“New mums bribed to breastfeed” ran headlines last week, as the Lancet reported that a pilot scheme offering women shopping vouchers worth up to £200 if they breastfed their babies will now be extended to more than 4,000 women. The ensuing debate worried away at the ethics of financially incentivising something so sacredly natural and freely given.

Yet the debate avoided a taboo at the heart of the story: the tricky matter of class. The scheme is targeted at low-income families in deprived areas of Yorkshire and Derbyshire, and is predicated on the fact that breastfeeding rates are much lower among working-class than middle-class women. In the UK, only 32% of women in the “routine and manual socioeconomic” group breastfeed beyond six weeks, compared with 65% in the “managerial and professional” group.

Despite – or perhaps because of – galloping socioeconomic inequality, class has become an excruciatingly embarrassing and forbidden topic. There is little research into why women on low incomes are less likely to breastfeed. Factors may include social stigma, a need to return to work, and the permanent sexualisation of breasts. Enticing those women with vouchers from Tesco and Poundland is an attempt to circumvent this murky cultural territory. Breastfeeding rates may increase, but the influences that shape lives in such contrasting ways remain unexamined and unchallenged.

Financial rewards are acceptable to many because, in an age of the supposedly sophisticated citizen-consumer savvily navigating a thoroughly marketised society, we remain wedded to the myth of homo-economicus, the rational human subject who makes clear-eyed decisions about cost and benefit. But poverty constrains free choice.

The scheme’s supporters cite the power of financial reward to trump social conditioning, but that undermines the claim that the women are acting as free agents. If the women are regarded as entirely self-determining, then the conclusion must be that their reason for not breastfeeding is a negligent lack of inclination.

Thus what appears to be a straightforward transaction sends a set of troubling messages to the women in the study and beyond. It begs the question of why middle-class mothers are so in tune with what’s best for baby that they don’t need incentivising. And it reinforces the guilt felt by mothers who have problems breastfeeding, or for whatever reason choose not to do it. The implication for them is that the controversy generated by the voucher scheme must be worth it. Not only is breast best; formula must be actually harmful.

This chimes with the plethora of media stories about how breastfeeding makes children slimmer, brainier and generally better behaved. The World Health Organisation and Unicef’s Baby Friendly Initiative states that “artificially fed” babies are at greater risk of stomach bugs and chest infections, eczema, ear infections, urinary tract infections and cot death, and are likely to have a lower IQ. NHS leaflets advise new mothers that breastfeeding helps to prevent obesity, diabetes, allergies and asthma.

But the scientific evidence is not what it seems. The only really consistent finding is that breastfeeding reduces a baby’s chance of getting a stomach bug. The protection only lasts for as long as you breastfeed. And it’s not clear whether the protection comes from something in the breast milk or from not using dirty bottles. The other supposed benefits are derived from contradictory and disputed evidence, suggesting that what is at stake in a country such as the UK with access to clean water, is not so much medical outcomes as an idealised version of motherhood that serves to stigmatise working-class women.

The really interesting thing is that the evidence is compromised by the very class differential that underlies the voucher scheme. The most reliable form of research is the randomised controlled trial (RCT). The way this works is you get a bunch of people to agree to take part in the trial. Then you randomly assign some of them to do one thing, and the rest to do another – and then you can see what difference it makes. If the people knew what group they were in, that would consciously or unconsciously influence their behaviour, skewing the results.

Where babies are concerned, it’s generally considered unethical to randomise trials. You’re only supposed to do an RCT if you genuinely don’t know what’s going to produce the best outcome. What this means is that even regarding RCTs on breastfeeding as unethical implies a value judgment about formula – that we’ve already decided it’s harmful.

So the vast majority of the research on what women eat and drink during pregnancy, and childbirth techniques, and baby-rearing, has to follow a different model: the observational study. These take an existing set of data about a group or population – surveys, for example – and look at what happened to the people who said they did one thing as compared to the people who said they did another thing.

The problem with observational studies is that they don’t reliably measure cause and effect. The women who breastfeed in these studies have deliberately chosen to do so, and the very things that may influence that decision may be responsible for how that baby turns out, rather than the fact of breastfeeding itself.

The more that social and educational background is taken into account, the smaller the differences between breast and bottle become. Crudely speaking, researchers see that children who were breastfed turn out better and regard breast milk as the determining factor, when it might well be because they’ve been given organic kale and flute lessons. When Clare Relton, who led the voucher scheme, defends it by saying that “not breastfeeding is a cause of inequality”, she is putting the cart before the horse. Class determines whether or not you breastfeed, but being breastfed doesn’t make you middle-class.