The Confidence Equation: Can You Use Math to Decide Your Future?

How can you be confident you are doing the right thing? How can you know if you are in the right job? If your partner really is the love of your life? You might just be wondering whether or not your vacation plans will turn out as you hoped. Or you might be more concerned about your social interactions with others. Do they treat you fairly? Do you treat everyone equally? What gives you confidence that you are the type of person you would like to be? 

These questions aren’t limited to your own life. How do we know if a company is guilty of sexual discrimination when hiring? How do we decide if our legal and health-care systems are fair to everyone? When a Black person applies for a job and a white person is hired, how can we be confident that this is racism? Amazingly, a single equation answers all these questions and many more. Voilà, the Confidence Equation.

Here’s how you can put it to use in your own life:

Jess isn’t sure about her career choice. She has a job at a human-rights organization. It is definitely a worthwhile cause, but her boss is horrible. She rings Jess up all hours of the day and makes unreasonable demands. Meanwhile, Jess’s friend Steve has been with Kenny for six months. Their relationship is volatile; one minute it’s hot, the next it’s cold. The arguments are terrible, but when it works, it is wonderful. 

The confidence equation can offer guidelines to both Jess and Steve—for exactly how many days she should stay in her job, and how long he should give his relationship before he gives up on Kenny. How? To see, let’s first detour into a smaller-scale problem. 

You are looking for a hotel on TripAdvisor. You are happy to stay at a place that gets 4-star reviews or better, but are skeptical about anywhere with 3.5 stars or less. 

Star reviews vary a bit on TripAdvisor. There are always a few enthusiasts who give straight 5s and a few disgruntled individuals who dole out single stars. To deal with all the variation in the reviews we start by calculating the standard deviation. This is done by summing the square differences between the average review and each of the individual reviews, then taking the square root of the...

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