0282 |

150 | -5.79 | -7.54 | -0.478 |

## Real GDP

Soot ejected into the stratosphere which caused the ASRS (Tg) | Relative variation in | ||
---|---|---|---|

Mean | 5th percentile | 95th percentile | |

5 | -20.5 | -56.0 | 1.33 m |

27 | -38.1 | -76.8 | -2.76 |

150 | -71.1 | -94.9 | -20.5 |

## Varieties of Democracy’s main index

Soot ejected into the stratosphere which caused the ASRS (Tg) | Relative variation in VoDMI due to the ASRS (%) - mean across countries | ||
---|---|---|---|

Mean | 5th percentile | 95th percentile | |

5 | 0.538 | -15.2 | 15.1 |

27 | 5.38 | -21.0 | 27.1 |

150 | -15.6 | -50.9 | 29.5 |

## Future Expected Value Index

Soot ejected into the stratosphere which caused the ASRS (Tg) | Relative variation in FEVI due to the ASRS (%) - mean across countries | ||
---|---|---|---|

Mean | 5th percentile | 95th percentile | |

5 | -0.743 | -6.39 | 3.24 |

27 | -2.22 | -12.6 | 6.20 |

150 | -10.9 | -22.0 | 6.27 |

## Global Future Expected Value Index

Soot ejected into the stratosphere which caused the ASRS (Tg) | Relative variation in GFEVI due to the ASRS (%) | ||
---|---|---|---|

Mean | 5th percentile | 95th percentile | |

5 | -0.463 | -3.81 | 2.79 |

16 | -2.47 | -8.21 | 2.57 |

27 | -3.47 | -9.29 | 2.28 |

37 | -6.63 | -12.0 | -0.477 |

47 | -6.97 | -12.3 | -0.549 |

150 | -11.8 | -22.3 | -1.21 |

## Future benefits of mitigating food shocks caused by ASRSs

### Global mitigation

**My results using a Monte Carlo simulation**

Soot ejected into the stratosphere which caused the ASRS (Tg) | Future benefits of globally mitigating food shocks as a fraction of the current value of the future (%) | |||
---|---|---|---|---|

Mean | 5th percentile | 95th percentile | Probability of being negative/harmful | |

5 | 0.216 | -2.44 | 3.01 | 41.2 |

16 | 1.20 | -3.23 | 7.85 | 35.2 |

27 | 1.67 | -3.75 | 9.54 | 31.8 |

37 | 3.18 | -5.56 | 14.0 | 27.1 |

47 | 3.35 | -5.77 | 14.3 | 26.5 |

150 | 5.54 | -9.74 | 22.7 | 26.2 |

Linear regression of future benefits of globally mitigating food shocks as a fraction of the current value of the future on soot ejected into the stratosphere | |||
---|---|---|---|

Slope (%/Tg) | Reciprocal of slope (Tg/%) | Intercept (%) | Coefficient of determination (%) |

0.0332 | 30.1 | 0.965 | 84.6 |

**My results using point estimates**

Soot ejected into the stratosphere which caused the ASRS (Tg) | Future benefits of globally mitigating food shocks as a fraction of the current value of the future | ||
---|---|---|---|

Point estimate (%) | Absolute error (pp) | Relative error (%) | |

5 | 0.125 | -0.091 | -42.2 |

16 | 1.15 | -0.0444 | -3.71 |

27 | 1.77 | 0.095 | 5.67 |

37 | 4.36 | 1.18 | 37.0 |

47 | 5.13 | 1.78 | 53.1 |

150 | 9.95 | 4.41 | 79.5 |

Model | Scenario | Reduction in far future potential (%) | ||
---|---|---|---|---|

Mean | 5th percentile | 95th percentile | ||

Survey | 10 % agricultural shortfall | 12.0 | 0.03 | 40 |

Full scale nuclear war | 24.2 | 1 | 90 | |

Anders Sandberg (E) | 10 % agricultural shortfall | 0.0266 | 0.001 | 0.1 |

Full scale nuclear war | 7.23 | 5 | 10 |

Model | Scenario | Additional mitigation of far future impact due to planning and R&D (%) | ||
---|---|---|---|---|

