Understanding the Birthday Paradox

How many people do you think it takes in a room for two of them to have more than a 50% chance of sharing the same birthday? Surprisingly, the answer is just 23 people!

The birthday paradox is a fascinating observation of the average person’s ability to estimate probability. This sheds light on human behavior and the tendency to be impacted by subconscious bias when estimating probabilities. The quiz above and the calculator below provide further evidence, illustrating that it only takes an average of 23 other individuals in a room to have a 50.7% chance of sharing a birthday ¹. With the awe-factor aside, there are several design-oriented lessons to be learned from the paradox.

Move the slider below to see how the probability of  shared birthday’s increases with the number of people in a room.

What does this have to do with design?

This post is an attempt to delve into the relationship between people and their ability to calculate probabilities ad hoc. Personally, I tend to overinflate my understanding of what is going to happen in the future. With this awareness, I think I’m supposed to temper my judgements?

This post was inspired by Daniel Kahneman’s book, Thinking Fast and Slow. In this book two distinct systems of thinking are outlined. The first system is characterized by rapid, autonomous responses that are reflections of an impulsive understanding of our current situation. System 1 can be seen in action when driving on a highway, for instance. Imagine the person in front of you slams on their brakes on the highway, coming to a complete stop. Your response to such an event (braking hard, switching lanes,… etc.) is an instance where system 1 is in control. System 2 is responsible for deliberate focus and mental efforts. System 2 is employed in complex calculations where sustained attention is required to ensure the accuracy of the results — maybe your taxes for instance.

System 1 detects simple relations and excels at integrating information about one thing, but it does not deal with multiple distinct topics at once, nor is it adept at using purely statistical information. (Thinking fast and slow, pg 36). With that being said, spontaneous probability calculations fall in system 1’s domain. The logical error in the birthday paradox occurs because system 1 specializes in focusing on one factor at a time, not multiple factors. Many who attempt to answer the birthday paradox compare themselves (one factor) to everyone else. The thinking generally comes up with a statement similar to “how many people in this room share a birthday with me”. This is likely a subconscious thought in the process of the calculation (which is typical of system 1 processes). However, the true question should focus on the connections between each person in the room. These simple diagrams illustrate how it is possible to have much greater odds of a shared birthday between two people in a relatively small group.

Introduction:
Welcome to Factors of Design! This is the first post on the site, so if you haven’t made it that way, check out our mission at factorsofdesign.com/about. Please email me at justus@factorsofdesign.com with any feedback, comments, or corrections.

Generic Trademarks and Names
The idea for this blog began with a discovery. It turns out that the Crescent wrench is named after a brand. This was revealed to me when I found a hex key set laying on a counter of a workshop. I was taken back. I had thought quite naturally that Crescent was a type of wrench.
This term, “Crescent Wrench”, is a generic term for a type of adjustable wrench. (It is unlikely I will ever refer to it as such.)  After finding the set, I was curious about the effect of trademarks and specifically generic trademarks on a company. Generic, in trademark law, refers to the status of a word or symbol commonly used to describe an entire type of product or service rather than to distinguish one product or service from another². When a product becomes generic, it can no longer maintain its trademark status because it is indistinguishable from other products within its categorization. This is bad if you are in the business of protecting products that have become associated with your company through time and/or popularity. Everyday products that succumbed to genericide include the Escalator, Yo-Yo, Thermos, Asprin, and Trampoline, amongst many others.

Why are generic trademarks relevant to designers? Because designers and people, in general, are in the position to bestow a name to their crafts. At one point in time or another, you have been in a position to name something– maybe it’s a document, a work of art, a bridge or building, a car, or even a pet. When engaged in the naming process maybe you were at a loss as to where to begin. Of course, there is millennia of heritage for most named things– so there are guidelines. There are multiple domains to consider when naming. For instance, considerations must be made with respect to trademarks for products, with respect to bullies for children, and flexibility for part numbers for example. There are endless options, but some are better than others. In this post, the focus will be on names used for products– especially names that are suitable for trademarks which give the trademark owner exclusive rights to identify their goods or services.

The Types of Trademarks
There is essentially a 1 to 5 scale in increasing levels of protectability for trademarks. The table below helps sort through the types of trademarks and their usability. The table below has been retrieved from https://ir.law.fsu.edu/articles/213 (Table 1)³. Linford did a nice job of providing a logical representation and classification of trademark categories. Note that the Inherent strength of the trademark lies in its ability to maintain legal standing when infringed on by competitive products.

The Function of Trademarks
When it comes to product names, you want them to be distinct and memorable. This is sometimes difficult to achieve because of the density of products on the market.  As it turns out, one of the core purposes of trademarks is to reduce consumer search costs. There is value in the consumer knowing what they want and where to look. “Under the economic rationale, the law protects a trademark as a unique source identifier so that consumers can more easily find a product from their preferred source.” ⁴  With brand recognition, the amount of effort to find a quality product is reduced with registered trademarks.

Another aspect of trademarks includes the moral perspective with a goal of “preventing injury to or misappropriation of mark owner goodwill and deception of consumers.” ⁵ I believe that this latter view is the popular understanding of trademarks.

Design Guidelines

Given that companies have some incentive to pursue registered trademarks, the following are useful guidelines to preserve trademarks that may be susceptible to becoming generic.