In October my master’s student had her work on modeling HIV interventions in China published in the journal AIDS, with me as second author. You can read the abstract at the journal website, but sadly the article is pay-walled so its full joys are not available to the casual reader. This article is a sophisticated and complex mathematical model of HIV, which incorporates three disease stages, testing and treatment separately. It is based on a model published by Long et al in the Annals of Internal Medicine in 2010, but builds on this model by including the effects of methadone maintenance treatment, and doesn’t include an injecting drug use quality of life weight. It also adds new risk groups to the model: Long et al considered only men who have sex with men (MSM), injecting drug users (IDU) and the general population, but we added commercial sex workers (CSW) and their clients, who we refer to as “high risk men.” Thus our mathematical model can consider the role of both injecting drug users and sex workers as bridging populations between high-risk groups and the general population, an important consideration in China.

The HIV epidemic in China is currently a concentrated epidemic, primarily among IDUs in five provinces, and amongst MSM. The danger of concentrated epidemics is that they give the disease a foothold in a country, and a poor or delayed response may cause the epidemic to jump to the rest of the population – there is some suggestion this may have happened in Russia, for example. The Chinese authorities, recognizing this risk, began expanding methadone maintenance treatment (MMT) in the early 2000s, but it still only covers 5% of the estimated 2,500,000 IDUs in China. Our goal in this paper was to compare the effectiveness of three key interventions to prevent the spread of this disease: expanded voluntary counseling and testing (VCT); expanded antiretroviral treatment (ART); and expanded harm reduction (MMT and needle/syringe programs); and combinations of these interventions. VCT was assumed to reduce risk behavior and expand the pool of individuals who can enter treatment per year; ART was assumed to reduce infectiousness; and harm reduction to reduce risk behavior. Costs were assigned to all of the programs based on available Chinese data, and different scenarios considered (such as testing everyone once a year, or high-risk groups more frequently than everyone else).
The results showed that all the interventions considered are cost-effective relative to doing nothing; that some of the interventions saved more money than they cost; and that the most cost-effective intervention was expanding access to ART. Harm reduction was very close to ART in cost-effectiveness, and would probably be more cost-effective if we incorporated its non-HIV-related effects (reduced mortality and crime). The Chinese government stands to reap a long-term benefit from implementing some of these programs now, through the 3.4 million HIV cases averted if the interventions are successful (there are a lot of “ifs” in that sentence).This is the first paper I’m aware of that compares ART and harm reduction head on for cost-effectiveness, though subsequently some Australians showed in the same journal that needle/syringe programs (NSP) in Australia are highly cost-effective as an anti-HIV intervention. This is also the most comprehensive model of HIV in China to date, and the first to conduct cost-effectiveness analysis in that setting. I think it might be the first paper to consider the detailed structure of risk groups in a concentrated epidemic, as well. There are obvious limitations to the conclusions that one can draw from a mathematical model, and some additional limitations on this model that are specific to China: the data on costs was a bit weak (especially for MMT) and of course there are questions about how feasible some of the interventions would be. We also didn’t consider restricting the interventions to the key affected provinces, which would have made them much cheaper, and we didn’t consider ART or VCT interventions targeted only at the high-risk groups, which would also have been cheaper. For example, legalizing sex work and setting strict licensing laws might enable universal, quarterly HIV testing and lead to the eradication of HIV from this group within 10 years, but we didn’t include this scenario in the model because a) legalization is not going to happen, b) enforcement of licensing laws is highly unlikely to be effective in the current context in China, and c) data on the size and behavior of the CSW population is probably the weakest part of our model, so findings would be unreliable. Despite the general and specific limitations of this kind of modeling in this setting, I think the results are a strong starting point for informing China’s HIV policy. China seems to have a very practical approach towards this kind of issue, so I expect that we’ll see these kinds of policies implemented in the near future. My next goal is to explore the mathematical dynamics of these kinds of models with the aim of answering some of the controversial questions about whether behavioral change is a necessary or effective part of a modern HIV response, and the exact conditions under which we can hope to eliminate or eradicate HIV. Things are looking very hopeful for the future of HIV, i.e. it’s going to be eliminated or contained in most countries within our lifetime even without development of a vaccine, and that’s excellent, but there is still debate about how fast that will happen and the most cost-effective ways of getting there: hopefully the dynamic properties of these models can give some insight into that debate. This article is a big professional achievement for me in another way. It’s extremely rare for master’s students to publish in a journal as prestigious as AIDS (impact factor over 6!), and my student’s achievement is a reflection of her amazing talent at both mathematics and English, and a year of intense work on her part, but I like to think it also is a reflection of my abilities as a supervisor. There were lots of points where we could have let things slide on the assumption that master’s students don’t publish in AIDS; but we didn’t, and she did. I like to think the final product reflects well on both of us, so read it if you get the chance!

Christianity’s fundamental promise is of eternal life, and the risk of refusing to accept God’s grace is generally accepted to be eternal damnation. While the truth of these statements is still subject to debate, there is little empirical evidence of the benefit of eternal life, and little research exploring the possible drawbacks of a decision to forego evil in exchange for the promise of eternal salvation. In a world of finite resources, decisions about how best to dispose of available resources while alive need to take into account the long-term and (if certain cosmological properties are shown to hold) potentially eternal consequences of the choice between good and evil. In this blog post, we will examine the costs and benefits of baptism and rejection of sin from an econometric standpoint. Of specific interest in this blog post is the relationship between the benefits of accepting God’s grace and the discount rate society applies to years of life not yet lived.

The immediate use of an analysis of the costs and benefits of accepting god’s grace is obvious, but from a wider perspective a clear understanding of the economic aspects of this theological decision may help us to understand the persistence of evil in a world where humans have free will, and to answer the eternal question: why does evil exist in a world shaped according to God’s will?


Standard cost-effectiveness analysis methods were applied to two simple decision problems. The first decision problem is the question of whether or not to baptize a child, on the assumption that baptism grants the child God’s grace, causing them to live a holy life but to lose the benefits that might accrue to an evil-doer. The analysis was then extended to consider a problem implicit in a great deal of modern rhetoric about the soul and sexuality, viz: if homosexuality is a choice, and that choice leads only to hell, is it cost-effective to choose to be homosexual? This question was answered in terms of numbers of partners foregone, and quality-adjusted life years gained from the sacrifice.

The basic decision problem: whether to baptize

The basic decision problem was addressed using standard measures of effectiveness. It was assumed that were a child to be baptized they would be eligible to enter heaven upon their death, and would thus be able to live forever. Were they not to be baptized, they are assumed to enter hell at death. Each year of life lived was assumed to grant the individual a full quality adjusted life year (QALY); each year in heaven (from now until the rapture, i.e. infinite years from now) was also assumed to grant 1 QALY; while entry into hell was considered to grant 0 QALYs. All QALYs were discounted using the standard formula, and the effect of the discounting rate on the benefits of each decision were calculated over three different life expectancies: 45 years (enlightenment-era), 70 years (biblical lifespan) and 80 years (the life expectancy granted by modern materialist living). Effectiveness was then assessed for a wide range of discount rates, varying from 0.5% to 5%. The difference in QALYs gained (the incremental effect) was then calculated for all these scenarios.

