This article shows you how to express your free will. Free will is controversial. Some scientists, called determinists, believe our past hardwires our present. This makes our decisions inevitable results of that hardwiring. The article's thesis is, that while our past creates deterministic challenges to our free will, we still have choice alternatives and those decisions have the potential to alter our future paths. We build upon a belief-updating approach with scientific and time-tested philosophical support. Then we apply Bayesian Inference to help guide how one updates their core beliefs. Bayesian Inference allows for uncertainty and Bayesian updating allows for new information to course correct prior beliefs. We will lightly touch on the math of Bayesian Inference. Our hunt is to showcase the mathematical intuition to reinforce the belief updating approach. Exploring the math is optional but recommended.
Armed with your newly acquired intuition, a smartphone tool called Definitive Choice is suggested that handles the math for you. We provide a job-changing example from Mia, who is considering changing her job. The example provides math in an intuitive framework to help you update your beliefs. The appendix starts by building the decision-first approach case to serve our free will. This approach encourages the use of choice architecture to positively impact our future.
"The future is your playing field!"
Table of Contents:
Introduction - Two questions
Uncertainty, Free Will, and Belief Updating
The Belief Bucket
Bayesian Inference – the general approach
Bayesian inference example – Should Mia seek a new job?
Conclusion
Appendix - Do we have free will or is the world deterministic? It is time to ask a better question….
Notes
Definitive Choice is a resource to help you make the best judgments. Please see the resource at the end of the appendix for more information.
About the author: Jeff Hulett is a career banker, data scientist, behavioral economist, and choice architect. Jeff has held banking and consulting leadership roles at Wells Fargo, Citibank, KPMG, and IBM. Today, Jeff is an executive with the Definitive Companies. He teaches personal finance at James Madison University and provides personal finance seminars. Check out his new book -- Making Choices, Making Money: Your Guide to Making Confident Financial Decisions -- at jeffhulett.com.
2. Introduction - Two questions
Two questions help us examine our habits and feelings about decision-making:
(A) Do you ever have a decision situation where you could go either way? In this situation, your go-to response is to defer the decision and stick with the incumbent choice. You are busy with other stuff, so going with the incumbent is the default choice.
This is called the "Default Choice Easy Button Decision"
- Alternatively -
(B) Do you ever have a decision situation guided by a very strong pre-existing belief about {fill in the blank}?
{Fill in the blank - choices may include "politics," "religion," "education," "personal responsibility," etc.}
The pre-existing feeling is strong - but you struggle to recall the origin of those strong beliefs. That strong feeling feels good. So you may not be motivated to inspect that belief for fear you may disturb the good feeling.
This is called the "Deceptively Obvious Decision"
Most people answer "yes" to at least one - and often both - of these questions. This means changing our minds can be difficult. Changing our mind is the expression of our free will. This article's core premise is that we are predisposed to not changing our mind. This predisposition creates a natural tension with expressing our free will. Sometimes not changing our mind is the right thing to do. However, this predisposition creates a lemming-like bias contrary to free will. Recognizing the tension and applying good decision processes are essential for accurately expressing our free will.
To start, we explore how to express our free will by investigating how beliefs impact our ability to change our minds. Our beliefs furnish readily available, time-saving, and attention-grabbing decision suggestions. Beliefs are cognitive features tuned to a world where personal decisions lead to success or survival. Beliefs are automatically activated when uncertainty weighs upon a decision. Beliefs are like uncertainty gap fillers. Unfortunately, fixed beliefs become rapidly outdated in our dynamic environment. Some beliefs may be helpful, but the new situation may not fit the older belief. So partially fitting beliefs will then represent information needed for a decision. The challenge is that this older representation tends to lack accuracy based on the inevitable uncertainty rendered by new, incomplete, or inaccurate data. Belief inertia results from our many cognitive biases. Belief inertia delays or obscures belief updating, which further reduces our belief-guided decision accuracy.
2. Uncertainty, Free Will, and Belief Updating
Some people become so fixed in their beliefs that updating becomes next to impossible. This may occur when people associate their self-worth with a belief. For example, political leaders may have a base of support from people who consider the leader a representation of who they are. In an extreme case like this, changing our mind becomes equivalent to challenging someone's internal sense of self. The next video shows both the challenges of confirmation bias and how overcoming that challenge helps you update your beliefs and to become a more nimble decision-maker.
The Changing Our Mind Challenge
When our beliefs lack accuracy
Donald Rumsfeld was the former U.S. Secretary of Defense during the Afghanistan and Iraq invasions in the early 2000s. Rumsfeld made a memorable observation about the sources of uncertainty and divining what we know for decision-making:
“There are known knowns, things we know that we know; and
There are known unknowns, things that we know we don't know.
But there are also unknown unknowns, things we do not know we don't know.” ― Donald Rumsfeld
It is how we handle the "unknowns" to add to our "knowns" that is the essence of updating our beliefs. Conversely, how we handle the assumed "knowns" that evolve to become "unknowns" because of our dynamic, ever-changing world is essential as well. [i]
The determinist crowd suggests we have little or no free will and argues that our environment and our genetics mostly hardwire our decision outcomes. Metaphorically, this is like our beliefs are the hardened result after being seared in a hot kiln. That kiln is fueled by our evolutionary biology, our DNA, our hormones, our neurotransmitter mixing, our childhood environment, and many other influences. The hardened result leaves little room for adaptation or choice usually associated with free will. Everyone's "hot kiln" is different and there is significant diversity across individuals in how that hot kiln is expressed. Some people's beliefs may be hardened more or differently by their kiln fire than others.
So what is someone to do!?
