Is selling placebos ethical?

Lying isn’t murder but murder is such a good morality yardstick that I’ll use it anyway. Imagine the truth as the victim, though people can and do actually die at the hands of disingenuity. From the US justice system:

  • First degree lie is any lie that is willful and premeditated.
  • Second degree lie is a lie that is not premeditated or planned in advance.
  • Voluntary falsehood is any intentional lying that involved no prior intent to lie, and which was committed under such circumstances that would “cause a reasonable person to become emotionally or mentally disturbed”.
  • Involuntary falsehood stems from a lack of intention to lie but involving an intentional, or negligent, act leading to falsehood. Note that the “unintentional” element here refers to the lack of intent to bring about the falsehood. All three crimes above feature an intent to lie, whereas involuntary falsehood is “unintentional”.
  • Assault could be related to telling misleading truths, or merely injuring veracity and not obliterating it. But that’s a story for another time.
  • Lies in self defense are generally considered acceptable if the lie doesn’t cause more harm than good.

To understand the scale of offense, here’s what the penalty for a corresponding murder in Arizona would be:

1st Deg Murder 25 – Life, or death penalty
2nd Deg Murder 10 – 25 years
Manslaughter 0 – 12.5 years
Negligent homicide 0 – 3.75 years

A criminal killer would be punished for every person harmed in crime. The same logic applies to a serial or mass misinformer.

Why is this interesting? First of all I recently enjoyed the Harvard course on Justice which was 12 hours of thought provoking discussion. I was amazed at how Professor Michael Sandel could sculpt even some seemingly moronic prepositions given by students into fine pieces of ethic argument. Thanks to this course I believe I may have the tools to tackle the moral dilemma of quackery, the promotion of unproven or blatantly fraudulent medical practices. Sadly the practice of quackery is still profitable and prevalent even after the 2000’s information revolution. But as much as I deplore the phenomenon I can’t bring myself to unequivocally denounce it because of its 10%-40% efficacy for certain ailments. I can’t even unequivocally denounce the expensive ones because the more expensive inert pills have been found to be more effective.

Health Fraud

To quote Tim Minchin:

Alternative Medicine […]
“Has either not been proved to work,
Or been proved not to work.
You know what they call “alternative medicine”
That’s been proved to work?

“Proved not to work” may refer to:

  • Tested and found equally effective to another placebo
  • Tested and found not effective at all, or detrimental

Advising and practicing alternative medicine that’s been proven worthless or harmful should be prohibited because they are only causing harm and profiting from it. As obvious as it may be, there are many people who have and will get away with this crime. But what about the effective placebos? From a consequential perspective, they’re helping people and thus perfectly legitimate. From a categorical perspective, these quacks are committing 1st degree lies or involuntary falsehood at the least. Either way, the truth is left dead. Quite a few people are left a lot poorer, but ~20% of these poorer individuals will actually feel better. Is that worth it?

My philosophical judgement

I’m an agnostic utilitarian, meaning to say I believe a global human utility function may exist though I don’t know exactly what it is. In fact I believe all philosophers were closeted utilitarians. They all tried to improve aspects of humanity, or at least fix wrongs. The difference between these great thinkers was merely their choice of utility function, or their methods of modeling it.

Philosopher Utility Function
Aristo Telos – The greater good is achieved by things meeting their purpose.
Immanuel Kant Universalizability – The greater good is achieved by committing actions which should be universalized.
Jim Rawls Max-min – The greater good is achieved by maximizing the benefit of those which have the least of it.

To summarize, I believe we should maximize the benefit of man kind. Preserving life being one of the most clearly visible tenants of any tribe.

Seeing as how doctors and scientists work so diligently to provide humanity with well-researched, candid and effective solutions to health problems, undermining their value is simply atrocious. The place of modern medicine in the modern home is tarnished by the likes of the keywords “natural”, “holistic”, “alternative” and relatives. This has gotten to the point where individuals who believe in alternative medicine are more likely to avoid a visit to the physician, this I’ve met first hand. I have no estimate on the amount of lives lost per avoidance of a visit to the doctor by a quack-fan, any data found is welcome. But still, I must conclude that the general damage of people avoiding life-saving treatment is fundamentally more detrimental than the benefits of allowing alternative medicine as it is today. Mainly because placebos and alternative medicine are mostly relevant for non-life threatening ailments.