Cost-effectiveness calculation for the baptism problem

Having calculated the incremental effect of baptism, the cost was then calculated under the assumption that evil people make more money. This assumption is implicit in, for example, Mark 8:36, when Jesus asks

What good is it for a man to gain the whole world, yet forfeit his soul?

which suggests that doing good requires some form of material sacrifice. This is, of course, also obvious in the early doctrine of the Dominican and Franciscan orders, and much of pre-enlightenment religious debate was focused around this struggle between material goods and goodness.

This contrast was modeled by a variable \alpha, which represents the percentage of additional annual income an unbaptized sinner earns relative to a person living in grace. For example, if a sinner earns 10% more than a convert, then \alpha=0.1. Then, assuming a fixed average income for god-fearing individuals, we can calculate the lost income due to being good. This is the incremental cost of salvation. From this calculated incremental cost and the incremental benefit, we can estimate an incremental cost effectiveness ratio (ICER), and estimate whether the decision to baptize is cost-effective.

In keeping with standard practice as used by, for example, the National Institute for Health and Clinical Excellence, we set the basic income of one of the saved to be the mean income of the UK, and define baptism as “cost-effective” if its ICER falls below a threshold of three times the annual mean income of the UK. We also establish a formula for the cost-effectiveness of salvation, based on the relative difference in income between the good and the evil, the discount rate, and the human lifespan.

All income in future years was discounted in the same way as future QALYs.

The costs and benefits of voluntary homosexuality

Finally, we address a problem implicit in some forms of modern christian rhetoric, that of the wilful homosexual. Many religious theorists seem to think (either implicitly or openly) that homosexuality is a choice. If so, then the choice can be modeled in terms of an exchange of sexual partners for eternal damnation. In this analysis, we calculated the number of sexual partners a potentially homosexual male will forego over a 20 year sexual career commencing at age 15. We assumed that all life years before age 15 are irrelevant to the calculation (that is, we assumed that all individuals make a choice at age 15 as to whether to be good or evil), and that a person foregoing homosexuality will have 0 partners. Other assumptions are the same as those made above. The ICER for being good was then calculated as the cost in foregone sexual partners (discounted over a wide range of rates) divided by the QALYs gained through foregoing this lifestyle and gaining access to heaven.

Faustian discount rates and the problem of heavenly utilities

Commonly used discount rates range from 3 to 5%, but these are potentially inconsistent with the discount rates preferred by evil-doers. In this study we did not model differential discount rates between evil-doers and the elect, but we did consider one special case: that in which everyone observes a discount rate equal to that observed by Dr. Faust. As is well known, Dr. Faust sold his soul to Mephistopheles in exchange for earthly power, and after 24 years his soul was taken into hell. Since he knew the time frame at the beginning of the deal, this implies that he was following a discount rate sufficient to rate all time more than 24 years in the future at 0 value. Under standard discounting practice such a rate does not exist, but we can approximate it by the rate necessary to value all time more than 24 years in the future at no more than 5% of current value. This discount rate, which we refer to as the Faustian Discount Rate, is approximately 12.5%. All scenarios were also tested under this discount rate.

A further problem is the problem of calculating utility weights for a year spent in heaven or hell. Given the lack of empirical data on utility of a year in heaven, and the paucity of first hand accounts, we assumed that a year in heaven was equivalent to a year without pain or suffering of any kind, i.e. one full QALY. According to the site What Christians Want to Know, Revelations 4:8 describes heaven as

a constant chant of holy angels that are continually proclaiming Holy, Holy, Holy over the throne of God.  The Mercy Seat in heaven where God sits is surrounded by magnificent angels full of glory and power that proclaim and bless the holy name of God without ceasing.  Some of these are described as beasts, full of eyes, with six wings and neither rest day or night in their proclaiming the holiness of God.

For those of us who don’t enjoy doom metal, this would probably have a utility value of less than one. In the interests of a conservative analysis, we assign heaven a utility of 1.

A similar problem applies to assigning utilities for hell. Many people claim to have been to hell and back, but their accounts of their time at a Celine Dion concert are not convincing and it is unlikely that accurate data on the state of hell exists. Popular conception of hell suggests a realm of eternal torture, but it is worth noting that in standard burden of disease studies even the most unpleasant and torturous diseases – such as end states of cancer, AIDS, and severe disability – are assigned positive utility weights, often quite a lot higher than 0. It is therefore reasonable to suppose that hell should be assigned a positive but small utility. However, again in the interests of conservative analysis, we assign a utility weight of 0 to a year spent in hell – that is, it is equivalent to death.


Incremental benefit of salvation

The formula for the incremental benefit of salvation can be derived as


where here,

  • LY_{g} is the incremental benefit of being good, in QALYs
  • r is the discount rate
  • l is the human life expectancy

Figure 1 charts this incremental benefit over a wide range of discount rates for three different life expectancies.

Figure 1: Incremental benefit of salvation for three different life expectancies

It is clear that as the discount rate increases the incremental benefit of salvation decreases rapidly. At the Faustian Discount Rate, the incremental benefit of salvation is a mere 0.03 QALYs for a 45 year life expectancy, or 0.0004 for a human with an 80 year life expectancy. That is, even if Faustus had been offered and then rejected his bargain at birth, and expected to live to 45 years only, he would have seen the benefit to himself as being only about 0.03 years of life, due to his tendency to discount the value of years far in the future.

The cost-effectiveness of baptism

We now consider the cost-effectiveness of baptism. Let the income of one of the saved be given by c_{g}, and that of an evil-doer be c_{e}=(1+\alpha)c_{g}. Then the income foregone in order to enter heaven is given by the formula

C=\alpha c_{g}(\frac{1-\exp(-rl)}{r})

where all parameters are defined as before. Then the incremental cost effectiveness ratio (incremental cost divided by incremental benefit) is

ICER=\alpha c_{g}(\exp(rl)-1)

The ICER is plotted in figure 2 for two common life expectancies across a range of values of the discount rate, assuming a mean annual income of 26,000 pounds and that evil-doers earn 10% more income than the saved.

Figure 2: Incremental cost-effectiveness of salvation for two different life expectancies

At a Faustian Discount Rate, life expectancy of 70 years, and 26,000 pound mean income, the ICER for baptism is 16,202,218 pounds per QALY gained.

We can estimate a general condition on society’s discount rate for baptism to be cost-effective, in terms of the additional income gained by being evil and the life expectancy. This formula is given by:

r \le \frac{1}{l}ln\Bigl (\frac{3+\alpha}{\alpha}\Bigr)

For a life expectancy of 70 years, assuming that the damned earn 10% more than the saved, the required discount rate for baptism to be cost-effective is 4.3% or less; if the damned earn 20% more this threshold drops to 3.5%. It is clear that damnation doesn’t have to be much more materially rewarding before it becomes attractive even under quite reasonable discount rates.

The costs and benefits of voluntary homosexuality

We now consider the situation of a callow 15 year old youth, considering embarking on a life of sodomite sin. What should he choose? Obviously, from the perspective of a simple youth, the costs need to be weighed up in terms of foregone lovers. Assuming an average of five sexual partners a year, a sexual career beginning at age 15 (which is set to time 0 in this analysis) and lasting 20 years, and the same conditions on discount rates, eternal damnation, etc. as described above, a simple formula for the number of partners this man would be foregoing by refusing to choose the love that dare not speak its name can be derived as


and from this the incremental cost effectiveness ratio (measured in partners foregone per QALY gained) as


Note that this ICER is not dependent on the human lifespan. It is in fact almost linear in the discount rate (Figure 3). At the Faustian Discount Rate, the potential gay man is looking at a cost of 4.6 lovers foregone for every QALY gained. Note these values change for different annual average numbers of lovers.