Free market economists generally suggest this hot kiln-based diversity is at the core of what makes market economics so successful. As such, diverse individuals expressing their free will is necessary to achieve overall societal benefit. [ii]
The remainder of this article is about how to express our free will. The determinism crowd is correct that the "hot kiln" that forged our being may certainly impact our free will. [iii] This article shows you how to overcome the kiln heat and express your free will by choice. If free will is important to you - then choice is your most powerful tool. This choice method helps you to adapt and update your beliefs at the essential transition point. This is where we transition from our kiln-fired past to the variable future. "Now" is the essential decision point where our future path can be recast and placed on a different trajectory from our kiln-fired past.
The blue, top portion of the next graphic demonstrates the hot kiln-fired past. Further down the timeline, the graphic also shows the present as the point at which we activate our future. The future IS probabilistically available. Your decisions today WILL impact the future. There are many paths you can take and each path leads to a different future. So, no matter your past, the future is available as a series of choices.
In the article, How to create your own opportunity: The garbage picker’s choice, a case study is provided to show how all people may access our free will.
The ability to change our minds, despite the heat of our kiln-fired past, is supported by science and philosophical schools. For example:
Psychologist Carol Dweck considers the "growth mindset" as the key to unlocking the probabilistic future. [iv] Her approach includes overcoming the challenges of the "fixed mindset" associated with determinism.
A core tenet of the Stoic Philosophy is called the "dichotomy of control" [v-a] and is found on 3 levels:
High influence: Our choices and judgments. To a stoic, this is our free will.
Partial influence: Health, wealth, relationships, and behavior outcomes flowing from our and others' choices and judgments.
No influence: Weather, environment, genetics, and most other environmental factors - this is the blue bar, representing the past, found in the previous graphic.
Anil Seth is a cognitive and computational neuroscience professor at the University of Sussex. Dr. Seth’s research conclusions [v-b] align with the ancient Stoics’ Dichotomy of Control framework: “[Free will] is a freedom to act according to our beliefs, values, and goals, and to do as we wish to do, and make choices according to who we are.”
3. The Belief Bucket
This section explores a belief framework and how those beliefs can be effectively updated. Think of the belief bucket as a way to collect our weighted evidence and associated preferences to form a belief. In our belief bucket metaphor, we collect evidence the way a child collects rocks.
However, unlike real rocks, those metaphorical belief bucket rocks regularly change size and perspective. Thus, the underlying belief represented by the bucket holding those rocks will also change regularly. The belief bucket metaphor works like this:
Imagine all the evidence you know about a belief could fill a bucket. The individual evidence is represented by rocks of different sizes and colors.
• The rock color represents whether the evidence supports your belief or not (to build our mental picture: pro is green, con is red), and
• The rock size represents the weight (or importance) of the evidence, either bigger or smaller than the other rocks.
The portion of the bucket filled with pro evidence acts like a belief probability.
So, if 70% of the evidence in the bucket supports our belief, then the belief may be sound, though there is some contrary evidence (30%).
“The best choices are the ones that have more pros than cons, not those that don’t have any cons at all”
-Ray Dalio - Chairman, Bridgewater Associates
So, what if new evidence is added to the bucket? If the new information is net pro (supporting) evidence, then the belief probability increases. Alternatively, if the new information is net con (contrary) evidence, then the belief probability decreases. For many people, reducing a belief probability is challenging. For some, it creates a mutinous feeling, like one is betraying their tribe. That is an unfortunate but natural feeling. Rationally updating a belief probability is a critical part of making the best decisions.
If the supporting belief probability then approaches the 50% threshold, we should seriously consider changing our mind. This approach is meant to provide some structure and flexibility to update as we learn. At a minimum, we should subjectively rank order and compare the existing and newly weighted evidence.
The evidence relates to our rock size and color. The concepts of conditional probability, known as “Bayesian Inference” are at the core of properly changing our minds. Understanding the related mathematics is helpful for a deeper understanding of our belief-updating approach. For more information and citations, please see the article: Changing Our Mind
Next, Bayesian Inference is explored. This concept provides the mathematical model for how to properly change our minds. In this article, we are going to provide a bucket example and focus on one of the job-changing rocks, both its size and color, to demonstrate how Bayesian Inference works. In the example, we will assume all the other rocks (or evidence) are the same. The example shows how we update our beliefs when we receive new evidence impacting an existing belief. But let's face it, assuming other rocks do not change is convenient to demonstrate the math, but not very practical because our world is so dynamic. For practical applications, the Definitive Choice app will handle implementing Bayesian Inference, such as dynamically determining when to change jobs. The statistician George Box said,
"All models are wrong, but some are useful."
This article shows how Bayesian Inference is a useful way of thinking about changing our minds and expressing our free will. In the context of Box's quote, Bayesian Inference recognizes that individual probability estimates are rough and may lack exacting precision. Also, over time, those probabilities will change. However, even though probability estimates may be rough and varying, their usefulness is provided by using an accurate decision and belief updating process such as Bayesian Inference.
The story of Thomas Bayes is remarkable. He lived over 250 years ago and created an approach to changing our minds. He deduced this by disaggregating the steps to updating our beliefs. Effectively changing our minds is a core human challenge - mostly unchanged by evolution. Bayes' work has stood the test of time. Bayes' treatise is a beacon for helping people change their minds when faced with uncertainty.
Math provides a helpful intuition and process for big decisions and our more practical day-to-day decisions. Bayesian Inference is commonly used today. Many consumer platform AI models have a basis in Bayesian Inference. Consider a "next product" recommendation by your favorite shopping or entertainment platform. Yep, they are using a form of Bayesian Inference for that recommendation.
4. Bayesian Inference – the general approach
"Today is only one day in all the days that will ever be. But what will happen in all the other days that ever come can depend on what you do today."
- Ernest Hemmingway
First, what is it that we are trying to accomplish?
We need to determine the impact on our existing beliefs given new evidence. As we will explore:
"Impact on our existing belief" is another way of saying the more formal "posterior probability."
