I expect most of us have come across people who are adamant that one or both of the above are true, with those that espouse alternative cancer treatments more likely to believe that "Big Pharma has cured cancer". Personally, I would expect that if the Big Pharma conspiracy theory was true, we'd well and truly know about it by now, since with cancer being so common, someone in the know would have either developed cancer or had a loved one develop cancer and spilled the beans.
An Oxford mathematician, Dr. David Grimes has just published research in PLOS One establishing a formula for determining the likelihood of a failed conspiracy — in other words, how likely some of its participants are to spill the beans. There are three main factors:
1) the number of conspirators - with it becoming increasingly difficult to keep the secret the more people 'in the know'
2) the amount of time passed since it started and
3) how often we can expect conspiracies to intrinsically fail (a value he derived by studying actual conspiracies that were exposed).
He then applied his equation to four famous conspiracy theories; the belief that:
1) the Moon landing was faked
2) climate change is a fraud
3) vaccines cause autism, and
4) Pharmaceutical companies have suppressed a cure for cancer.
Dr. Grimes's analysis suggests that if these four conspiracies were real, most are very likely to have been revealed as such by now. Specifically:
1) Moon landing 'hoax' would have been revealed in 3.7 years
2) the climate change 'fraud' in 3.7 to 26.8 years
3) the vaccine-autism 'conspiracy' in 3.2 to 34.8 years and
4 the cancer 'conspiracy' in 3.2 years.
Full article On the Viability of Conspiratorial Beliefs by David Robert Grimes: