‘I=PAT’ means nothing, proves nothing

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Quoting a mathematical formula might look smart, but algebra is only meaningful when it is given a meaningful content.

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by Ben Courtice
from [bcc:green socialist]

I=P×A×T (commonly pronounced “eye-pat”) is a formula, often cited, describing the factors that cause environmental degradation.

In this formula, I stands for impact; P stands for Population; A stands for Affluence (or amount consumed); T stands for Technology.

The population, multiplied by the “affluence” (or amount of stuff consumed), multiplied by the technology used to produce the stuff that is consumed, gives the impact of humans.

At first glance this is an indisputable description of the overall impact of humanity taken as a whole. Its use lies in this division of impact into different factors: having done so, we can consider how each separate factor works in our further inquiry.

But by itself, eye-pat is really not a useful description of the problem. It is almost mathematically meaningless, because A and T simply describe averages, per capita. Taken together, they add up to the average ecological footprint of each unit of population (each person, that is). So the total impact equals the average impact multiplied by the number of people.

The mathematics of this is as profound as saying that a number equals half of itself multiplied by two.

The formula is also based on, and biased toward a population focus. It divides impact by person, not by income bracket, nation, bio-region, or any of the other possible ways of dividing up society’s overall impact. This predisposes the formula to an individualist and consumerist approach to solving environmental impact and it predisposes the formula to suggesting population control measures. Yet population is just one arbitrary factor among many that could have been chosen, and our impact as individuals is only caused by our interactions with others, through work as much as through consumption.

To take apart the formula some more, it is commonly (and fairly) criticised that “affluence” takes no account of the vast differences between rich and poor, or the consumption and technology in which we have no direct say – like the resources used to maintain the world’s war machinery and armies for example.

To really examine how an increase in the amount of consumption (or what is consumed) can impact, you have to look at who is doing the consuming and why – not a statistical average of the whole world or whole nation. Population, equally, has to be analysed as an independent factor with its own dynamic of change driven by social and environmental factors to gain any real insight.

But more profoundly, the formula says nothing about how pollution/impact grows in relation to the three factors: each is given an equal weight, independent of way they interact with each other, which is only measured in the end figure of “I”.

Population grows incrementally, generation after generation, at various rates around the world. In Australia, it is only growing due to immigration, as the birth rate is currently below the rate of replacement. Growth due to immigration is not growth in population overall, because population is a global phenomenon. The whole world’s population is projected to peak this century, and its rate of growth has already begun to slow.

Changes in technology and consumption, however, can leap in rapid bounds. Any changes in consumer items or production practices are multiplied through the social mechanism of the market economy.

Imagine a newly released consumer item is put on the market and rapidly taken up by consumers. This addition of one technologically produced consumer item results in an impact that is rapidly multiplied by that part of the population that buys it.

Markets tend to expand because capitalism is a system that requires economic growth to survive, so if an item is successful in a part of the market it is sold fairly quickly to the whole population, or large parts of the population. This applies to SUVs or McMansions as much as iPods or fresh produce imported by fast refrigerated air-freight.

So an increase in technology is rapidly multiplied by the whole population. Yet an increase in population does not multiply by the whole ecological footprint of everyone else added up: it only multiplies by the average of their footprints. (Here I am taking ecological footprint as equivalent to A×T).

So population growth only adds incrementally to overall impact, whereas changes in technology and production for the market multiply the impact.

Taken on a regional or national level, many factors are quite unrelated to population. Coal for export will continue to be mined and shipped, whether Australia’s population doubles or halves, unless political measures entirely independent of the individualist I=P×A×T paradigm are taken.

A simplistic reliance on eye-pat to “prove” the importance of population controls for environmental protection is very wrong. Population cannot be reduced to one of only three factors that determine ecological impact.

Quoting a mathematical formula might look smart, but algebra is only meaningful when it is given a meaningful content. I=PAT does not impart much meaning.


  • The late Donella Meadows, one of the co-authors of the 1972 book The Limits to Growth, wrote the following in 1995:

    I didn’t realize how politically correct this [IPAT] formula had become, until a few months ago when I watched a panel of five women challenge it and enrage an auditorium full of environmentalists, including me.

    IPAT is a bloodless, misleading, cop-out explanation for the world’s ills, they said. It points the finger of blame at all the wrong places. It leads one to hold poor women responsible for population growth without asking who is putting what pressures on those women to cause them to have so many babies. It lays a guilt trip on Western consumers, while ignoring the forces that whip up their desire for ever more consumption. It implies that the people of the East, who were oppressed by totalitarian leaders for generations, now somehow have to clean up those leaders’ messes.

    As I listened to this argument, I got mad. IPAT was the lens through which I saw the environmental situation. It’s neat and simple. I didn’t want to see any other way.