"Given new evidence" is another way of saying the more formal "conditioned upon the new evidence."
We seek to determine how our belief is impacted by the new evidence. Being open to changing a belief is essential and not always natural. Being open to changing our minds requires both willingness and capacity. This article focuses on building your capacity for change. The good news is that your willingness to change is inspired by your capacity for change. Focusing on capacity enables your willingness! Philip Tetlock is a forecasting expert and a professor who has dedicated his life to helping people change their minds. Dr. Tetlock's comment encourages both capacity and willingness to change our minds:
"Beliefs are hypotheses to be tested, not treasures to be guarded."
The deterministic crowd suggests our decisions may be altered by cognitive biases, noise in our environment, hormones, childhood impacts, our DNA, and many other factors over which we have little control. This is true. The point is, when it comes time to make a choice, there is a consistent, repeatable decision process we can rely upon to make the best decision despite those factors. By practicing and regularly using the best decision process, we can achieve free will.
We also need to get accustomed to how Bayesian Inference uses probabilities to make belief evaluations. This means nothing is certain unless it has already happened AND we need to appropriately evaluate that past reality. [vi] Bayesian Inference requires us to place probabilistic bets on the future. By chunking the belief evaluation down into its subparts, Bayesian Inference provides an approach to making accurate belief forecasts and regularly updating those forecasts. [vii] Once you get used to the Bayesian approach, you will find updating your beliefs to be quick, easy, and ACCURATE! This is the essence of expressing our free will. At the end of the article, we suggest a smartphone tool to make those belief updates even easier. Choice architecture, the toolset of behavioral economists, has made great strides to help people intuitively express Bayesian probabilities.
Physicist Enrico Fermi uses a Bayesian-inspired "Chunking it down" approach: Properly "chunking it down" is an approach to forecasting with a history dating back to Thomas Bayes. Enrico Fermi was a University of Chicago physicist during World War II. He was a leading physicist of his day and helped with the nuclear program and war effort. Fermi developed a back-of-the-envelope approach to forecasting that was accurate and required almost no data. It relies on a Bayesian-inspired forecasting approach to chunking down - more formally known as 'disaggregating' - the problem into analyzable subparts. The magic to deliver a reasonably accurate forecast is in the chunking process.
Let’s start with defining the disaggregated categories of the standard belief updating process to evaluate changing our minds.
The posterior probability is called a conditional probability and is found on the left side of the equation. This is where one determines a probability, like our existing belief (“EB”), as conditioned by the impact of new evidence (“NE”). To properly determine our posterior probability, we need to determine the 3 subparts - or "chunks." Those 3 subparts get aggregated and transformed to determine the appropriate posterior probability. Here is the high-level equation:
Next - provided are the probabilities and the definitions of each subpart to build our new posterior probability, AFTER the new evidence is evaluated. We add the math notation for conditional probabilities. The vertical bar is the symbol for conditional probability. In the Posterior probability, this is read as “The probability of the existing belief (‘EB’) as a condition of the new evidence (‘NE’).”
The equation for transforming the new posterior probability is:
You could be wrong about your probability point estimate and that is ok! In the Bayesian Inference formula, we must choose a probability point estimate (P) for the different subparts. But behind every probability point estimate is a probability distribution. That point estimate is the probability of what is most expected to happen. The probability distribution summarizes your knowledge of all that could happen, inclusive of that point estimate. This means that just because the point estimate is most expected, does not mean that something else could not happen. That "something else" is found in the rest of the probability distribution. Probability distributions take many shapes - such as normal, Poisson, chi-squared, Bernoulli, exponential, and many others. Next are Bayesian considerations, then followed by Bayesian practices. This will help you make an accurate future forecast even given the other possibilities.
Bayesian Considerations: Regardless of the distribution shape, next are three things to consider for your probability distribution when deciding your probability point estimate:
The height of that distribution demonstrates how confident you are about the point estimate – the higher the point estimate is relative to the other possibilities indicates the point estimate is surer to happen. With the opposite being true - a lower point estimate relative to the other possibilities - suggests you are less sure about the point estimate. This is known as Kurtosis or the 4th statistical moment.
Whether that distribution is left-leaning or right-leaning – if your point estimate is wrong, the lean suggests the direction it is more likely to be wrong. A left-leaning distribution means that if you are wrong about the point estimate, you are more likely to be wrong to the higher probability side. With the opposite being true, a right-leaning distribution means that if you are wrong about the point estimate, you are more likely to be wrong to the lower probability side. This is known as Skewness or the 3rd statistical moment.
The distribution similarity between your prior and likelihood distributions - If the distributions are similar - like both the prior and likelihood distributions are roughly the shape of a normal distribution - then comparing these two prior and likelihood probability point estimates is easier. Similar distributions have a mathy name called "Conjugate Priors." However, if the distribution differences are truly different, then assuming they are the same may lead to making an imprecise probability point estimate.
For more information about statistical moments, please see the article:
Bayesian Practices: In practice, next is how to handle these considerations:
Increase your distribution height: Increase your confidence by learning about your belief and that new evidence. Do your best to learn about the evidence most likely to impact your outcome. I suggest the 80/20 rule - or the "Pareto Principle" - for deciding when to stop analyzing and make the probability point estimate call. People are prone to "analysis paralysis" leading to inappropriately defaulting to their priors. To avoid this, I attempt to gather most of the information I can about the important stuff (80%) but stop at that point. The work-to-benefit tradeoff required to collect the remaining 20% is too costly, so I am better off stopping and deciding once I reach 80%. People tend to confuse the “how difficult it is to find information” with the “power of that information” to impact their outcome. These information categories are very different. Focus on understanding 80% of the decision outcome power and overcoming any difficulty.