Figure 3: Incremental cost-effectiveness of foregoing a life of sodomy

It might be possible to construct an experiment that assessed individuals’ discount rates using this formula: their answers to the question “how many years of life would you give up to win an additional 5 lovers” could be used to identify their value of r.


In Mark 8:36, Jesus asks the rhetorical question

What good is it for a man to gain the whole world, yet forfeit his soul?

Although usually presented as a question with no clear answer, it is actually quite easy to investigate this question empirically, and to draw conclusions about its implied cost-effectiveness analysis. The results presented here show that, in general, the good gained by forfeiting one’s soul is quite great, and the decision to forego baptism and live a life of evil (including wilful homosexuality) is generally the best decision one would expect a rational actor to make. At very low life expectancies and unrealistically low discount rates it is more beneficial to forego evil and embrace salvation, but at the discount rates usually used by economists, and assumed to reflect rational decisions made by ordinary individuals, salvation is not a profitable course of action.

These findings have interesting theological implications. First, we note that the Church is most likely to gain converts in a society which has a very low discount rate – but in general, the societies where the Church first took hold were societies with high rates of infant mortality and all-cause mortality, which were likely to put a low value on the later years of life – that is, to have high discount rates. But such societies are not naturally sympathetic to the message of eternal damnation, unless they can be convinced to forego rationality in moral decision making. This might explain the Church’s historical resistance to scientific endeavour, and willingness to foment superstitious practices.

These findings also explain christianity’s historical opposition to usury. It is naturally the case that buying something today and paying for it later – i.e. borrowing – is inconsistent with a very low discount rate, which tends to value future years of lost income almost as much as now. Furthermore, usurers operating in the open market will set interest rates well above 0.05%, and it is likely that the practice of usury plus the publishing of interest rates will encourage a society with higher discount rates (in fact, it is likely that this would be encouraged by the lending class). This directly undermines the church’s lesson of salvation, which depends on very low discount rates to work.

Finally, low discount rates are often associated with environmentalism – care for future generations, priority setting that considers costs in the distant future, etc. – but on the central issue of our time (global warming) many of the born again religious organizations that most fervently preach the message of salvation also vehemently oppose any message of custodianship and environmental care. These organizations would probably make better progress in convincing people to give up the joys of the here-and-now for an indeterminate heaven (that seems to involve a lot of noise pollution) if they could find a theoretically consistent approach to discount rates.

This post has shown a simple explanation for the problem of evil: most people operate with discount rates closer to Dr. Faust than to St. Christopher, and as a result they are unlikely to accept the distant benefits of heaven over the joys of the material world. Until the church can find a way to convince us that all our tomorrows are as important as today, the problem of evil will never be solved.

One possible consequence of the collapse of the summer arctic ice cover is that storms like Sandy will become the new normal. There are reasons to think that the freak conditions that caused Sandy to become so destructive are related to the loss of arctic ice, and although the scientific understanding of the relationship between the arctic and northern hemisphere weather in general is not robust, there seems to be at least some confidence that the ice and weather around the Atlantic are related.

It’s worth noting that what is happening in the arctic this year is well in advance of scientific expectations. The 2007 Intergovernmental Panel on Climate Change (IPCC) report, for example, predicted an ice free arctic in about the year 2100. The cryosphere blogs, however, are running bets on about 2015 for “essentially ice free,” and no ice in 2020, as shown, for example, in this excellent post on ice cover prediction by Neven. Results presented by the IPCC are one of the main mechanisms by which governments make plans to manage climate change – in fact this was their intention – and one would think that events happening 80 years sooner than the IPCC predicts would make a big difference to the plans that governments need to consider.

One of the biggest efforts to make policy judgments based on current predictions of future effects of climate change was the Stern Review, published in 2006 and based on the best available scientific predictions in the previous couple of years. The key goal of the Stern Review was to assess the costs and benefits of different strategies for dealing with climate change, to answer the question of whether and when it was best to begin a response to climate change, and what that response should be.

The Stern Review received a lot of criticism from the anti-AGW crowd, and also from a certain brand of economists, partly because of the huge uncertainties involved in predicting such a wide range of events and outcomes so far in the future, and partly because of it particular assumptions. Of course, some people rejected it for being based on “alarmist” predictions from organizations like the IPCC, or rejected its fundamental assumption that climate change was happening. But one of the most persistent and effective criticisms of the Review was that it used the wrong discount rate, and thus it overemphasized the cost of rare events in the future compared to the cost of mitigation today.

I think Superstorm Sandy and the arctic ice renders that criticism invalid, and instead a better criticism of the Stern Review should now be that it significantly underestimates the cost of climate change, regardless of its choice of discount rate. Here I will attempt to explain why.

According to its critics, the Stern Review used a very low discount rate when it considered future costs. A discount rate is essentially a small percentage by which future costs are discounted relative to current costs, in order to reflect the preference humans have for getting stuff now. The classic, simplest discount rate simply applies an exponential reduction in costs over time with a very small rate (typically 2-5%), so that costs incurred 10 years from now are reduced by an amount exp(-10*rate). I use this kind of discounting in cost-effectiveness analysis, and a good rough approximation to its effects is to assume that, if costs are incurred constantly over a human’s lifetime, actually only about 40% of the total costs a person might be expected to incur will actually be counted now.

For example, if I am considering an intervention today that will save a life, and I assume that life will last 80 years, then from my perspective today that life is actually only really worth about 30 years. This reflects the fact that the community prefers to save years of life now, rather than in 70 years’ time, and also the fact that a year of life saved in 20 years time from an intervention enacted today is only a virtual year of life – the person I save tomorrow could be hit by a bus next week, and all those saved life years will be splattered over the pavement. The same kinds of assumptions can be applied to hurricane damage – if I want to invest $16 billion  now on a storm surge barrier for New York, I can’t offset the cost by savings from a $50 billion storm in 50 years time, because $16 billion is worth more to people now than in 50 years’ time, even if we don’t consider inflation. I would love to have $16 billion now, but I probably wouldn’t put much stock on a promise of $16 billion in 50 years’ time, and wouldn’t change my behavior much in order to receive it[1]. Stern is accused of rejecting this form of discounting, and essentially using a discount rate of 0%, so that future events have the same value as current events.

There are arguments for using this type of discounting when discussing climate change, because climate change is an intergenerational issue and high discount rates (of e.g. 3%) fundamentally devalue future generations relative to our own. Standard discounting is probably a logic that should only be applied when considering decisions made by people about issues in their own lifetimes. This defense has been made (the wikipedia link lists some people who made it), and it’s worth noting that many of the conservative economists who criticized the Stern Review for its discounting choice implicitly use Stern’s type of discounting when they talk about government debt – they complain extensively about “saddling future generations” with “our” debt, when their preferred discounting method would basically render the cost to those generations of our debt at zero. This debate is perhaps another example of how economists are really just rhetoricists rather than philosophers. But for now, let’s assume that the Stern Review got its discounting wrong, and should have used a standard discounting process as described above.