Mean | 5th percentile | 95th percentile | ||

Survey (S) (N = 8) | 10 % agricultural shortfall | 21.2 | 2 | 70 |

Full scale nuclear war | 28.0 | 3 | 90 | |

Anders Sandberg (E) | 10 % agricultural shortfall | 31.5 | 10 | 70 |

Full scale nuclear war | 25.2 | 10 | 50 |

Model | Scenario | Future benefits of additional planning and R&D to mitigate food shocks |
---|---|---|

Survey (S) (N = 8) | 10 % agricultural shortfall | 0.359 |

Full scale nuclear war | 6.78 | |

Anders Sandberg (E) | 10 % agricultural shortfall | 8.40 m |

Full scale nuclear war | 1.82 |

### Local mitigation

**5 Tg**

Countries by descending order of future benefits | Future benefits of locally mitigating food shocks as a fraction of the current value of the future ( | |||
---|---|---|---|---|

Ranking | Country | Mean | 5th percentile | 95th percentile |

1 | United States | 38.2 | -57.4 | 256 |

2 | Japan | 17.0 | -26.5 | 113 |

3 | Germany | 11.0 | -15.6 | 75.9 |

4 | Canada | 9.92 | -16.7 | 57.3 |

5 | France | 9.49 | -14.4 | 64.3 |

6 | South Korea | 7.67 | -12.2 | 51.2 |

7 | Italy | 7.59 | -11.9 | 50.9 |

8 | Australia | 6.85 | -11.5 | 43.5 |

9 | Sweden | 5.22 | -8.96 | 28.1 |

10 | Poland | 4.96 | -8.62 | 26.2 |

143 | Iran | -5.65 | -38.0 | 8.77 |

144 | India | -8.67 | -60.5 | 11.6 |

145 | China | -92.7 | -595 | 158 |

Mean across countries | 0.284 | -7.83 | 9.16 |

**27 Tg**

Countries by descending order of future benefits | Future benefits of locally mitigating food shocks as a fraction of the current value of the future (bp) | |||
---|---|---|---|---|

Ranking | Country | Mean | 5th percentile | 95th percentile |

1 | United States | 214 | -365 | 1.03 k |

2 | Japan | 92.3 | -160 | 434 |

3 | Germany | 73.9 | -137 | 425 |

4 | United Kingdom | 57.9 | -107 | 307 |

5 | France | 42.3 | -78.1 | 260 |

6 | Canada | 41.8 | -70.3 | 184 |

7 | South Korea | 39.2 | -70.6 | 192 |

8 | Italy | 32.0 | -59.0 | 194 |

9 | Netherlands | 19.2 | -36.2 | 111 |

10 | Sweden | 17.7 | -29.6 | 76.0 |

143 | Iran | -16.6 | -95.2 | 32.2 |

144 | Russia | -32.6 | -136 | 56.4 |

145 | China | -214 | -940 | 418 |

Mean across countries | 3.57 | -21.5 | 35.7 |

**150 Tg**

Countries by descending order of future benefits | Future benefits of locally mitigating food shocks as a fraction of the current value of the future (bp) | |||
---|---|---|---|---|

Ranking | Country | Mean | 5th percentile | 95th percentile |

1 | United States | 858 | -1.42 k | 3.46 k |

2 | Germany | 629 | -1.10 k | 2.72 k |

3 | Japan | 573 | -1.02 k | 2.50 k |

4 | United Kingdom | 473 | -865 | 2.09 k |

5 | France | 449 | -825 | 1.99 k |

6 | Italy | 355 | -674 | 1.60 k |

7 | South Korea | 317 | -610 | 1.44 k |

8 | Canada | 305 | -587 | 1.38 k |

9 | Spain | 293 | -568 | 1.33 k |

10 | Brazil | 234 | -481 | 1.15 k |

143 | Egypt | -91.5 | -448 | 208 |

144 | Iran | -97.8 | -447 | 210 |

145 | China | -278 | -1.22 k | 625 |

Mean across countries | 45.3 | -135 | 261 |

# Discussion

## Future benefits of mitigating food shocks caused by ASRSs

### Global mitigation

According to my results, the future benefits of globally mitigating food shocks caused by ASRSs as a fraction of the current value of the future are:

- For 5 Tg, 0.216 % (-2.44 % to 3.01 %, 5th to 95th percentile).
- For 27 Tg, 1.67 % (-3.75 % to 9.54 %).
- For 150 Tg, 5.54 % (-9.74 % to 22.7 %).