Protect yourself from the lean: You will almost certainly be wrong in your point estimate, but understanding the direction of where being wrong hurts the most helps focus your research attention. If you are deciding whether to change jobs, what could have more downside, staying or leaving? Be honest! In the next example, we show that Mia's company is laying off people. In this situation, "the lean" shows there is more downside to staying, since that job may not exist in the near future. By the way, being wrong in your point estimate is to be expected, that is the whole point of Bayesian inference, which is to update your belief understanding. It is the Bayesian process for updating that reduces the penalty for being wrong.
Understand the nature of what could have happened: Today, our priors are a given. But there was a time in the past when they were less sure. Go back in time and inspect your priors as if they were unknown. What were the other possibilities? For example, for a job change, what happened when you - or credible others - made that past job change decision? What were the possibilities and the benefits then? Now, today, apply that distribution of possibilities to your new evidence (NE). In the context of your existing belief (EB) does the set of new evidence conform to the distribution of the prior possibilities? If so, this raises your confidence. Even if they are different distributions, focusing on the probability distribution height (1) and lean (2) will help ensure a reasonably precise posterior probability estimate. Think of practice 1) and 2) as a compensating factor for 3). Also, using choice architecture helps to manage this and the first two Bayesian practices.
Definitive Choice is a helpful choice architecture to manage the accuracy of probability point estimates and their distributions.
The next section is a practical example showing Bayesian Inference in action. Before helping Mia decide about her job, the general Bayesian Inference lifecycle is summarized in the following graphic. The "hot kiln" is shown as the past winding road. Your past certainly contains valid judgments, but it also contains bias. Today is the decision point - a potential opportunity for change. A good decision process helps you separate the good judgment from the bias. The idea is to own our priors and overlay a consistent, repeatable decision process to make the best decisions today for better outcomes tomorrow.
5. Bayesian inference example – Should Mia seek a new job?
Science teaches us that people are notoriously inaccurate when it comes to changing jobs. [viii] Sometimes employees hold on too long and sometimes they jump too quickly. But, on average, people seem to hold on longer than they should.
"Success does not lie in sticking to things. It lies in picking the right thing to stick to and quitting the rest."
Annie Duke, author of Quit: The Power of Knowing When to Walk Away
Fear, uncertainty, and inertia are powerful forces. We may get emotional value and identity from our jobs - like our jobs are who we are. We worry that, if we jump, did we do the right thing? Because of the uncertainty, it is challenging to know for sure. That is why having a process to evaluate and recommend when it is time to consider changing our jobs is important. In the article, A Lifelong Approach to Job Decisions and Being the Best Version of You, a detailed approach is provided, including the app to assist you.
But for this example, we will focus on one aspect of the job decision process as an example of how to use Bayesian Inference to change your job.
Best Practice: As a best practice, the subparts should be evaluated independently of each other. Sometimes our priors are like an invisible weight on the posterior probability scale. Since judgment is involved in assigning the subpart probabilities, it is best to assign those weights with minimal interaction with the other subparts or a desired outcome. Being a good scientist means evaluating evidence without a preconceived outcome interfering with the evaluation.
Mia’s job change example:
Mia is 25. Growing up, she was taught to "Never give up," and "Winners never quit and Quitters never win." Based on her upbringing and initial job experience, she believes that hard work (“H”), performance (“P”) , and perseverance (“P”) will be rewarded with regular promotions and job security. We will call this the belief by its initials – “The HPP.” As discussed earlier, the HPP is from Mia's 'hot-kiln' impacted past that makes up her priors. This example demonstrates how Mia may update those priors.
She is early in her career and is working for her first firm. Recently, she learned a few of her co-workers got laid off. She has received excellent performance reviews but is concerned about the company. She is considering leaving but her prior beliefs are giving her the signal to stick to it. What should she do? What is the probability she should stay in her job and not seek to change?
First, let’s restate what Mia is trying to understand, in the context of Bayesian Inference.
What is the appropriate probability of Mia’s HPP belief about work, given (conditioned upon) the new evidence she received about her company and the layoffs?
Next, the posterior probability is disaggregated into its 3 core subparts – priors, likelihood, and new evidence.
Subpart 1, Priors: This is Mia’s best guess about how sure she was about her belief that her HPP would be rewarded. Her priors should be pretty high but with a little room for uncertainty. If this probability holds even after the new evidence, she would likely not look for a new job because she is mostly sure she will be rewarded where she is today.
Mia’s priors are set to an 85% probability.
Subpart 2, Likelihood: This is the likelihood that the new evidence concerning the layoffs is valid given her existing HPP beliefs. It turns out, this likelihood is low for Mia. This is because, while the chance of layoffs is very high - 100% - it is the layoff's relationship to Mia's existing beliefs that makes the overall likelihood low. Here is the explanation: A job change decision, like many personal decisions, is impacted by the degree to which Mia has control (another word for "agency") over the new evidence. It turns out that Mia's control regarding the company's layoffs is pretty low.
Mia needs to figure out if the people who got laid off were because they were not good or because the company was having business troubles. Stepping back, this is the likelihood that:
The new evidence is "in her control" - like her HPP or
The new evidence is "not in her control" - like the overall company or the condition of the general economy.
If people got laid off that were not good, this supports her HPP belief probability - I.e.: "in her control." If people got laid off because of some other reason, like the company’s economic performance, this does NOT support her belief probability - I.e.: "not in her control." At this point, Mia could raise her thumb, squint, and say "Given my low level of control over this situation, I'm going to set my likelihood below 50% - so I will set it at 40%." Alternatively, Mia could take a more precise approach as follows. Please notice that Mia gets to the same place.