The Stern Review also made judgments about the effects of climate change, largely along the lines of the published literature and especially on the material made available to the world through previous rounds of IPCC reports. For example, if you actually access the Stern Review, you will note that a lot of the assumptions it makes about the effects of climate change are essentially related to the temperature trend. That is, it lists the effects of a 2C increase in temperature, and then applies them in its model at the point that the temperature crosses 2C. For example, from page 15 of Part II, chapter 5 (the figure), we have this statement:

If storm intensity increases by 6%, as predicted by several climate models for a doubling of carbon dioxide or a 3°C rise in temperature, this could increase insurers’ capital requirements by over 90% for US hurricanes and 80% for Japanese typhoons – an additional $76 billion in today’s prices.

The methods in the Stern Review are unclear, but this seems to be suggesting that the damage due to climate change is delayed in the analysis until temperature rises by 3C[2] – which will happen many years from now, in most climate models.

The assumptions in the Stern Review seem to be that the worst effects of climate change will begin many years from now, perhaps after 2020, and many (such as increased storm damage) will have to wait until the temperature passes 2C. There seems to be an assumption of a linear increase in storm damage, for example, which loads most storm damage into the far future.

This loading of storm and drought damage into the far future is the reason the discount issue became so important. If the storm damage is in the far future, then it needs to be heavily discounted, and the argument becomes that we should wait until much closer to the time to begin mitigating climate change. This argument is flawed for other reasons (you can’t stop climate change overnight, you have to act now because it’s the carbon budget, not the rate of emissions, that is most important to future damage), but it is valid as it applies to the debate about whether we should be acting to prevent climate change or prepare for climate change.

However, recent events have shown that this is irrelevant. Severe storm damage and droughts are happening now, and at least in the Atlantic rim these events are probably related to the collapse of the arctic ice load, and reductions in snow albedo across the far north. Stern’s analysis was based on most of these events happening in the far future, not now, and as a result his analysis has two huge flaws:

  1. It underestimates the total damage due to climate change. Most economic analyses of this kind are conducted over a fixed time frame (e.g. 100 years), but for any fixed time frame, a model that assumes a gradual increase in damage over time is going to underestimate the total amount of damage that occurs over the period relative to a model that assumes that the damage begins now. Stern couldn’t assume the damage begins now, because those kinds of things weren’t known in 2006. But it has begun now – we need to accept that the IPCC was wrong in its core predictions. That means that the total damage occurring in the next 100 years is not going to be $X per year between 2050 and 2100, but $X per year between 2010 and 2100 – nearly twice as much damage.
  2. The discount rate becomes irrelevant. Discount rates affect events far in the future, and have minimal effect now. If Stern had used a standard discount rate of 3%, then from his perspective in 2006 the current estimates of storm damage in the USA due to Sandy ($50 billion) would be about $42 billion. Also, all the damage in the USA due to Sandy is excess damage, because without the collapse of the arctic ice fields, Sandy would probably have headed out to sea, and done 0 damage. The estimated cost of the storm surge barrier mentioned above was $16 billion, so assuming that this cost is correct (unlikely) and it could have been built by now (impossible), that investment alone would have been worthwhile. Whereas if we assume a storm like Sandy won’t happen until 2050, the cost of the storm from Stern’s perspective is $14 billion, and we shouldn’t bother building the barrier now.

This means that the main conservative criticism of the Stern Review is now irrelevant – all that arcane debate about whether it’s more moral to value our future generations equally with now (Amartya Sen[3]) or whether we should focus on building wealth now and let our kids deal with the fallout (National Review Online) becomes irrelevant, because the damage has started now, and is very real to us, not to our potential grandchildren.

The bigger criticism that needs to be put is that Stern and the IPCC got climate change wrong. The world is looking at potentially serious food shortages next year, and in the last two years New York has experienced two major storm events (remember Irene’s storm surge was only 30cm below the level required to achieve the flooding we saw this week). Sandy occurred because of a freak coincidence of three events that are all connected in some way to global warming. We need to stop saying “it’s just weather” and start recognizing that we have entered the era of extreme events. Instead of writing reviews about what this generation needs to do to protect the environment for its children, we need to be writing reviews about what this generation can do to protect itself. Or better still, stop writing reviews and start acting.

fn1: This is a problem that has beset the organized religions for millenia. An eternity in heaven is actually not equivalent to many years on earth, if you discount it at 3% a year.

fn2: Incidentally, I’m pretty sure I was taught in physics that the use of the degree symbol in representing temperatures is incorrect. Stern uses the degree symbol. Economists!!! Sheesh!

fn3: Incidentally, I think in his published work, Sen uses the standard discounting method.

In looking at the cost-effectiveness of health interventions in fantasy communities we have shown that the infinite lifespan of elves creates analytical problems, and other commenters have suggested that the cost-effectiveness of clerical interventions to reduce infant mortality should be balanced against the need for clerics to go to war. Well, Professor John Quiggin at the Crooked Timber blog recently broached the issue of doing a benefit-cost analysis of US military spending, and has found that the US defense department has killed a million Americans since 2001. His benefit-cost analysis is really just an exercise in peskiness, though it does have a valid underlying point, and I think actually you could show with a simple cost-effectiveness analysis that the wars of the last 10 years have, under quite reasonable assumptions, not been a cost-effective use of American money. Of course, we don’t make judgments about military spending on cost-effectiveness or cost-benefit grounds.

In comments at Crooked Timber[1], I listed a few examples of how US Defense Department money could be better spent, and one of those examples was vaccination. Obviously, disease eradication would be a very good use of this money, because of its long-term implications, but in thinking about the cost-effectiveness (or cost-benefit) of this particular intervention, I think we can see another clear example of how these purely economic approaches to important policy debates just don’t work. So, here I’m going to look at this in a little more detail, and give some examples of how we can come to outrageous policy conclusions through looking at things through a purely econometric lens. I think I came to this way of thinking by considering the cost-effectiveness of interventions in elven communities, and ultimately it’s relevant to the debate on global warming, because a common denialist tactic is to demand that AGW abatement strategies be assessed entirely in terms of cost-benefit analyses, which are very hard to do and, as one can see from the comments thread at Crooked Timber, are anathema to supporters of the military establishment. As we can see here, they also break down in quite viable real-life circumstances.

The Problem of Disease Eradication

So, you’re the US president in 2001, and you’re reading a book on goats to some schoolkids, and as happens in this situation, you have to make a snap decision about how to spend 200 billion US $ over the next 10 years. You could spend it going to war with a small nation that harbours terrorists; let’s suppose that if you don’t your country will be subject to one 9/11 -style attack every year for the next 20 years (until OBL dies). If you do, you’ll commit your own and the next administration to spending 200 billion US $. Is this a good use of your money? 200 billion US $ to save about 50,000 US lives over 20 years, minus the casualties (wikipedia tells me it’s about 5000). So you get a net benefit of 45,000 lives, or 4,444,444  US $ per life – this actually comes under the US government’s 5 million US$-per-life-saved threshold, so it’s a viable use of your money. But one of your alternatives is to spend the money on eradicating HIV using a vaccine that was recently developed, and it has been shown that by spending 200 billion US$ over 10 years you could eliminate HIV from the face of the earth. You don’t care about the face of the earth, but you need to eradicate it everywhere to make Americans safe from it. Should you ignore the terrorist attacks and spend the money?