In addition, I estimate the probability of global mitigation being harmful decreases from 41.2 % for 5 Tg to 26.2 % for 150 Tg. This suggests even seemingly benign interventions to increase food security may prove harmful to the future. However, the heavy right of future benefits arguably makes their expectation robustly positive.

Relative to the future benefits suggested by the guesses of __Denkenberger 2022__ for the reduction in far future potential, my estimates for an ASRS of:

- 5 Tg are 1.80 % as large as those for a 10 % agricultural shortfall
^{[3]}in its survey model (= 0.216/12.0), and 8.10 times as large as those in Anders Sandberg’s model (= 0.216/0.0266).

- 150 Tg are 22.9 % as large as those for a full scale nuclear war in its survey model (= 5.54/24.2), and 76.7 % as large as those in Anders Sandberg’s model (= 5.54/7.23).

In other words, my estimates for the future benefits are:

- For mild ASRSs, much smaller than those from the survey, and larger than those from Anders Sandberg.
- For severe ASRSs, smaller than those from the survey, and similar to those from the survey and Anders Sandberg.

Additionally, my results predict an ASRS of:

- 27 Tg to be 7.75 (= 1.67/0.216) times as bad as one of 5 Tg. In comparison,
__Xia 2022__estimates, without adaptation (see table here):- 3.59 (= 97/27) times as many direct fatalities.
- 5.59 (= 1.426/0.255) times as many people without food at the end of the 2nd year.

- 150 Tg to be 3.32 (= 5.54/1.67) times as bad as one of 27 Tg. In comparison,
__Xia 2022__estimates, without adaptation (see table here):- 3.71 (= 360/97) times as many direct fatalities.
- 3.75 (= 5.341/1.426) times as many people without food at the end of the 2nd year.

Finally, I am happy the results I got using point estimates (setting all distributions to their means) closely match the ones from the Monte Carlo simulation. The relative error of the point estimates ranges from -42.2 % for 5 Tg to 79.5 % for 150 Tg. These errors are not negligible. Moreover, one should be careful to set point estimates to means, which can be quite different from the medians or modes in heavy-tailed distributions. Anyways, even if the Monte Carlo simulation did not output significantly different expectations, it would still be useful to obtain a range of plausible results in a principled way (5th and 95th percentiles).

### Local mitigation

The future benefits of local mitigation vary significantly by country. Those of the 1st country, i.e. the one whose local mitigation leads to the largest future benefits, are:

- For 5 Tg, 7.70 (= 38.2/4.96) and 135 (= 38.2/0.284) times as high as those of the 10th and mean countries.
- For 27 Tg, 12.1 (= 214/17.7) and 60.0 (= 214/3.57) times as high as those of the 10th and mean countries.
- For 150 Tg, 3.66 (= 858/234) and 19.0 (= 858/45.3) times as high as those of the 10th and mean countries.

Democratic countries with large real GDP significantly affected by ASRSs top the rankings of future benefits. Canada, Germany, Japan, and the United States are in the top 3, which is not surprising. Countries which are more democratic have higher FEVI^{[38]}, and ones with larger real GDP have a greater influence in the value of the future (via having a greater weight in GFEVI).

For similar reasons, antidemocratic countries with large real GDP have the lowest ranking. China, Egypt, India, Iran, and Russia are in the bottom 3, being the ones for which local mitigation of food shocks is the most harmful to the future. There is a tension here:

- On the one hand, the worse antidemocratic countries come out of the ASRS, the less influence they will have over the future, and so the more democratic and better it will be.
- However, antidemocratic countries coming out of the ASRS worse entails greater suffering for the people living there.

To be blunt for the sake of transparency, in this model, the future would improve if the real GDP of China, Egypt, India, Iran, and Russia dropped to 0, as long as that did not significantly affect the level of democracy and real GDP of democratic countries. However, null real GDP would imply widespread starvation, which is obviously pretty bad! I am confused about this, because I also believe worse values are associated with a worse future. For example, they arguably lead to higher chances of global totalitarianism or great power war.