    IPAT is just what you would expect from physical scientists said one of the critics, Patricia Hynes of the Institute on Women and Technology in North Amherst, Massachusetts. It counts what is countable. It makes rational sense. But it ignores the manipulation, the oppression, the profits. It ignores a factor that scientists have a hard time quantifying and therefore don’t like to talk about: economic and political POWER. IPAT may be physically indisputable. But it is politically naive.

    I was shifting uneasily in my seat.

    There are no AGENTS in the IPAT equation, said Patricia Hynes, no identifiable ACTORS, no genders, colors, motivations. Population growth and consumption and technology don’t just happen. Particular people make them happen, people who shape and respond to rewards and punishments, people who may be acting out of desperation or love or greed or ambition or fear.

    Unfortunately, I said to myself, I agree with this.

    Suppose we wrote the environmental impact equation a different way, said the annoying panel at the front of the auditorium. Suppose, for example, we put in a term for the military sector, which, though its Population is not high, commands a lot of Affluence and Technology. Military reactors generate 97 percent of the high-level nuclear waste of the U.S. Global military operations are estimated to cause 20 percent of all environmental degradation. The Worldwatch Institute says that “the world’s armed forces are quite likely the single largest polluter on earth.”

    Suppose we added another term for the 200 largest corporations, which employ only 0.5 percent of all workers but generate 25 percent of the Gross World Product — and something like 25 percent of the pollution. Perhaps, if we had the statistics, we would find that small businesses, where most of the jobs are, produce far less than their share of environmental impact.

    Suppose we separate government consumption from household consumption, and distinguish between household consumption for subsistence and for luxury, for show, for making us feel better about ourselves. If we had reliable numbers, which we don’t, we might be able to calculate how much of the damage we do to the earth comes from necessity, and how much from vanity.

    An equation was beginning to form in my head:

    Impact equals Military plus Large Business plus Small Business plus Government plus Luxury Consumption plus Subsistence Consumption

    Each of those term has its own P and A and T. Very messy. Probably some double counting and some terms left out. But no more right or wrong, really, than IPAT.

  • Ben,

    You are a unwitting stooge of big business and globalisation which loves
    people like you doing the heavy lifting for them…all in the name of naive
    political correctness.

    Why do you think big business wants massive population growth ?

    1. to sell more things ( read more greenhouse )
    2. to keep wages low for higher profits (read exploitation of
    workers..less scarce labour is, the less it’s worth, like any other
    3. to lend on housing with massive mortgages
    (read mortgage/rent slaves) Housing cost inflation and speculation is
    caused by increase in demand through population growth.

    Finally, you are a specist. That is you don’t care about the destruction of
    all the other species we share the planet with, by having the forests and
    water habitats wrecked, by the needs of more of our species.

    Come out of your seedy manipulation and promote having around 2 children at
    30 years of age and replacement immigration ( ie 80,000 leave bring in
    80,000 ) and the Planet will breath a sigh of relief.

    Your a talented person….become a force for good.

    Cheers and best wishes for your new future,

    ( P.S. http://www.populationparty.com gives us some hope that compassionate, sane, non-zenophopic people may finally be heard )

  • “The myth of overpopulation is one of the most pervasive myths in Western society, so deeply ingrained in the culture that it profoundly shapes the culture’s world view. The myth is compelling because of its simplicity. More people equal fewer resources, and more hunger, poverty, environmental degradation, and political instability. This equation helps explain away the troubling human suffering in that “other” world beyond the neat borders of affluence. By procreating, the poor create their own poverty. We are absolved of responsibility and freed from complexity.

    “The population issue is complex. To put it into proper perspective requires exploring many realms of human experience and addressing difficult philosophical and ethical questions. It entails making connections between fields of thought that have become disconnected as the result of narrow academic specialization. It demands the sharpening of critical faculties and clearing the mind of received orthodoxies. And above all, it involves transcending the alienation embodied in the very terms “population bomb” and “population explosion”. Such metaphors suggest destructive technological processes outside human control. But the population issue is about living people, not abstract statistics.

    “The myth of overpopulation is destructive because it prevents constructive thinking and action on reproductive issues. Instead of clarifying our understanding of these issues, it obfuscates our vision and limits our ability to see the real problems and find workable solutions. Worst of all, it breeds racism and turns women’s bodies into a political battlefield. It is a philosophy based on fear, not understanding.”

    – Betsy Hartmann, Reproductive Rights & Wrongs: The Global Politics of Population Control, rev. ed. 1995, p. 4.

  • I agree that the I=PAT formula is problematic. I’ll take the definition from Paul Ehrlich, who invented the concept: “The relationship is summarized in the classic I=PAT identity: Impact is equal to Population size, multiplied by per capita consumption (Affluence), in turn multiplied by a measure of the damage done by the Technologies chosen to supply each unit of consumption.” (From an address to the 1994 Cairo Conference, interestingly entitled “Too many rich people”).