For a standard cost-effectiveness analysis you would calculate the incremental benefit (in lives saved) from this vaccine compared to the war on terror. Lives saved in the future are discounted at a fixed rate (usually about 3% a year) and decline in value over the term of the intervention. But the problem with this calculation for disease eradication (specifically) is that the term of the intervention is infinite. All future lives saved forever go into the calculation. The actual formula for this calculation is the integral over (the negative exponent of (discount rate*time t)) multiplied by (lives saved at time t)[2]. Usually we model a policy over 20 or 30 years, giving a finite result; but in this case we need to model the benefit over all future time, and the integral of any bounded function multiplied by the negative exponent, over an infinite range, is infinite. So even with furious discounting we get an infinite benefit from eradicating any disease. Not only does this make comparing disease eradication decisions – e.g. smallpox vs. HIV – impossible, but it makes comparing disease eradication to any other policy objective impossible, and it tells us – quite reasonably, I should say – that we should bend all our health care resources to this task.

In this case, the president of the USA should decide not to go to war because 20 September 11ths are a small price to pay for the eradication of HIV. Eventually Osama bin Laden will give up[3]; HIV won’t. But the stupidity of this decision doesn’t end here. If it costs a trillion dollars to eradicate HIV, the president would be better off defunding his army and paying the price than not; and if Mexico were to invade, killing a million Americans, the infinite benefit of having eradicated HIV would still outweigh the loss.

Now, one argument against this logic is that you shouldn’t include the yet-unborn in a policy evaluation; yet this is standard practice. For example, in considering the cost-effectiveness of different interventions to reduce HIV transmission, we might run a model on the 15-64 year old population, and when we do this we allow for maturity into and out of the population; if we run the model for more than 15 years we are implicitly allowing the yet-unborn into the model. Furthermore, you could surely argue that modeling disease eradication without including the unborn devalues the whole concept – what is disease eradication except a project to protect the unborn generations of the future?

So we can’t use econometric analyses by themselves to assess the value of interventions, because a perfectly reasonable economic analysis of a valid healthcare goal throws up an impossible contradiction. The world expects – with significant help from Bill Gates, I might add – to eliminate polio by 2015 and with the recent announcement of a vaccine for malaria you can bet that the international health movement will turn its gaze on that bastard protozoan next. And there is no economic argument you can mount against spending money on it – even if the cost is everything you own.

Implications for the Global Warming Debate

A common argument mounted by “hard-headed realists” and AGW deniers is that money spent on AGW mitigation needs to be justified by a solid cost-benefit analysis, because the alternative is to spend this money on targeting real problems now, especially in third world countries (often also the countries most vulnerable to AGW’s worst effects). Money spent on infant mortality now, they argue, is far better than money spent on AGW mitigation in the future – even if you accept that the negative effects of AGW are a certainty. This is a particularly powerful argument since we don’t have solid evidence for exactly how bad the effects of AGW will be, and we know that the future benefits of reducing infant mortality now are huge. This economic defense will usually also depend on discount rates – we’re much more interested in lives saved now than in the future, and AGW mitigation’s effects will be felt in the future, not now. Exactly what the relative benefits of mitigation will be are very sensitive to discount rates.

In this case, though, one can argue: well, let’s spend the entire defense department’s money on eradicating HIV. If we test everyone in Africa every 6 months – surely possible with the full funding of the US military on the case – and treat them immediately (or, hey, just treat everyone in Africa with anti-HIV drugs for the next 30 years – let’s put them in the water!) then we can eliminate HIV, and save an infinite number of lives. It’s guaranteed on both cost-benefit and cost-effectiveness grounds, with the added benefit that you don’t need to quibble over the discount rate – it’s guaranteed to be cost-effective under any finite discount rate. The natural argument against this will be that someone might invade America. But we can say in response to this, “uh uh! Precautionary principle! You don’t know how bad that invasion will be or even if it will happen.” If the precautionary principle doesn’t apply to the putative risks of AGW, why should it apply to defense? Or rather, if we need to attach a monetary value to the future risks of AGW, why not attach one to the future invasion of the USA? And when we do, it will be of lower value than the benefits from elimination of HIV, even if the entire population is wiped out during the invasion.

Which brings us back to the simple problem that we can’t assess any policy in isolation using only the econometric tools at our disposal. Everyone understands this, of course, which is why people on the Crooked Timber thread are bridling at Professor Quiggin’s analysis. They attach additional, non-economic considerations to these problems. But one of the rear-guard actions of the anti-AGW movement is to demand that we use exclusively economic methods for assessing the value of AGW mitigation – and it was in response to this fiction that the Stern review was commissioned. I think it needs to be recognized that these econometric tools offer false clarity, and only apply within a very limited framework, that of limited improvements in a limited temporal framework (pacemakers vs. aspirins, essentially). Defense, disease elimination, and AGW mitigation lie outside that framework. This should be abundantly clear to anyone who has tried to do a cost-effectiveness calculation of the relative merits of slavery and genocide for elven communities. It’s just a shame that most economists haven’t bent their mind to these truly important questions; fortunately, we at the C&C University are here to help with the more profound philosophical questions. No, don’t thank me, we do it for free. Or, alternatively, pick apart the argument in the comments … I’m eager to hear how a valid mathematical framework can be constructed for the analysis of disease eradication goals, because it’s relevant to my work…


Actually while I was watching a band in Kichijoji at 3am last night I realized that my interpretation of the formula for total effectiveness in the disease eradication was wrong[5]. Ultimately, the benefits that accrue from disease eradication are approximately (1/(discount rate))*average number of lives saved in any year. So for a discount rate of 3% and 1,000,000 lives saved per year from (e.g. ) eradicating malaria you would get a total benefit of about 33 million. It’s not infinite but it’s very very large. So the general argument holds, but it is possible to compare disease eradication programs. Note that there’s an argument that can be made for a lower discount rate in the case of disease eradication (it is all about saving future generations, not the current generation) and even a small change in the discount rate makes a big difference to the outcome. Also, under certain conditions (exponential population growth bigger than the discount rate) the benefits of disease eradication are infinite; I think most people expect the population to stabilize at 7 billion though so this doesn’t apply on earth.

fn1: for historical reasons I comment there as sg

fn2: or something similar

fn3: Actually it’s an interesting question, isn’t it? If you ignore a terrorist who is incapable of waging a conventional war on you, refuse to give into his demands, mount a purely law-enforcement operation to prevent his worst excesses, and wait him out, how long will it be before he just gives up and goes away? How long can OBL recruit people for if killing Americans leads to … nothing? And if after a few years the US said quietly to the Taliban, “we’ll give you a billion a year in aid if you get rid of him,” how long would it be before he had no safe bases?

fn4: I find this very interesting. A few years ago it was getting hard to find doctors in the west who would perform circumcisions on babies; ten years ago doctors were equivocal on the issue and there has been a long-standing community opposition to circumcision for non-medical reasons; yet now we’re recommending it (and funding it!) en masse in African countries. I wonder how Americans would have felt if, in 1987, Nelson Mandela or Robert Mugabe had come to the USA and suggested that the solution to their growing HIV problem was to circumcise all adult gay men?

fn5: I did this calculation only recently, so I really should have got this right from the start…

Today I am celebrating my first publication in my new job, and since it’s about a topic I’ll probably be coming back to a lot in the next year, I thought I’d cover it here. It’s not much of a publication – just a letter in the journal Addiction – but it covers what I think is an interesting topic, and it shows some of the complexity of modern health policy analysis. The article, entitled Equity Considerations in the Calculation of Cost-Effectiveness in Substance Use Disorder Populations[1], can be found here[2]. It’s only 400 words, but I thought I’d give an explanation in more detail here, and explain what I’m trying to say in more detail. The background I’m presenting here may be useful for some future material I’m hoping to post up here. I’ll give a brief overview of the “cost effectiveness” concept, explain what the problem is that I’m addressing in this paper, and then give a (slightly) mathematical example in extremis to show where cost-effectiveness analysis might lead us. I’ll also add some final thoughts about cost-effectiveness analysis (CEA) in fantasy populations, with perhaps a final justification for genocide. Or at least an argument for why Elves should always consider it purely on cost-effectiveness grounds.

