Here at chalkdust HQ one of our philosophies is that mathematical thinking and reasoning can be applied to all walks of life. For example, in our first issue we had an interview with Dr Hannah Fry, who discussed the mathematics of love. In this blog post, I’m going to talk about a growing movement of people applying mathematical reasoning to another area of life that is often considered emotional: donating money to charity. This group of people, called “effective altruists”, believe that choosing which charity we donate money to shouldn’t be an entirely emotional decision, dictated by which organisation can best tug at your heartstrings. Instead we should be guided by evidence and find a way of rationally measuring which charities do the most good.
You might be thinking: “Do the most good? That’s a highly subjective question.” And you’re right. But let me give you an example. In the developed world, it costs about \$40,000 to train a guide dog and its owner. However in the developing world there are millions of people suffering from trachoma-induced blindness, which can be cured with a simple operation for only about \$20. Already we have 3 orders of magnitude in the cost of the intervention. This simple example leads us to ask: is there some way a discerning altruist might be able to compare different charities in a quantifiable way? Or as a mathematician might say: can we define a good measure on the set of charities to analyse their effectiveness?
In terms of charities working in health, there are in fact well defined metrics to measure how effective an intervention is. One frequently used is the Quality Adjusted Life Year (QALY). The basic idea underlying the QALY assumes that a year of life lived in perfect health is worth 1 QALY, and that a year of life lived in a state of less than this perfect health is worth less than 1. The way to assign weights to different health conditions of course has some subjectivity associated with it, but there are a few methods which are commonly used by health economists. One method is called the time trade off (TTO) which works by asking respondents to choose between remaining in a state of ill health for a period of time, or being restored to perfect health and having a shorter life expectancy. Weighting like this does lead to some problems which need to be taken into account, e.g. respondents who don’t suffer from an affliction tend to overestimate the detrimental effect on the quality of life. But nonetheless the QALY is a very good metric and along with its cousin the DALY (Disability Adjusted Life Year) is used extensively by health economists.
So if you measure how many QALYs a charity’s intervention on average produces, then the effectiveness of the intervention is that number of QALYs achieved per dollar spent. To measure the average QALY/dollar of a particular intervention you have to take into account a lot of factors. For example, with a vaccination only a certain proportion of those vaccinated would ever actually develop the disease, and most will not in fact die from the illness, so in order to measure the effect of a dollar being spent on vaccinating people we would need to take in account the prevalence of the disease (how many people suffer from it) and its impact. Deciding how much we as a society should spend for this extra year of life is a very big question, and we won’t go to the philosophical and economic implications here; this is a maths magazine! But to give you an idea of the numbers involved; the NHS uses a limit of around £20,000 per QALY to determine whether a drug is worth approving for use.
What do we find when we examine the QALYs/dollar of various charities’ different health interventions? Well we find an extraordinary range of effectiveness, with some charities up to 1000 times more effective than others. It has been suggested that this distribution of charity effectiveness follows a log-normal distribution, which, as the name suggests, is a probability distribution whose logarithm follows the normal distribution. This distribution has a far greater scope for a few large outliers than a classical normal distribution. However a full comprehensive study of this claim has not been completed; organisations evaluating which are the most effective charities tend not to focus on measuring charities at the low end, you probably don’t need to waste resources trying to measure how effective a charity such as “Homeopaths without borders” is for example…
So which charities do well? Givewell are a US-based organisation who have conducted brilliant and extensive analysis into a range of health intervention charities. They estimate that it takes the best charities somewhere in the region of \$3000 to save an entire person’s life (note: whole life, so enough QALYs to live to the age of average life expectancy in that country, not just 1 QALY!). Their recommendations of top charities can be found here; the current list involves charities distributing malaria nets in Africa and treatment against neglected tropical diseases. Of course the measurements are uncertain, but Givewell post all their reasoning and explain all the uncertainty involved openly on their website.
The analysis I’ve discussed here focuses entirely on charities in the field of health, since we have a simple measure in terms to compare the effectiveness of different interventions. But this might mean we miss even better opportunities that are harder to quantify; for example climate and political change, leaving you to miss even better opportunities. These are legitimate questions, and extensive research into “cause selection” by the Effective Altruism community is ongoing. Givewell no longer solely look into charities working in health; the charities they recommend have to satisfy the following criteria: that they are evidence-backed, cost-effective, and capable of effectively using more funding. Picking a Givewell recommended charity will certainly make sure you get a lot more “bang for your buck” than just picking a charity by gut feeling or randomly. However you wish to do it, it’s certainly worth thinking about whether you are maximising your donation when donating to a charity?
If you’re interested in learning more about the effective altruism movement, there are a number of excellent resources available. Givewell have a very detailed website. In the UK an organisation called Giving What We Can are actively involved in encouraging donations to Givewell’s top charities; you can watch a video here with their founder Toby Ord, who is donating everything he earns above £18,000 a year to charity.
The eminent philosopher Peter Singer has just released a book on effective altruism “The most good you can do”; and we recommend you to watch his TED talk below.
You might also like…
- Using Markov chains to calculate some interesting tennis stats!
- The discovery of gravitational waves offers a new way of looking at the universe. Who knows what we will discover?
- We speak to one of Britain's most successful popularisers of maths
- Amaze your friends with our top facts about the new largest known prime number
- We have received loads of feedback from people telling us their favourite function
- Chalkdust visits popular maths' biggest conference