Wednesday, October 17, 2018

Flow-through effects of saving a life through the ages on life-years lived

Summary: Historically, human populations were much smaller, and humans have long contributed to a process of technological accumulation that lead to current enormous human populations. Thus, saving a drowning child 10,000 years ago would have, by increasing economic output and technological advance, lead to hundreds of additional human lives by today, and potentially far more in the future. Because past populations were smaller by a greater factor than they were poorer, the ancients' opportunities to bring about QALYs may be much greater and closer to those of moderns than is sometimes thought, at least within the field of local direct life-saving. Impacts were also enormously greater in comparatively non-Malthusian periods, when a saved life could compound at high local population growth rates. In some ways, this is a historical analog to Nick Bostrom's 'Astronomical Waste' argument, showing that the basic logic of longtermism has held in the past in at least some domains. However, expediting growth is a relatively easy change to transmit over long periods, whereas trajectory changes that attempt to shape the character or actions of society at future technology levels (rather than when they are reached) face the problem of decaying influence.

Suppose you come across a drowning child, and enter the water to save them, even at the expense of a ruined suit. On average you would expect that child to then enjoy their remaining statistical life expectancy. However, there are several ways that someone can affect the quantity of years of life lived:

  1. They live out their own lives
  2. They change the lengths of the lives of their contemporaries
  3. They have children or otherwise affect contemporary births (with those children then having their own impacts)
  4. They contribute to economic output and the accumulation of technology (which has gradually enabled vastly higher populations). 
  5. They shape the world in some other lasting way that leads to a trajectory change in the character of the long-run future other than the pace and sustainability of technological development, e.g. extinction or some other very stable shift

Historically, it appears that impact on human life-years lived from a marginal life saved has been vastly larger through the very long-run impacts of channel #4 rather than effects on contemporary (within a few generations) life-years lived. The basic reason is that today world population is orders of magnitude greater than it has been for most of the last 10,000 years since the development of agricultural civilization, and even moreso compared to the hunter-gatherer humanity of the preceding tens of millennia:

This growth reflects an accumulation of technology over time, which permitted increasingly large populations. Because economic growth was slow compared to human reproduction, conditions were largely Malthusian, so per capita incomes stayed consistently near subsistence, but technological advancement translated into larger populations. And larger populations with more advanced tools in turn generated further improvements.  We can see this relationship as larger geographically isolated regions were able to sustain faster technological (and population) growth:

“Searching for a case where economic integration does not pollute the cross-section, Kremer (1993) and Jared Diamond (1997) document their famous example of regions isolated by the melting of the polar ice caps at the end of the last ice age. Five regions that began as similar hunter-gatherer societies around 10,000 BC look extremely different when the world is reintegrated by the time of Columbus, around 1500 AD. These outcomes correlate perfectly with the land areas and initial populations, just as the increasing returns associated with nonrivalry would predict. The Eurasian-African continent is the region using large ships to explore the rest of the world. The Americas contain the Mayan and Aztec civilizations with their cities and calendars. Australia has advanced somewhat with the boomerang, polished stone tools, and fire-making technologies, Tasmania remains a primitive hunter-gatherer society, and the people of the tiny Flinders Island have died out completely.”
Under Malthusian conditions, saving a life would temporarily boost population and economic activity until famine, pestilence, or war brought death and population returned to the prior oscillation around (very slowly rising) equilibrium. But the additional economic output before that would mean that the new technology level and equilibrium population would be slightly higher.

For example, suppose one saved a drowning child 10,000 years ago, when the human population was estimated to be only in the millions. For convenience, we'll posit a little over 7 million, 1/1000th of the current population. Since the child would add to population pressures on food supplies and disease risk, the effective population/economic boost could range from a fraction of a lifetime to a couple of lifetimes (via children), depending on the frequency of famine conditions. Famines were not annual and population fluctuated on a time scale of decades, so I will use 20 years of additional life expectancy.

So, for ~ 20 years the ancient population would be 1/7,000,000th greater, and economic output/technological advance. We might cut this to 1/10,000,000 to reflect reduced availability of other inputs, although increasing returns could cut the other way. Using 1/10,000,000 cumulative world economic output would reach the same point ~ 1/500,000th of a year faster. An extra 1/500,000th of a year with around our current population of ~7 billion would amount to an additional ~14,000 life -years, 700 times the contemporary increase in life years lived. Moreover, those extra lives on average have a higher standard of living than their ancient counterparts.

Readers familiar with Nick Bostrom's paper on astronomical waste will see that this is a historical version of the same logic: when future populations will be far larger, expediting that process even slightly can affect the existence of many people. We cut off our analysis with current populations, but the greater the population this growth process will reach, the greater long-run impact of technological speedup from saving ancient lives.