Cost-Effectiveness Analysis, QALYs and the IDU Weight

Traditional epidemiological analysis of interventions is pretty simple: cholera, for example, kills X people, so let’s prevent it. However, we run into problems when we have limited resources and need to compare two different interventions (e.g. turning off a pump vs. handing out disinfectant pills). In this situation we need to compare which intervention is more effective, and we do this by assessing the cost per life saved under each intervention – if turning off the pump is cheaper and saves more lives, then it’s better. This is usually represented mathematically as the ratio of the cost difference between the intervention and some control (the incremental cost) and the effect difference (the incremental effects). The ratio of the two is the incremental cost effectiveness ratio (ICER). This is what I used in assessing clerical interventions to prevent infant mortality. However, when we are dealing with chronic diseases the incremental effects become harder to measure, because a lot of interventions for chronic illness don’t actually save lives: they extend life, or they improve the quality of life a person experiences before they die. In this case we use Quality-Adjusted Life Years (QALYs). These are usually defined by conducting a study in which people are asked how they would weight a year of their life under some condition relative to fully healthy – or, more usually, relative to their health as it is now. For example, blindness in one eye might be rated a QALY of 0.9 relative to being fully-sighted. There is some interesting debate about whether these ratings should be assessed by those who have the condition or the community as a whole; the logic here can be perverse and complex and is best avoided[4].

So in essence, you rate one year of life as having the value of 1 when fully healthy, and then other states are rated lower. We can use the issue of Voluntary Testing and Counselling as an HIV intervention to see how this works.

Example: Voluntary Testing and Counselling

It’s fairly well-established that good post-test counselling can successfully reduce a person’s risk behavior, so if you can get people at high risk of HIV (e.g. men who have sex with men (MSM)) to undergo voluntary testing, you can catch their HIV disease at an early stage and get them to change their behavior. In theory, doing this fast enough and effectively will reduce the rate at which HIV spreads. Furthermore, catching HIV earlier means initiating treatment earlier (before it becomes symptomatic), and early treatment with anti-retroviral drugs leads to longer survival[5]. However, discovering one is HIV positive is not a pleasant experience and knowing you are HIV positive lowers your overall quality of life, even if the disease is asymptomatic. So if the survival benefits of early testing don’t outweigh the loss of utility, then it’s not worth it. So 10 years ago, when treatment extended your life by perhaps 10%, but testing reduced your remaining QALYs from 1 to 0.9, then the benefits might not outweigh the costs. Additionally, treatment is expensive, and it might be more cost effective on a population level to run health promotion campaigns that reduce risk behavior: reduced risk behavior means less infections, means less QALYs lost to HIV.

In essence, it’s a kind of rigorous implementation of the old bar room logic: sure I’d live longer if I didn’t drink, but why would I want to?

Recently, however, some analysts have introduced a sneaky new concept, in which they apply a weight to all QALY calculations involving injecting drug users (IDUs). The underlying logic for this is that IDU is a mental illness, and people with a mental illness have a lower utility than people without. This weight is applied to all QALY calculations: so a year of life as a “healthy” IDU is assigned a value of, e.g. 0.9, and all other HIV states (for example) are given a value of 0.9 times the equivalent values for a non-IDU.

What is Wrong with the IDU Weight

This has serious ramifications for cost-effectiveness and, as I observe in my article, fucks up any attempt to get a cost-effectiveness analysis past the British NICE, since it breaks their equity rule (for good reason). In addition to its fundamentally discriminative nature, it’s also technically a bit wonky, and in my opinion it clouds cost effectiveness analysis (“which treatment for disease X provides better value for money?”) with cost-benefit analysis (“who should we spend our money on?”). It’s cool to do the latter vs. the former, but to cloud them together implicitly is very dangerous.

Technical Wonkiness

Suppose you have a population of IDUs with a weight of 0.9, and you need to compare two interventions to prevent the spread of HIV. One possible intervention you could use is methadone maintenance treatment (MMT), which is very good at reducing the rate at which IDUs take injecting risks. You want to compare this with some other, broader-based intervention (e.g. voluntary testing and treatment, VTT, which also affects MSM and low-risk people).  Then the average QALY for an MSM with asymptomatic HIV is about 0.9 (to pick a common value). Because you’ve applied the weight to IDUs but not to (e.g.) MSM, the average QALY for an IDU with asymptomatic HIV is 0.9*0.9=0.81. Now suppose that you implement MMT: this intervention reduces the risk of transmission of HIV, but it also treats IDU’s mental illness, so the weight for all the successfully-treated IDUs drops away and you gain 0.09 QALYs per IDU you treat; but then you gain 0.1 additional QALYs for every case of HIV prevented by the MMT intervention. This means that VTT has to be almost twice as effective as MMT to be considered cost effective, if they cost roughly the same amount. That is, in this case the cost-effectiveness of MMT is exaggerated relative to VTT by dint of your weighting decision – even though half of the benefits gained don’t actually have anything to do with reducing the spread of HIV (which implies you can prevent half as much HIV for the same QALY gains). On the other hand, if you implement an intervention that doesn’t treat IDU but does prevent HIV in IDU (such as needle exchange), its effectiveness will be under-estimated due to the IDU weight. In both cases, introducing the cost-benefit element to the analysis has confused your outcome.

Opening Pandora’s Box

The real problem with this IDU weight, though, is if we decided to extend the logic to all cost-effectiveness analysis where identifiable groups exist. For example, we could probably argue that very old people have lower QALYs than younger people, and any intervention which affects older people would gain less benefit than one which affects young people. An obvious example of this is anything to do with road accidents: consider, for example, mandatory eye testing vs. raising the minimum driving age. Both would result in lower rates of injury (and thus gain QALYs) but the former would primarily affect older people, and so would be assigned lower effectiveness, even if it prevented a hugely greater number of injuries[6]. When we start considering these issues, we find we’ve opened Pandora’s box, and particularly we’ve taken ourselves to a place that no modern health system is willing to contemplate: placing a lower value on the lives of the old, infirm, or mentally ill. As is often the case with social problems, the marginalized and desperate (in this case, IDUs) are the canaries in the coalmine for a bigger problem. I don’t think any health system is interested in going down the pathway of assigning utility weights to otherwise healthy old people (or MSM, or people with depression, or…)

An Example in Extremis

Let’s consider an obscene example of this situation. Suppose we apply a weight, let’s call it beta, to some group of recognizable people, who we call “the betamaxes.” Now imagine that these people are the “carriers” for a disease that doesn’t afflict them at all (i.e doesn’t change their quality of life) but on average reduces the quality of life of those who catch it to a value alpha. Suppose the following conditions (for mathematical simplicity):

  • The people who catch the disease are on average the same age as the betamaxes (this assumption makes comparison of life years easier; breaking it simply applies some ratio effects to our calculation)
  • The disease is chronic and incurable, so once a member of the population gets the disease their future quality of life is permanently reduced by a factor of alpha
  • One betamax causes one case of disease in his or her life
  • Preventing the disease is possible through health promotion efforts, but costs (e.g.) $10000 per disease prevented
  • Betamaxes are easily identifiable, and identifying and killing a betamax costs $10000

I think we can all see where I’m going here. Basically, under these (rather preposterous) conditions, identifying and killing betamaxes is a more cost-effective option than the health promotion campaign whenever alpha>1-beta. Obviously permanent quarantine (i.e. institutionalization) could also be cost-effective.