Additionally, my country rankings neglect important considerations. For instance:

- R&D on
__resilient foods__conducted in one country may be leveraged by other countries. - One country increasing its reliance against food shocks caused by ASRSs may motivate other countries to increase theirs.
- The cost (difficulty) of achieving my estimated future benefits will vary across countries.

All of these influence prioritisation among countries, so my rankings only offer a starting point. I think one should target democratic countries with large real GDP significantly affected by ASRSs, or ones which could plausibly influence them.

## Metrics weighted by real GDP can be counterintuitive

My results apparently (but arguably not actually) underestimate the severity of the worst ASRSs. On face value, an ASRS of 150 Tg may seem more than 3.32 times as bad as one of 27 Tg, given this is 7.75 times as bad as one of 5 Tg. Moreover, the relative reduction in the value of the future increases linearly with the amount of soot (see 2nd table here).

I think the apparent underestimation of the severity of the worst ASRSs is explained by GFEVI being a mean weighted by real GDP. This may lead to counterintuitive conclusions if the real GDP in the worst year of the ASRS is concentrated in countries with socioeconomic indices much better than the current (real GDP weighted) average. This is possible:

__Xia 2022__estimates Australia’s calorie production without adaptation would increase 24.2 % relative to baseline for the ASRS of 150 Tg (see Table S2__here__).- As an extreme case, judging from
__this__article by Steve Brusatte, the__impact winter__which played a role in the extinction of the dinosaurs contributed to the emergence of mammals. In turn, the shift in influence over the future towards mammals ultimately led to the rise of humans, who arguably have better values than dinosaurs.

## Speculative assumptions

This analysis is quite shallow, and relies on somewhat speculative assumptions. By descending order of importance (to me):

- It is super unclear whether the structure of my model (see diagram here) meaningfully captures the dynamics which might lead to a worse future. In particular, it is quite high level, and does not explicitly model the possible infrastructure destruction due to the event which caused the ASRS, possibility of losing order due to civil or interstate wars, and collapse of governance.
- I guessed the recovery factor describing the elasticity of the value of the future with respect to GFEVI.
- I did not explicitly account for interactions between countries. Relatedly, I calculated the future benefits of local mitigation from the counterfactual value, instead of the Shapley value, which is better (see this post from Nuño Sempere).
- I guessed the parameters of the distributions describing the relationship between calorie production without adaptation and calorie supply.
- The worst year of the ASRS being the reference endpoint to calculate the future benefits (based on GFEVI) is a little arbitrary. Ideally, I would account for the whole duration of the ASRS.
- I modelled the relationships between calorie supply and real GDP per capita, and this and VoDMI based on historical data, from which causation cannot be robustly inferred.
- Such historical data may well provide a poor basis to predict what would happen in ASRSs, as it does not contain information about large food shocks. Between 1990 and 2020, the largest decrease in global cereal production was only 2.76 %
^{[39]}(from 1994 to 1995).

That being said, explicit modelling increases __reasoning transparency__, and therefore enables criticism to be more constructive. So I believe it is __better__ than relying solely on guesses.

## Next steps

As next steps, it would be valuable to:

- Determine the probability distribution of the ASRS severity by year, which is arguably driven by the risk of nuclear war. I have a very early draft for this
__here__. - Do an analysis combining the one of this post with that suggested just above. This can include a sensitivity analysis to figure out which parameters drive the results, thus informing eventual further research.
- Leverage the findings about the risk of ASRS to more accurately assess and improve the
__cost-effectiveness__of interventions which aim to mitigate it.

^{^}The future can be quite valuable. For example, Nick Bostrom estimates

__here__10^38 human lives per century.^{^}^{^}__Xia 2022__predicts a shortfall of 7.0 % for 5 Tg without adaptation (see last row of Table S2).^{^}Rescaling the indices is not only useful to define FEVI, but also to make comparisons between different indices.

^{^}For 100 k random samples per variable, the Colab takes me 50 min to run, but only 3 min without computing the future benefits of local mitigation (changing “local_mitigation = True” to “local_mitigation = False” at the top).

^{^}This relationship is discussed in

__Toon 2008__,__Mills 2014__,__Denkenberger 2018__,__Reisner 2018__,__Toon 2019__,__Wagman 2020__, and__Hess 2021__.^{^}Maize, rice, soybean, and spring wheat.