The ancients may have been comparably positioned to create life-years with linear direct life-saving aid to modern effective altruists
Effective altruists sometimes discuss how their principles would have applied to other eras, both to see whether the results would have been good or bad, and to make arguments that our opportunities to do good are unusually great.

As population has increased over the ages the proportional share of one life in global output has fallen, which would tend to reduce the growth effects discussed above by orders of magnitude. However, per capita incomes have increased, as have inequality and knowledge about ways to help people, which can boost the opportunity for the relative rich to save lives.

A person in the global 1% (e.g. an American software engineer) today earns hundreds of times subsistence income a rich country today may earn income, but there are still people in absolute poverty who are only moderately above subsistence incomes in the poorest parts of the world, and they can be helped with means like the cash transfers or bednets that GiveWell recommends. The corresponding income percentile in ancient times would deliver a far lower ratio.

Saving lives in ancient times was relatively simple in that simple providing food to the hungry in times of need could save lives, while GiveWell estimates a cost per life saved of many years of subsistence income, so there doesn't seem to be a vast cost disparity on that front (although more leveraged donation opportunities such as antimalarial gene drives may be better, contributing to ancient public goods could also have outperformed).

On the downside, today economic output is unevenly distributed: the lives that are cheapest to save are those of the poor who cannot produce much output in their current state. But since people from poor countries can migrate to rich ones and improve their productivity, or see their own countries develop, the expected impacts of saving the lives of the global poor still involve a lot of economic gains when they or their descendants gain the opportunity to realize high output and income.

Saving lives in booming populations would have even greater impact
Consider the tiny population of Paleolithic hunter-gatherers that crossed the Beringia land bridge over 10,000 years to settle the Americas. For generations to come their descendants would be able to simply move on to rich new lands with high food resources per person and enjoy rapid growth, growth far faster than technological advancement. Saving the life of a single person in those early days could meaningfully expedite the completion of human settlement of the Americas, and populations of tens to hundreds of millions achieved before renewed contact with Eurasia, since they were a large proportion of the population of the geographically isolated Americas, even if a small portion of the global population. The multiplier on life-years for flow-through effects might well have exceed 100,000 times.

Since the Industrial Revolution, technological advance and economic growth have outpaced population growth, so that a life saved has been able to compound through subsequent fertility. In colonial times, North American colonies saw 100x population growth, so that saving a single life then would result in more than 100x additional lives (not just the current population of descendants weighted by ancestry, but all the intermediate generations). Today, some regions have a population doubling time of 20 years, while others are growing at rates that correspond to a doubling of 40 or 80 years, or undergoing population decline. Such population trends cannot continue forever, but they mean that saving a life might have severalfold different impacts on life-years lived through the channel of added descendant lives.

Temporally, these effects meant that life-saving philanthropy in the period from the Industrial Revolution population booms to demographic transitions was especially impactful, with an advantage relative to both the ancients and ourselves.

Some thoughts on implications for longtermism
It is comforting for fans of longtermism to see that indeed historically long-run effects of life-saving interventions have been so much larger than short-run ones (and the analysis indicates that non-life-saving investments in technological development and economic activity were fruitful too, plausibly moreoso, during the Malthusian period), and that indeed early people enjoyed special impacts as a result of their special position of being among the relatively small populations of their times. This comes with the caveat that prehistoric humans would not have been able to recognize technical progress, but after agricultural civilization humans who noticed and chose to act on it would have had impacts that were astonishingly large relative to their history.

However, global output and technology are unusual in their remarkably sustained and accelerated growth, where more output begets yet more in a positive feedback explosion. Many other processes suffer negative feedback (like short-run Malthusian population dynamics that are currently loose) or just decay (if you found a religion you may have vast sustained impact, but the overwhelming majority of religions die out, moreso as time passes). When growth rates of your impact less decay rates fall beneath world growth rates one's proportional influence will decline over time, and the ancients may be worse positioned to shape the long-run than we are.

It seems to me that decay and negative feedbacks have been more important for trajectory changes, e.g. changing culture to more wisely make use of advanced technologies. People thousands of years ago attempting to shape culture and embed long-term cultural payloads would have faced the problem that selective forces shape culture (negative feedbacks), that ideas are invented independently (so their contribution could be mooted), and books, religions, and cultures have frequently been destroyed in history. To determine whether ancients or moderns had more influence over trajectory changes we would have to assess and compare these sorts of factors against the ancients' greater proportional influence in their low population eras.

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