After asking around and doing some back-of-the-envelope analysis, Mia determines the company is having economic trouble, and she "heard" the people who got fired were good workers. She is more certain about the company’s troubles. So, Mia places that weight at 70%. Since this is in the "Not in Mia's control" category, she takes the complement or 1-.7 = .3 or 30%. This is "Not in Mia's control" because a company laying off means one’s ability is not going to help as much if the company is struggling. She is less certain about the laid-off people's quality. This relates to the "In Mia's control" category. If one is hard working, performing, and persevering, then they will be most likely to be kept by a healthy company. Mia places that weight at 50%. She averaged the two to get the likelihood.
Mia sets the likelihood at 40%, which is the average between 30% and 50%.
Subpart 3, New evidence: The layoffs are happening, so this is set at 100%. If the layoffs were more of a concern than a reality, Mia would need to determine the chances of layoffs. Please note that since the new evidence probability is in the denominator, the lower the NE probability, the higher the posterior probability. They move in opposite directions.
When considering new evidence, it is essential to evaluate both the materiality of the evidence (size of the rock) and its relative power (color of the rock). It is possible one or both factors could be quite small. If the probability of the new evidence is small, then it is not worth considering for belief updating. Mathematically, a small denominator will not move the needle on the over all posterior probability. Save yourself some time by evaluating the new evidence to determine if it is worth your time.
Now let’s step through the math and make a recommendation:
We insert the 3 subparts – which are the priors, likelihood, and the new evidence. The updated probability is:
Thus, Mia’s original HPP belief would make her less likely to look for a new job. However, her belief has been updated and it has dropped from 85% to 34%.
Back to the big rock metaphor, Mia’s HPP belief change is significant. The overall belief that she should stay with the job has dropped below the 50% change threshold. There are now more red rocks than green rocks.
It certainly makes sense for Mia to test the job market and consider any other job criteria.
Admittedly, this is an extreme example. Very likely, Mia saw the signs of her company's troubles before the layoffs. Next, we simulate how to prepare for change as part of your regular job evaluation. Just like companies do performance reviews to judge you, you need a performance review process to judge your work environment. We will accomplish this pre-layoff simulation with a little sensitivity analysis.
What if Mia was considering a job change before the layoffs? So now, instead of the layoff probability [P(NE)] being 100%, it is only 50%. So, in this case, Mia's posterior probability is now 68%.
Sensitivity Analysis
This is certainly higher than the post-layoff posterior probability of 34% and the change threshold, but still well below the 85% priors. This means that even without layoffs, Mia's HPP belief is evolving. It still likely makes sense to test the job market. Mia can use the same job evaluation preference model she used for her current company to apply to other alternatives as she networks, interviews, etc. The good news is - once Mia routinizes her job evaluation decision process, applying it as a consistent, repeatable process becomes easier, faster, and more accurate. Mia's decision model, which measures the size and color of her evidence "rocks," will be her little decision concierge as she interviews and networks. With her model, she will quickly be able to compare new opportunities to each other and her existing job.
At this point, you may be thinking: "Hey, this makes sense. But I have more than one factor impacting my job decision. How do I use Bayesian Inference in this situation?" First, it makes perfect sense you have more than one factor impacting any decision. Most people do. Also, those factors are both objectively and judgmentally informed. Economists call these factors "preferences" that roll up to your overall "utility" for the benefit you receive. The simple answer is to use the app. It applies Bayesian Inference for our dynamic, diverse multiple criteria. [ix]
Another relevant question is: “Got it, but my job environment changes and is dynamic. I can see how Bayesian Inference works assuming things do not change, but they DO change. How do I handle my dynamic environment?” Great question! Most environments like our job are dynamic, interrelated, and change. Also, a chaotic, changing environment is often preceded by a longer, seductive period of calm - like the proverbial "calm before the storm." The idea is to use the app as part of a regular decision process. In the conclusion section, provided is a job change process article. The article shows how to prepare for change by creating a premortem. The point is that the more we emotionally prepare for change and use an effective decision process, the better we are able to quickly and confidently make those changes.
A third frequently asked question includes: “My current company is in fine shape, there is not economic trouble on the horizon that I know of. However, I am more of a climber. I want to accelerate my upward mobility - both in responsibility and compensation. How does Bayes help?!” This Bayesian framework works great. Understanding your current job plus other job alternatives in the context of your benefit preferences is essential. If there are other companies that better support your climbing and compensation preferences, then you should seriously consider them. That article suggested in the conclusion, plus the supporting smartphone tools will help you “get Bayesian” with your career climbing preferences.
6. Conclusion
A practical application of Bayesian Inference is demonstrated. It was shown that, with not much additional effort, one can use Bayesian Inference to accurately disaggregate the testing of an existing belief with new evidence. The essential point is that existing beliefs can and should be updated by using a transformational process that reduces your decision factors into discrete, analyzable subparts. By regularly evaluating our priors, we can minimize the impact of belief inertia and other cognitive biases inappropriately impacting our decision process. We achieve decision accuracy and conviction in our decision confidence by using a proven decision process. While the determinists suggest we have little control over our future, this Bayesian-inspired approach helps you to be successful no matter the impact of the many past influences on your life.
The future is your playing field!
Most people can conceptually grasp the incremental belief updating intuition of Bayesian Inference. Not everyone feels comfortable implementing the math in their day-to-day lives. The good news is the Definitive Choice app harnesses our judgment to help make those change decisions. For a job and career case, please see the article for an app-supported process to regularly update your beliefs in the service of knowing when it is time to find a new job.
Job change is only one of many examples for making practical use of Bayesian Inference. For more personal finance-related examples and app applications, see my book, Making Choices, Making Money: Your Guide to Making Confident Financial Decisions -- at jeffhulett.com.
Please follow the next link to the model used in this article.
7. Appendix: Do we have free will or is the world deterministic? It is time to ask a better question….
Much has been written about the question of free will v. determinism. This article suggests decision-making is critical to successful outcomes. Naturally, this suggests we have some free will to make different decisions. But do we? Even more importantly, are we asking the correct question?