A better future with regulation

Considering the danger of undermining proper medicine, dispensers of alternative medicine should be licensed, registered and labeled as such and may only treat those ailments to which a placebo has been tested effective. I’m pretty sure these clinics wouldn’t mind posting on their walls and brochures “Licensed Alternative Medicine Clinic” or “Licensed Alternative Medicine Pill”. Hopefully this label is clear enough so a person who wishes to avoid ignorance can do so with ease.

Treatments statistically shown ineffective or detrimental should be prohibited by a government agency. Tight controls in the form of license revocation, fines and arrests of quacks promising more than they’re worth should allow a legitimate placebo market. That way doctors needn’t ever sacrifice their honesty to effectively prescribe placebos, and the general public can enjoy them at their leisure.


Precision, recall, sensitivity and specificity

Nowadays I work for a medical device company where in a medical test the big indicators of success are specificity and sensitivity. Every medical test strives to reach 100% in both criteria. Imagine my surprise today when I found out that other fields use different metrics for the exact same problem. To analyze this I present to you the confusion matrix:

Confusion Matrix

Confusion Matrix

E.g. we have a pregnancy test that classifies people as pregnant (positive) or not pregnant (negative).

  • True positive – a person we told is pregnant that really was.
  • True negative – a person we told is not pregnant, and really wasn’t.
  • False negative – a person we told is not pregnant, though they really were. Ooops.
  • False positive – a person we told is pregnant, though they weren’t. Oh snap.

And now some equations…

Sensitivity and specificity are statistical measures of the performance of a binary classification test:



sensitivity and specificity

Sensitivity in yellow, specificity in red


In pattern recognition and information retrieval:



Let’s translate:

  • Relevant documents are the positives
  • Retrieved documents are the classified as positives
  • Relevant and retrieved are the true positives.
Precision, recall

Precision in red, recall in yellow

Standardized equations

  • sensitivity = recall = tp / t = tp / (tp + fn)
  • specificity = tn / n = tn / (tn + fp)
  • precision = tp / p = tp / (tp + fp)

Equations explained

  • Sensitivity/recall – how good a test is at detecting the positives. A test can cheat and maximize this by always returning “positive”.
  • Specificity – how good a test is at avoiding false alarms. A test can cheat and maximize this by always returning “negative”.
  • Precision – how many of the positively classified were relevant. A test can cheat and maximize this by only returning positive on one result it’s most confident in.
  • The cheating is resolved by looking at both relevant metrics instead of just one. E.g. the cheating 100% sensitivity that always says “positive” has 0% specificity.

More ways to cheat

A Specificity buff – let’s continue with our pregnancy test where our experiments resulted in the following confusion matrix:

8 2
10 80

Our specificity is only 88% and we need 97% for our FDA approval. We can tell our patients to run the test twice and only double positives count (eg two red lines) so we suddenly have 98.7% specificity. Magic. This would only be kosher if the test results are proven as independent. Most tests are probably not as such (eg blood parasite tests that are triggered by antibodies may repeatedly give false positives from the same patient).

A  less ethical (though IANAL) approach would be to add 300 men to our pregnancy test experiment. Of course, part of our test is to ask “are you male?” and mark these patients as “not pregnant”. Thus we get a lot of easy true negatives and this is the resulting confusion matrix:

8 2
10 380

Voila! 97.4% specificity with a single test. Have fun trying to get that FDA approval though, I doubt they’ll overlook the 300 red herrings.

What does it mean, who won?

Finally the punchline:

  • A search engine only cares about the results it shows you. Are they relevant (tp) or are they spam (fp)? Did it miss any relevant results (fn)? The ocean of ignored (tn) results shouldn’t affect how good or bad a search algorithm is. That’s why true negatives can be ignored.
  • doctor can tell a patient if they’re pregnant or not or if they have cancer. Each decision may have grave consequences and thus true negatives are crucial. That’s why all the cells in the confusion matrix must be taken into account.