    Let’s consider the measure of damage done to be CO2 emissions. Over a whole population group, the unit of consumption is GDP. This means:

    Impact=(population X (GDP/population) X (CO2emissions/GDP)

    Numerically, the total impact is just the CO2 emissions of the population group as the population and GDP terms cancel out. I think what Erlich is trying to say is that you could reduce the impact (CO2 emissions) by either reducing population or GDP per head, or the carbon intensity of production, or a by combination of the three. (To digress: Hawken, Lovins and Lovins in their book “Natural Capitalism” argue that technology can reduce the later term by a factor of 100, which begs the question of why one of them is on the board of the Carrying Capacity Network, which attacks immigration into the USA on climate change grounds).

    Ehrlich edoes apply I=PAT to specific groups of people, hence the title of his Cairo talk, and it could be applied to individuals as well.

    In addition to the problem of the formula generally being used over whole populations, irrespective of the impacts of different classes, it has two other problems:

    1) The working class and oppressed do not control the economy, so they have no control as a class over their impacts, i.e. over the carbon intensity of production. In order to do that, they would need to control production.

    2) GDP is a very blunt measure. It has meaning in the context of I=PAT. However, under capitalism GDP is used as a measure of “our” living standards, or well-being, when in fact it includes massive waste, planned obsolescence, production of car rather than other transport means, building of offices for corporate executives, accountants and lawyers, military expenditure, the costs of crime (more prisons = higher GDP), ill-health etc. So as well as controlling production, there is a need to control what is produced.

  • The critical point made is that “But by itself, eye-pat is really not a useful description of the problem”
    But it is an important starting point.
    For example the paragraph dealing with Australia makes the assumption that because migration is merely a shifting of a population from one part of the planet to an other is an indication that the formula has neither been properly understood nor used as a starting point.
    If one looks at the table in Lincoln’s Challenged Earth (about p74) from memory one can see that Australia’s per capita ecological footprint is among the highest in the world therefore to increase our population will in more cases than not bring in people from an area of low consumption to join us in our obscene feeding frenzy.
    However, that said, the point remains that just to rely on the eye pat forumla does not get us very far.
    Part of the problem lies with using averages. David Schweickart is a mathematician who exposes that myth in his book After Capitalism (a more detailed account is given in Beyond Capitalism) Societies where the average is not greatly different from the mean will be more egalitarian similarly consumption levels will be roughly the same across the society.
    In an an other forum I was asked why population looms so large in my concerns regarding climate change.
    If one is going to develop an ecosocialist perspective then I would suggest that population has to play a big role in one’s considerations.
    Part of the problem in this debate seems to be the propensity to look at population in isolation of a range of factors that contribute to human alienation as described in Marx’s pre 1848 writings.
    With regard to population there are a number of propositions that need to be taken on board:

    1. The larger the population the larger the labour force; in a capitalist system that erodes workers ability to bargain for fair wages. (Especially when they are not united as is the present case.)
    2. The larger the population the greater the demand on finite resources – technological innovations can forstall the day of reckoning but it will come. (I agree with those who argue that we simply do not know what the earth’s carrying capacity is; but that does not imply that we should promote policies of population growth.)
    3. All living organisms are in competition with one another either directly or indirectly – population growth in one organism comes at the expense of an other. Lovelock illustrates this in his example of Daisy world – human population growth implies a reduction in bio diversity. Again part of this is natural – to mourn the extinction of species is railing against the natural order, to object to the avoidable extinction of species demonstrates an awareness of our obligation to consider the impact out actions will have on future generations.
    4. Climate Change is a product of the activity of human kind. Given that we need to bring our emissions back to somewhere close to zero population growth makes that task even more difficult. ( Although population growth in the developed world is sitting close to zero the drive in Australia and some other developed countries to increase our population means that we have to make even deeper cuts in emissions just to meet the absurdly inadequate targets we have already set.)
    5. There is a link between poverty and population growth – our focus needs to be to reduce poverty which will in turn, over time, reduce population in the under developed world.

    However, I need to reiterate that I do not see population growth as the number one enemy. I see it as yet another manifestation of a social order that is ultimately self defeating.

  • Most ecological footprint calculations make the eyepat error, but the study below is a step in the right direction.

    It still only addresses personal consumption, but it breaks that down by income decile, showing that “the richest 10% of Canadian households create an ecological footprint of 12.4 hectares per capita – nearly two-and-a-half times that of the poorest 10%.” The biggest reason is…transportation.

    Size Matters: Canada’s Ecological Footprint, By Income from http://www.policyalternatives.ca.

  • Sorting formulas doesn’t matter – they don’t get used for the purpose anyway. Not by those that (should) count.