Ben starts to wrap up his exploration of critical thinking principles with a look at the power of numbers to persuade and, sometimes, deceive.
Hearing about the idea of mathematical fallacies reminded me of a major paper I wrote last year for history class. The paper was on the death penalty, and I wrote about a number of reasons why it is ineffective and illogical. The reason that struck me most was the idea of imperfection in all systems, which seems to contradict the finality of the death penalty.
To set our minds straight, we invest money in checks and protections to somehow perfect a system that can’t be perfected. So much so, that the death penalty becomes more expensive than incarceration (a topic for another time).
When imperfect systems are described numerically, you can end up with what are known as a “mathematical fallacies” built on the idea of treating “hard numbers” as more “real” than other kinds of information. When applied to things like elections, this doesn’t mean that the system is bad or should not be trusted. It just means we should leave room for doubt. We shouldn’t treat numbers as the holy grail of the information we’re given since they can be wrong or twisted and manipulated as much as words can.
Even when you’re not talking about straight misinformation, numbers often give just a fraction of the picture. For example, Critical Voter discussed the “wage gap,” the widely held idea that women make seventy cents for every dollar earned by men. This ratio can be somewhat misleading, given that it groups both male-dominated surgeons (who are highly paid) and more mixed-gender physicians (who are paid less) into the same job of “doctors.” The data behind that number also doesn’t consider factors like hours worked, commission for sales jobs, and other things. The funny thing is that there is inequality in pay for men and women, it’s just that the data can’t be wrapped up into a satisfying and surprising little data point like that 70 cent one. But for someone pushing it as part of their legitimate agenda, it works.
Even in cases where you can’t poke a hole in the data, it’s valuable to maintain doubt about numbers. This is hard because humans are more trusting in numbers than they are in other kinds of information and this can lead to misunderstanding. For example, some data, like an election poll, simply captures a moment. A poll can be informative, but we should stay updated with newer polls to create an aggregate understanding that is more valuable than any individual set of poll results.
Numbers can be intimidating because they give the impression that the person using them has done their research. It’s interesting how powerful they can be, considering how many word-based fallacies come down to flawed mathematics, including arguments that fail because they make hasty generalizations or jump to conclusions.
I hypothesize it’s the idea of numbers generates confidence since they seem like signals that a person using them knows what they’re talking about. Numbers might not lie, but they can mislead and our trust in them adds to their ability to persuade. So keep looking at data, but never take for granted that it truly represents what it claims. For whether numbers are telling us about who is going to win an election, COVID or climate change, the data tables and graphs you’re seeing might be just as deceptive as biased headlines.