Brian Klaas asks a thoughtful free will vs. determinism question. That is, “If you could rewind your life to the very beginning and press play, would everything turn out the same?” [x] This is like rewinding a tape where the past is a single tape but the future is potentially a choice of many tapes. Determinists, like Robert Sapolsky, believe we would end up on the same tape path and with the same outcome even if we rewound the tape to some point in the past. [iii] Our nature and nurture environment is so powerful that we have no choice but to go down the same path. In fact, determinists generally believe choice is an illusion, generated as a protective feature from our brains’ evolutionary biology.
Alternatively, free-will folks believe we can end up on different paths and with different outcomes based on the application of our free will. So to a free-will person, choice is real and we can impact our paths and outcomes. Our culture, especially Western culture, creates deep-seated expectations of personal responsibility originating from their free will. As an example, The American form of government is based on free will. The United States Declaration of Independence unambiguously states:
“We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.”
Think of these "unalienable rights" as choices generated from free will. For example, Americans may choose to speak, assemble, pray, report, and petition the government as per the First Amendment to the U.S. Constitution. Most importantly, within reason, Americans are free to choose how they express these unalienable rights. As an ironclad cultural doctrine, people are expected to make their own pursuit-of-happiness decisions. Free will is popularly considered one of the most precious rights we have in a free country. Many other countries have some form of free will integrated into their culture and constitutions.
For a deeper dive into free will, please see Solving the Decision-making Crisis: Making the most of our free will
Free will folks believe we can end up on different paths and with different outcomes based on the application of our free will. So to a free-will person, choice is real and we can impact our paths and outcomes.
The essence of the free will vs. determinism debate is this:
To evaluate the free will vs. determinism question, we must rewind the tape of our lives. Thus, the evaluation of free will vs. determinism is a backward-facing question. Whereas our choices, regardless of the degree to which free will and determinism impact us, require us to face forward. Choice requires us to make predictions about the uncertain future. They are somewhat related but entirely different questions. As discussed next, decision-making must consider information understood in the present to forecast the future. This difference in forward vs. backward time perspective means the question of free will vs. determinism is the wrong question.
Why the free will vs. determinism question is the wrong question.
“Life can only be understood backwards; but it must be lived forwards.”
― Søren Kierkegaard
Please consider the outcomes of our decisions as an information and uncertainty question at the point a decision is made. Today, those decision-makers have an incomplete set of information about the future. Thus, decision-makers must do their best to forecast based on their understanding of the benefits they desire from that decision. Our deterministic environment impacts the perceived benefits. Economists call the components of those benefits “preferences” and the aggregation of those preferences as one’s decision utility.
It is our assessment of our benefits or utility that has wild volatility. The essence of our wild volatility is what behavioral psychologists and behavioral economists call a “failure of invariance.” A failure of invariance is a term with a rich history. Nobel laureate Daniel Kahneman suggests a human failure of invariance is at the core of why individual rationality is both situationally and individually variant. [xi] So, not only will any two people have different perspectives on their rationality, but the same person will also vary in their definition of rationality across different but seemingly identical situations. A failure of invariance challenges the traditional concept of rationality as a single point. The new definition of rationality indicates that it is user-defined and based on varying situations and individuals. [xii] F.A. Hayek, the economist and Nobel Laureate, suggests the way people utilize knowledge is the most basic problem of a rational economic order. Hayek said: "It is a problem of the utilization of knowledge not given to anyone in its totality."
For a deeper dive: Please see the article How behavioral economics redefined rationality
It is acknowledged that our world has deterministic features based on physics such as Einstein’s famous Special Theory of Relativity equation -> E= MC^2 or Newton’s Second Law of Motion equation -> F=MxA, and many others. Also, our past nature and nurture environment has a massive influence on the availability of and the challenge to make certain decisions. Sapolsky does a great job describing those challenges.
However, and this is the essential point, how we experience the world, over time, is as if the world is indeterministic so long as the agents act with wild volatility. As an individual agent in the highly complex and information-incomplete world, the best that can be hoped for is that they make the best decision at the time the decision needs to be made.
As a thought experiment, let us say you could play back the tape to an exact moment in the past. Would we make the same decision and would the world turn out the same? Without any more information and with the same decision processes - a determinist would argue we would not make a different decision and the world would turn out the same.
At that point, the deterministic features of that world would have been identical. Let’s call our played-back world ‘Universe A.’ Now, what if we could clone Universe A? We call this cloned world Universe B. In both cases, Universe A and Universe B start at the same tape play-back point with identical deterministic features. In the next moment of our two cloned worlds, those worlds will diverge because of that wild volatility. This occurs because, in that next moment, Universe B will have small, randomly occurring differences from Universe A. Those small, random differences could be a butterfly that flapped its wings a little differently, that we woke up a little bit earlier as compared to the other universe, or that one more person in Universe A randomly decided to read this article.
In two different universes with the same starting point and deterministic features, uncertainty and wild volatility will cause Universe A to vary from Universe B at the next point in both those universes’ future. The differences between the universes may be small, but over time chaos theory tells us their differences will grow substantially. Those two universes are metaphors for different people and different situations of the same person as found with wild volatility. We can track back our current world to identify the past deterministic features that sculpted our current world. However, it is the beautiful, uncertain, and contingent current moment inclusive of deterministic features that leads into a future world where we must behave as if it is indeterministic.
So, the degree to which the world is deterministic or we have free will is the wrong question. I propose the correct question is -- How can people make the most of the present decision moment to make the best decision, given both their priors and their opportunities? In this case, we do not have perfect information and we need to make the best decision we can TODAY. Then, in the moments that follow, we will need to make varying decisions because wild volatility ensures those future moments include uncertainty. Part of this is recognition of what Buddhists call "emptiness." This is the idea that we are the sum of all those around us. Effectively, our existence is only a reflection of the world around us. We are an empty, ever-changing vessel crafted by our impermanent environment.
