The Affect Heuristic
score: 3 (3 votes) ·
Many of the examples given here suffer from what look to be deliberate ambiguities that leave the exact meaning of one of the compared elements wide open to interpretation. Note that I have not examined the source materials for consistency with your summary results, so perhaps this is an issue with the phrasing of your summary rather that the original research. For example:
My mind interprets "a disease [that kills] 1,286 people out of every 10,000" as: "for any given person, there is a 12.86% chance of dying of disease (A)". Since the statement made no qualification on people, I must infer that it is not a constrained sample, especially since this form of phrasing is often used to describe the death statistics for disasters, epidemics, or mass killings, which will often affect an entire population.
Conversely, a disease "that is 24.14% likely to be fatal" reads as "for a given person who already has disease (B), there is a 24.14% chance of dying from it". Without information about the infection rate, it stands to reason that disease (A), which has a fatality rate of somewhere between 12.86% and 100% and is known to infect somewhere between 12.86% and 100% of the total population (inversely to the fatality rate), is likely more dangerous.
Thus I would argue that the issue in this case is more about inferring particular meanings in the presence of ambiguity than a fault of mathematics of logic.
For another example:
A measure that saves [exactly] 150 lives is objectively worse than a measure that saves 98% of [a sample of] 150 lives, for any group of individuals larger than 150/0.98 = 153.06 people.