This may seem like a preposterous example (it is), but there’s something cruel about these calculations that makes me think this weighting process is far from benign. Imagine, for example, the relative QALY weights of people with dementia and their carers; schizophrenia and the injuries caused by violence related to mental health problems; or paedophilia. I think this is exactly why health systems avoid applying such weights to old people or the mentally ill. So why apply them to IDUs?

Cost-Effectiveness Analysis in Fantasy Communities

There’s an obvious situation where this CEA process breaks down horribly: if you have to apply it to elves. Elves live forever, so theoretically every elf is worth an infinite amount of QALYs. This means that if a chronic disease is best cured by drinking a potion made of ground up human babies, it’s always cost-effective for elves to do it, no matter how concentrated the baby souls have to be. If a human being should ever kill an elf due to some mental health problem, then it’s entirely reasonable for the elven community to consider exterminating the entire human community just in case[7]. Conversely, any comparison of medical interventions for chronic disease amongst elves on cost-effectiveness grounds is impossible, because all treatments will ultimately produce an infinite gain in QALYs: this means that spending the entire community’s money on preventing a single case of HIV has an incremental cost effectiveness of 0 (it costs a shitload of money, but saves an infinite number of QALYs). But so does spending the entire community’s money to prevent a single case of diabetes. How to compare?

Similar mathematical problems arise for Dwarves, who have very long lives: you’d have to give them a weight of 0.25 (for being beardy bastards) or less to avoid the same problems vis a vis the use of humans in medicinal treatment that arise with elves.

This might explain why these communities have never gone for post-scarcity fantasy. When you have an infinite lifespan, no intervention of any kind to improve quality of life is cost-effective. You might as well just live in squalor and ignorance, because doing anything about it is a complete waste of money.

Cost Effectiveness Analysis as a Justification for Goblin Genocide

Furthermore, we can probably build a mathematical model of QALYs in an AD&D world: some people have better stats than others, so they probably have better quality of life. We could construct a function in terms of the 6 primary stats, and obviously goblins come out of this equation looking pretty, ah, heavily downward weighted. Given that they lead short and brutish lives, and are prone to kill humans when the two communities interact, the obvious effect of weighting their QALYs from this mathematical model is pretty simple: kill the fuckers. The QALY gains from this (and the low cost, given the ready availability and cheap rates of modern adventurers) makes it a guaranteed investment. In fact, compared to spending money paying clerics to prevent infant mortality, it could even be cost-effective.


Cost-effectiveness analysis needs to be applied very carefully to avoid producing perverse outcomes, and the logical consequences of applying weights to particular groups on the basis of their health state are not pretty. We should never weight people “objectively” to reflect their poor health in dimensions other than that under direct consideration in the cost-effectiveness analysis, in order to avoid the risk of applying a cost-benefit analysis to a cost-effectiveness situation. Furthermore, even if we are comfortable with a “discriminatory” weight, of the “oh come on! they’re just junkies!” sort, it can still have perverse outcomes, leading to over-estimates of the cost-effectiveness of treatments for the mental illness compared to other interventions. Furthermore, we should never ever ever allow this concept to become popular amongst elven scholars.

I’ll be coming back to this topic over the next few months, I think, in a way I hope is quite entertaining for my reader(s). Stay tuned…

fn1: The slightly cumbersome title arose because the journal now doesn’t like to refer to “substance abuse” or “substance abusing populations” so I had to change it to the un-verbable “Substance Use Disorder”

fn2: If you download the pdf version it comes with a corker of a letter about French tobacco control policy[3]

fn3: Which is a contradiction in terms, surely?

fn4: For a full explanation of this and other matters you can refer to the famous text by Drummond, which is surprisingly accessible

fn5: In fact we are now looking at very long survival times for HIV – up towards 30 years, I think – provided that we initiate good quality treatment early, and so it is no longer necessarily a death sentence, if one assumes a cure will be available within the next 30 years

fn6: This applies even if you ignore deaths and focus only on short-term minor injuries, and thus avoid the implicit bias in comparing old people with young people (interventions that save life-years in old people will always be less “effective” than those that save life years in young people, unless the effect of the intervention is very short-lived, because old people have less years of life to save).

fn7: In fact you can go further than this. All you need is for an elven propagandist to argue that there is a non-zero probability that a single crazy human will kill a single elf at any point in the future, and the expected value of QALYs lost will always be greater than the QALY cost of killing all humans on earth, no matter how small the probability that the human would do this

Continuing to flog the dead horse of post-scarcity fantasy, I thought I’d bring my day job to bear on the task, and test the cost-effectiveness of a cleric-based public health measure to reduce infant mortality in a developing (medieval) nation.


Infant mortality was a significant public health problem in the medieval era, and in the absence of explicit evidence to the contrary it is reasonable to assume that it is also a significant cause of morbidity and mortality in medieval fantasy settings. Reduction of infant mortality leads to increased wealth as families devote resources to tasks other than childbirth, and also to reduced family sizes, a significant element of economic growth in most developing nations. Furthermore, control over fertility is considered a significant element of women’s emancipation, and reduced infant mortality reduces family size.

As a public health task the reduction of infant mortality is not particularly challenging, but ultimately relies on access to advanced medical care for the small minority of mothers for whom drastic complications arise. Such medical care is not available in many developing nations, but in medieval fantasy settings it is easily provided by divine spell-casters, through the wide range of magical healing technology available. Until recently, it was believed that this technology was too rare and expensive to be used for non-adventuring tasks. In this report we investigate the cost-effectiveness of devoting divine magic to averting infant mortality, under two different intervention models, and show that even under the extremely inequitable economic conditions of a classic medieval fantasy setting, this intervention is cheap, cost-effective, and likely to lead to significant economic gains at very low cost.


A simple decision model was developed for a medieval fantasy setting under the assumption that its mortality profile was approximately similar to that of Afghanistan. The model was tested for a small community of 2000, but consideration given to its extension beyond this small community. Two intervention models were tested:

  • The Clerical Attendance model: in which clerics attend every birth at the point where complications ensue, and use either of the cure light wounds, cure moderate wounds, and Remove Disease spells to intervene and prevent infant mortality
  • The Potion Distribution model: Because medieval fantasy settings have very poor transport networks, an alternative model based on distributing potions to skilled birth-attendants was considered

Both models were compared to a control model in which skilled birth-attendants were the only healthcare available to the population. Under the Clerical Attendance Model, it is assumed that these women can call a cleric when a woman begins to experience difficulties in labour, and relative risks of infant mortality were assumed on the basis that clerical intervention would improve childbirth outcomes but would sometimes come too late. Under the Potion Distribution Model, the skilled attendant would apply the potion when it was judged necessary, eliminating the need for a cleric to be present and significantly improving outcomes.