The Empty Spot - A Buddhist “Emptiness” Metaphor: Imagine all the people you know, and the different elements of your environment are pieces of a mosaic. The pieces start in a jar near an empty canvas. The canvas represents the entire scope of your life. All the things that make you "you" will be found somewhere on that canvas. Over time, those pieces get poured out of the jar, some will fall haphazardly and some will fall with purpose. All those pieces have one thing in common - they will all affect that canvas. But unlike paint, the pieces never dry to become fixed. Your life’s mosaic pieces change – some slowly and some more rapidly. The jumble of moving pieces of your life leaves an empty spot in the middle of the canvas. That empty, ever-changing spot is you.
This Buddhist approach is descriptive of wild volatility. That is, we cannot help but be impacted by the wild volatility of the world around us. Since all those around us are subject to wild volatility, then we must have a way to respond that makes the most of those fluid and dynamic situations. Our choices are our response to wild volatility and ultimately influence others and our own future.
To summarize, our choices:
Our choices are based upon an impermanent reflection of those around us -> Buddhism
Our choices can be made with a growth mindset to make the most of an indeterministically-perceived future -> Behavioral Psychology
Our choices can be made with appropriate judgments in the decision moment -> Stoicism
What I am calling “free will” is a function of the wild volatility that creates an environment behaving with what we perceive as indeterministic in the moments that follow. Our perception of free will empowers our choices in a world with deterministic features and wild volatility. If we perceive the world as fixed or pre-wired by determinism, we are less likely to own and energize those high-influence choices impacting our future.
Depending on where one falls on the free will vs. determinism question, our past path to the present may have been impacted by free will, determinism, or some combination of both. However, regardless of that past path source, it is the quality of the choices we make in the present that will impact our outcomes in the indeterministic future.
As such, individuals can greatly help themselves by improving their decision-making ability and by frequently updating beliefs as new information is realized.
Now, a strict determinist would say – “If you did improve your decision-making ability, it was because of a complex web of determinist physics, environmental factors, and behaviors that made this better decision moment inevitable. It was not an actual choice based on free will.”
My response is, “It does not matter the source of that choice to learn better decision-making. I am glad you read this article! Do your best to choose better decision-making processes. Plus, tell other people as well. Think of yourself as a pebble being dropped in the pond of good decisions. The more and bigger the pebbles then the bigger and more frequent the emanating waves of good decisions will occur.”
In the article, How to create your own opportunity: The garbage picker’s choice, a case study is provided to show how all people may access our choices to change our future.
N.N. Taleb does a nice job describing life’s inevitable volatility. Taleb said: “Some things benefit from shocks; they thrive and grow when exposed to volatility, randomness, disorder, and stressors and love adventure, risk, and uncertainty.” We can take advantage of that inevitable volatility via our relationships with things that benefit from volatility. In mathematics, those things are known as inputs to convex transformation functions. [xiii]
1) We can identify things that expose ourselves to those volatility-benefiting convex functions. The time value of money, maintaining long-term healthy behaviors, and intentional exposure to serendipity are examples of such convex functions. As an example, Taleb suggests one of his favorite pastimes is "flaneuring," which is his way of exposing himself to the convexity benefits of serendipity. Thus, flaneuring is an input to the serendipity convex transformation function. This is just like savings are an input to the time value of money convex transformation function and healthy habits are an input to our long-term health convex transformation function.
2) We can and should make choices that take advantage of inevitable upside volatility and protect us from the ruin associated with inevitable downside volatility. In the personal finance world, dollar cost averaging by consistently investing in well-diversified growth portfolios is an example of a convex function that takes advantage of upside volatility and protects us from the ruin associated with downside volatility. [xiv]
The idea of this graphic is that our choices matter. While we can completely control almost nothing, we can influence virtually everything. In a world of wild volatility, we can think of our decisions as a portfolio of many choices, with each one influencing the probabilistic outcome of those decisions. Physicist and ergodicity expert Luca Dellanna said [xv]:
"The best strategy depends on whether you are the gamble or the gambler"
The gamble vs. gambler metaphor applies to our day-to-day choices. A good decision-maker seeks exposure to the upside - such as frequent, relatively small investments in health or savings. This is a gambler's behavior. All the while, minimizing or insuring against catastrophic downside - by using strategies including diversified investments or high deductible medical insurance. This is a recognition of an individual gamble's downside. The little bell curve on each path indicates we do not know for sure how we will reach the next node. We may not know which of those good green or red outcomes we will achieve. However, by exposing ourselves to convex functions and a good decision process, we increase our confidence that the green or positive outcomes will increase over time, the red or negative outcomes will stay small, and the net sum of all those outcomes will increase in value over time.
Why the free will vs. determinism question is a good question. (but still leads us back to why it is the wrong question!)
Thus far, our focus has been on what economists call ”Positive Economics.” That is, assessing the world as it is. The answer to “Why the free will v determinism question is the right question” will now divert away from positive economics. We now explore the realm of policies for how we change the world if we do not like it as it is. Through laws, social programs, and other human interventions, we cross into the policy world of “Normative Economics” or “so, what do we do about it?”
Regardless of the degree to which free will and determinism impact our decisions in the present, the deterministic factors we mentioned earlier certainly exist. Strict determinists make a good point because people have no control over those deterministic factors. As such, how can people be held accountable if they have little ability or agency to impact those deterministic factors? For example, our genome, hormones, and neurobiology are almost completely a result of our parents and early childhood conditions. Adults cannot “rewind the tape” and undo those factors in the present. Next are a couple of examples:
Criminal Justice: This deterministic thinking could certainly impact criminal justice policy. Clear punishment guidelines may make sense to discourage people from choosing a criminal action. However, a determinist suggests the individual had little choice based on their priors, thus a regime of rehabilitation and training makes good sense. So, if we “lock ‘em up” without rehabilitation, we are only reinforcing the priors creating the criminal predisposition in the first place. When unrehabilitated criminals are released from prison, we should expect nothing else than recidivism.
