The More Intersections You Have to Traverse, the Less Likely You Are to Reach Your Destination

Take a moment and think about the decisions you make on a regular basis at home or at work.  For many of them, you probably consider (perhaps quickly and quietly in your own mind) several possible future scenarios that could stem from your decisions, including their potential consequences and how you would feel about those effects, before making your decision.  A few decision scenarios you may have thought about recently might include:

1. What’s the probability I won’t get stuck in traffic when I go to drop my children off at school, my kids will have a great time at school, and I will have an enjoyable, productive day at work?

2. What’s the probability the economy will recover, businesses will locate and flourish in my community, and stakeholders will revive and commence long-stalled development projects?

3. What’s the probability (a) I’ll manage a specific project well, (b) my supervisor will notice and appreciate my good work, and (c) my entire organization will be in a better position after I finish the project?

Image Source: quesucede.com

Now that you’ve read these three scenarios, do you think the probability of each scenario increases or decreases as it becomes longer and more detailed?  For example, is the likelihood you’ll manage a specific project well greater than the likelihood of the complete abc-scenario, or is the likelihood of the complete abc-scenario greater than that of the individual component?  Take a moment.  What do you think?

Long on Details, Short on Likelihood

Most people tend to think the probability of a given scenario increases as it becomes longer and more detailed.  That is, if you were to ask one group of people to assess the probability of (a) alone, another group of people to assess the probability of (a) and (b) both occurring, and a third group of people to assess the probability of (a), (b), and (c) all occurring, it’s likely you would receive assessed probabilities in ascending order; for example, 0.50 for (a) alone, 0.65 for (a) and (b) both occurring, and 0.70 for (a), (b), and (c) all occurring.  The problem with this reasoning is that it goes against the logic of probability theory.

According to probability theory, the joint probability of two events, like (a) and (b) both occurring, cannot be greater than the smaller of the probabilities associated with the two events.  This means that the probability of (a), (b), and (c) all occurring cannot be greater than the probability of (a) and (b) both occurring, and the probability of (a) and (b) both occurring cannot be greater than the probability of (a) alone.

Image Source: en.wikipedia.org/wiki/Venn_diagram

A Picture is Worth a Thousand Words

One way to think about this logic is to visualize a Venn diagram (i.e. two overlapping circles).  One circle represents the probability of one event, e.g. event (a), and the other circle represents the probability of the other event, e.g. event (b).  With this image in your mind, it’s easier to “see” that the joint probability of the two events, (a) and (b), which is represented by the intersection of the two circles (i.e. the area of overlap), cannot exceed the smaller of the probabilities associated with the two events.  That is, the area of overlap can’t be larger than either of the individual circles.  If you’re considering more than two events, you need to visualize additional circles and areas of overlap among the circles, but the idea remains the same.

Overcoming Overestimation and Overconfidence with OverVenn Diagrams

As you can imagine, the logic of probability is applicable to many decision situations we face every day and has important implications for how we consider and use scenarios for planning and forecasting purposes.  If we fall prey to the illusion that long, detailed scenarios are more likely to occur than any of their individual components, we are likely to overestimate the likelihood of those complete scenarios and be overly (and inappropriately) confident in our predictions.

Image Source: coolopticalillusions.com

One way to straighten out the logic and probability of a scenario you’re evaluating is to draw a Venn diagram, where each circle represents the probability of an event in the scenario.  By drawing overlapping circles and assigning estimated probabilities to each of the circles, you will be able to see (literally) the probability of the complete scenario, denoted by the area of overlap of all the circles, shrink as that area of overlap becomes smaller and smaller.

Drawing Pictures Beats Telling Long Yarns

Many of the decisions we face every day force us to think about and assess the likelihood of different scenarios.  We tend to think long, detailed scenarios are more likely to occur than any of their individual components; however, this reasoning contradicts probability theory.  To guard against accidentally succumbing to this fallacy of logic, you can draw Venn diagrams and other illustrations, like decision trees.  By keeping track of the logic and probability of the scenarios you’re dealing with, you will improve your ability to accurately assess the likelihood of those scenarios and position yourself to make well-informed decisions.

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