^{^}I replaced the occurrences of “-100.0 %” by -99.975 % (= -(100 % + 99.95 %)/2). The 167 nations studied by

__Xia 2022__encompass the 145 countries for which there is data on VoDMI.^{^}Excluding calories produced for animal feed or biofuels.

^{^}Maximum between 0 and a normal distribution, which makes sense given calorie production cannot be negative.

^{^}The formulas swap when the sign of RV changes.

^{^}The distance between the unrectified 5th and 95th percentiles is -2*RV*(1 + RV), which is a parabola with zeros -1 and 0, and maximum 0.5 for RV = -0.5.

^{^}Except for the samples with null CPWAf/CPWAi, in which case I set CPf/CPi to 0 (the other formula would produce infinities for samples with null CPWAf/CPWAi, and negative E_CP_CPWA).

^{^}The concept of elasticity is often used in economics to model how the change in one variable affects the change of another variable (see

__this__page from Wikipedia).^{^}For example, the extent to which calories used for animal feed and biofuels are directed toward human consumption.

^{^}According to

__this__article from Maryam Rezaei and Bin Liu:- “

**Food loss**is mainly caused by the malfunctioning of the food production and supply system or its institutional and policy framework. This could be due to managerial and technical limitations, such as a lack of proper storage facilities, cold chain, proper food handling practices, infrastructure, packaging, or efficient marketing systems”.- “

**Food waste**refers to the removal from the food supply chain of food which is still fit for human consumption. This is done either by choice or after the food is spoiled or expired due to poor stock management or neglect”.^{^}The calorie loss and waste cannot exceed the calorie production.

^{^}Maximum between 0 and a normal distribution, which makes sense given calorie loss and waste cannot be negative.

^{^}The distance between the unrectified 5th and 95th percentiles is -2*RV*(1 + RV)*CLWi/CPi, which is a parabola with zeros -1 and 0, and maximum 0.5*CLWi/CPi for RV = -0.5.

^{^}The elasticity of calorie supply with respect to calorie production is the slope of a linear regression of the logarithm of calorie supply on the logarithm of calorie production. Data on calorie production could be derived from

__FAOSTAT__’s data about the quantity of food produced in terms of mass, and caloric density tables.^{^}See cells for which there is data in column T of tab “Indices for baseline conditions”.

^{^}The regression on the reciprocal of the real GDP per capita also has this property, but it is more common to deal with the logarithm of real GDP per capita.

^{^}This has the technical advantage of preventing overflow errors in the estimation of the real GDP per capita in the worst year of the ASRS.

^{^}Calculated in tabs “Calorie supply and real GDP per capita” and “UK calorie supply and real GDP per capita”.

^{^}1990 and 2020 are the earliest and latest year for which The World Bank has data about the real GDP and cereal production. I used

__these__data from The World Bank for the cereal production.^{^}For each country, I only considered the years with data for both the real GDP per capita and VoDMI. The former was the limiting factor for all countries except Kazakhstan and Montenegro, which had data in 1990 and 1997 for the real GDP per capita, but not VoDMI. To prevent this from being the sole limiting factor, I estimated VoDMI for Kazakhstan in 1990, and Montenegro in 1997 via linear interpolation.

^{^}See O2:P2 of tab “V-Dem's main index and real GDP per capita”.

^{^}^{^}Except for that of the linear regression to data of the UK, as 61.9 % is materially lower than 86.6 %.

^{^}Calculated in tabs “V-Dem's main index and real GDP per capita” and “UK V-Dem's main index and real GDP per capita”.

^{^}The point respecting the relative variations from 1918 to 1919 is the only which is not visible.

^{^}^{^}Rescaling does not change the correlations (see

__here__).^{^}For the cases in which calorie production increases, there is no decrease in real GDP nor FEVI to be eliminated, so GFEVIf*(C) = GFEVIf, and there are no future benefits.

^{^}^{^}According to David Denkenberger, the survey was conducted in 2018.

^{^}Calculated from the product of the means in the previous tables, since all distributions were assumed to be independent in

__Denkenberger 2022__.^{^}There is a correlation in the baseline conditions between VoDMI and FEVI of 0.894 (see last table

__here__).^{^}See tab “Global cereal production and real GDP”.