The population of the medieval fantasy setting was assumed to have a demographic profile approximately equivalent to modern day Afghanistan:

  • High birth rate: 37.5 per 1000
  • High infant mortality: 134 per 1000 live births

Population was assumed to be 30 million where overall population figures were required. For a hamlet of 2000 people, this leads to the following outcomes:

  • 75 births
  • 10.0275 infant deaths

Infant mortality was modeled on the assumption that women fall into 3 risk categories, with different probabilities of complications in each category. Where complications occur they were assumed to always lead to mortality under the control case (skilled birth attendant only). The ratio of risk groups was:

  • Low risk: 50 births, risk of complications 1.75 %
  • Medium risk: 22 births, risk of complications 30%
  • High Risk: 3 births, risk of complications 85%

This produces 10.025 deaths from 75 births, so is closely similar to the expected number of deaths. The interventions were expected to experience similar rates of complications (used for calculating costs) but reduced death rates. For the Clerical Attendance model, relative risks of death were:

  • Low risk: 0 risk of complications (RR=0)
  • Medium risk: 0.33
  • High risk: 0.25

That is, medium risk women had 1/3 the chance of dying of complications under this intervention, and high risk women 1/4 the risk.

For the Potion Distribution model, deaths in all 3 groups were assumed to be eliminated completely.

Costs for the both models were calculated on the assumption that when complications occurred the following spells were necessary:

  • Low risk: Cure Light Wounds
  • Medium Risk: Cure Moderate Wounds
  • High Risk: Cure Light Wounds, Cure Moderate Wounds, Remove Disease

Spells were cast at a cost of 50gp per level; potions were generated at the costs given in the Dungeon Master’s Guide.

Clerical load was also calculated for the Clerical Attendance model; that is, the number of clerics per 1000 required to support this model on the assumption that a cleric works no more than 200 days a year and sees one case per day.

Quality-adjusted life years (QALYs) saved were calculated assuming life expectancy in the medieval fantasy world was equal to that of Afghanistan (44 years) and outcomes expressed as incremental cost effectiveness ratios (ICERs), that is, the additional cost per QALY. Costs were in gold pieces, on the assumption that a basic medieval fantasy job (Maid) earns 36 gps per year (see Table 4-1, DMG). The wages of the skilled birth attendant were assumed to be 100Gps per year, i.e. approximately 3 x that of a maid in the era.

Sensitivity analysis was not conducted, because this is a blog.


In one year, the 2000-population hamlet could expect to experience 10.025 deaths. Under the two interventions, expected deaths are as follows:

  • Clerical Attendance model: 2.8
  • Potion Distribution Model: 0

That is, at least 7.5 lives were saved per 2000 population. QALYs for the base case and interventions are:

  • Birth Attendant Only: 2878.4
  • Clerical Attendance: 3198.5
  • Potion Distribution: 3322.5

And costs were:

  • Birth Attendant Only: 100 Gps
  • Clerical Attendance: 1978.8 Gps
  • Potion Distribution: 4828.75 Gps

Giving ICERs for the two interventions of:

  • Clerical Attendance: 6.2 Gps / QALY
  • Potion Distribution: 10.9 Gps/ QALY

Both ICERs are significantly less than the annual income of the person saved (36 Gps). The cost per birth was:

  • Clerical Attendance: 26.4
  • Potion Distribution: 64.4

Thus, childbirth could be managed with improved safety at less than the cost of a cure light wounds spell, or less than a year’s wages for a lower-class job in this world; childbirth could be rendered completely safe for less than the cost of 2 such spells. The total income for this community in one year is at least 72,000 GPs, so even the more expensive program could be paid for through a tax of no more than 10%.  Under such a tax system the cleric offering the services would be expected to pay at least 400 Gps tax, and this income could be easily diverted into a partial subsidization scheme for the poorest members of the community.

Note also that under the Potion Distribution model all child deaths are averted. Given that this would probably lead to a reduction in parity of, on average, 3 children per woman, this would lead to an increase in productivity of probably 2.25 years per woman, which gives an income of slightly more than the cost of the scheme under a free market model.

Clerical Load

With approximately 10 complications per 75 births, i.e. 10 complications per 2000 population, we expect that there would be 400 complications per 80000 individuals. A single 7th level Cleric could cover these 400 complications, so we expect not to need more than 1 such cleric per 80000. Under the Potion Distribution model, we need only 2.55 complications in the high risk group per 2000, or 200 complications per 157000 individuals. So we would need a single 7th level cleric per 157000 individuals, making one Remove Disease per day. This cleric would lose 6000 xp per year, so would need to adventure for the remainder of the year; or, for a more reasonable human resources regime, we could allow 1 7th level cleric per 80000 individuals on the assumption that one was adventuring at any time. To allow for death during adventuring, we should assume one cleric per 55,000 individuals. In a population the size of Afghanistan, we would require 545 clerics of this level or higher.

Reduction in Service Load

Given that reduced infant mortality leads to reduced birth rates and lower levels of parity, we would expect a rapid reduction in the number of births per year, and a concomitant reduction in costs and clerical load. Over the long term, we should expect the total cost under both schemes to drop rapidly.


Both schemes proposed here are highly cost-effective, being less than the income gained from the lives saved over their entire life course. Divine intervention to reduce infant mortality is an extremely effective public health intervention that simultaneously reduces personal suffering, death rates, and poverty and has significant demographic and economic effects. It can be paid for easily through a low rate of taxation and the cost reduces over time. In every sense, it is a model public health intervention. Policy-makers, hereditary kings and infernal dictators are advised to adopt this policy as soon as practicable in order to guarantee that they are Universally Loved. Churches of healing that are not already doing this gratis should hang their heads in shame. Paladins everywhere should hang their heads in shame anyway. Fantasy authors should ask themselves if they considered this cost-effectiveness analysis before they wrote their bubblegum-world stories, or if they were just being lazy.

It’s worth considering the extent of poverty in the lower classes of these worlds. A Cure Light Wounds spell costs 50gps, but the average maid earns 36 gps. Being a maid in the medieval era is not exactly the lowest class of job one can expect; it’s not tanning, bone-picking or any of the other taboo jobs, and many women aspire to this sort of work. What Paladin isn’t shagging his maid[1]? What maid isn’t lovin’ it[2]? The WHO defines “catastrophic health expense” as any health care event that costs more than 40% of your annual household consumption. Assuming no savings, cure light wounds costs a maid 140% of her annual consumption. Compare and contrast: in modern Japan a trip to hospital for a broken arm will cost me a maximum of 210,000 Yen without insurance, and if I work full time at Lawson (a pretty low-paid job) I earn 1400000 yen a year. Lower-class people in D&D are poor. But through clerics working together in an organized system, they can eliminate one of the most tragic and significant health problems facing our “advanced” world, at less than (or at least, little more than) the cost of a year’s wages for a reasonably low-class member of society. Even when these clerics are extremely rare, they can still do it. This should serve as a strong hint at the fact that even with scarce sources of magic, medieval fantasy settings should become rich very fast.

fn1: What do you mean “none of them”? Are you suggesting paladins are gay? That’s … blasphemy!

fn2: I’ve read George RR Martin[3], you can’t fool me

fn3: Actually I haven’t, but I’ve watched the TV series