Systemic bias in banking data: Deterministic thinking also impacts credit policy and how we think about assessing people’s credit. Traditionally, the FICO score assesses a credit applicant’s ability to repay a loan in the future. This is accomplished by evaluating the credit applicant’s past payment behavior. At its core, usage of the score assumes a one-way causality arrow. That one’s past payment behavior will affect one's future loan performance. However, the determinists argue, with good effect, that people’s past data and performance were CAUSED by a lack of opportunity and their priors. Thus, to the determinist, the causality arrow is reversed. One's lack of opportunity CAUSES poor payment behavior. The systemic bias in the data used for the FICO score is a result of using a subset of banking data only representing that lack of opportunity. A broader source of data, including data traditionally outside the banking system, like utility payments or rent payments, will create a more fulsome picture and help correct systemic bias found in the bank-only data.
These are relevant “so what do we do about it?” questions and suggestions. There are certainly many more. These are for policymakers to debate. Naturally, there are different perspectives, usually divided into political party camps and other organizations attempting to affect change. The implications of what to do about it are beyond the scope of this article.
However, circling back to the “Why the free will v determinism question is the wrong question,” this brings us to one observation upon which stoic philosophy would agree. That is: Focus on what you can control. In the dichotomy of control framework, those are our choices and judgments TODAY. Since most of us are not policy makers, we have little control over policy, other than our vote. This leaves us with practical success advice:
Focus on what we can control, like choices and judgments
To get the most out of those choices and judgments, develop and grow a high-quality decision process.
Resources
To put a finer point on an essential Stoic teaching → It is our judgments of something that often lead us astray, not the thing itself. So if something “bad” happens, we tend to assign “bad” to the thing. A grounded Stoic appreciates it is the judgment that relates to assigning “bad” not the thing itself. The thing is just a thing.
For example, if an investment goes down in value, we may consider the investment as “bad.” It may or not be. The point is that it is our judgment that assigns it as bad, not the investment itself. In fact, the stock market is incredibly volatile and subject to broad randomness. Most investment price changes can only be explained by randomness. So, our quick “bad” judgment of a downward-moving investment is often wrong. We need a decision process that helps us overcome our quick-to-judge nature by better managing our judgments. The point is that our judgments have value but only in the correct context. Choice architecture, like Definitive Choice, provides that structure to make the most of our judgments.
8. Notes
Please note that in the article Changing Our Mind, by the same author, a full set of citations covering many of the concepts of this article is provided. In many cases, those citations are not repeated in this article.
[i] The following graphic shows the HRU framework consistent with Rumsfeld's remarks:
Please see this article to implement the HRU in the context of data curation.
Hulett, Achieving the known – how to implement the best information curation framework, The Curiosity VIne, 2023
[ii] This is a broad subject area for economists. Next are sources for exploring the power of market economics in the context of human diversity:
Hulett, Our world in data, our reality in moments, The Curiosity Vine, 2023
Roberts, The Choice: A Fable of Free Trade and Protectionism, 2000
[iii] Sapolsky, Determined, 2023
[iv] Dweck, Mindset: The New Psychology of Success, 2006
[v-a] The Roman Stoic Epictetus introduces the dichotomy of control at the very beginning of his Enchiridion (Handbook). By the way, the book was written by one of Epictetus' students. They are notes from his class.
Epictetus, Enchiridion, 125 CE
To be fair - Free will deniers do not dispute that people make “high influence” choices and judgments. The difference between free willers is that determinists don't believe people have independent causal agency over the physical matter in our bodies and brains. Thus, decision-making is both deterministic and "internally caused," rather than caused by an independent top-down process from a separate consciousness.
Thanks to Brian Klaas for his input.
[v-b] Seth, Being You: A New Science of Consciousness, 2020
[vi] How to explore and best interpret our past reality is addressed in the article:
Hulett, Our world in data, our reality in moments, The Curiosity Vine, 2023
[vii] Tetlock, Gardner, Superforecasting: The Art and Science of Prediction, 2015
[viii] Levitt, Heads or Tails: The Impact of a Coin Toss on Major Life Decisions and Subsequent Happiness. National Bureau of Economic Research, WORKING PAPER 22487,
DOI 10.3386/w22487, 2016
Duke, Quit: The Power of Knowing When to Walk Away, 2022
[ix] The long answer for multicriteria weighting involves the Analytical Hierarchy Process or AHP. AHP was invented in the 1970s by Thomas Saaty at the University of Pittsburgh. It handles multicriteria probability weighting using an ingenious application of matrix algebra, eigenvectors, and eigenvalues.
Saaty, How to make a decision: The analytic hierarchy process, European Journal of Operational Research, Volume 48, Issue 1, Pages 9-26, 1990
For an example of AHP in action. Please see:
Hulett, How To Overcome The AI: Making the best decisions in our data-saturated world, The Curiosity Vine, 2023
[x] Klaas, Fluke: Chance, Chaos, and Why Everything We Do Matters, 2024
[xi] Kahneman, Thinking, Fast and Slow, 2011
[xii] Hulett, Becoming Behavioral Economics — How this growing social science is impacting the world, The Curiosity Vine, 2023
[xiii] Taleb, Antifragile: Things That Gain from Disorder, 2012
[xiv] Hulett, Achieve Personal Finance success with a little math intuition, The Curiosity Vine, 2023
[xv] Dellanna, Ergodicity: Definition, Examples, And Implications, As Simple As Possible, 2020
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