THINKING PROBABILISTICALLY FOR PERSONAL DECISIONS
Thornton Bradshaw Professor of Public Policy, Decision Science, and Management
Harvard Kennedy School
"If you go to Martha Stewart’s web page for wedding planning (something I am not advising you do), she asks rhetorically, “Wouldn’t it be great if wedding planning were an exact science?” Unfortunately, the rhetorical question is just a teaser. According to Ms. Stewart’s website, “When it comes to predicting how many guests will attend a wedding, it’s nearly impossible to accurately estimate what percentage of the overall guest list will affirmatively respond to your invite.”[i]
When my (now) husband Brian and I were planning our wedding back in June 1998, my mother held the same view. Unless an invited guest specifically had a reason for not attending, and told us so, my mom believed that every person on the list would attend and we had to plan accordingly.
Enter conflict: My husband and I did not share this view. We wanted to plan probabilistically. We researched average attendance rates based on how far people had to travel and plugged those rates into our algorithm for attendance. My mom was horrified. It seemed to her like a cold-hearted exercise to anticipate that some people would not attend our wedding, even if they hadn’t specifically told us so. And in my Jewish and Italian family where feeding people is a cherished, sacred event, the idea of not having an excess of food, let alone enough dinners for every single person invited, triggered more than mild disagreement.
Rather than argue it out, my husband and I (poor doctoral students at the time who needed to save every penny) decided to keep our probabilistic estimates to ourselves. Only the two of us and the caterer knew that we expected some invitees would not attend. I’m happy to report that it was a wonderful wedding. Some invited guests were not able to attend at the last minute and we had not overpaid."
[i] Alyssa Brown, “There’s No Lucky Percentage of Guests Who Will Attend a Wedding.” July 03, 2018. https://www.marthastewart.com/7923646/ percentage-how-many-guests-attend-wedding.
Founder, Dobility Inc.
"I left Richard’s course with an essentially different view of the world, one that is fundamentally more accurate and powerful, and this idea of viewing the world probabilistically is at the heart of it. Just as Morpheus helped Neo in The Matrix, Richard helped me to see a deeper reality, one in which uncertainty and probability distributions are behind everything that happens. None of us ever fully control outcomes – even our own thoughts and behavior! – but we act to influence probability distributions as best we can. Philosophically, I may view the world as deterministic, but in practice I have to accept that I am far from omniscient and even farther from omnipotent. Accepting that everything is effectively uncertain and that my thoughts, hopes, and actions can at best indirectly influence the world by influencing probability distributions: this has brought me a kind of peace through acceptance, and a greater mastery over the world around me.
What can I do to control an outcome? That’s the wrong question. What can I do to influence the odds? Now that’s productive. That I can work with – in my life and in my job."
HETEROGENEITY IN COVID TRANSMISSION
LEE HSIEN LOONG
Prime Minister of Singapore
“The COVID-19 pandemic offers two vivid examples of the importance of understanding heterogeneity. Countries and cities are tracking their R0, the reproduction rate of the virus, and the death rate. These global parameters gloss over important heterogeneity in the population.
Singapore started having COVID-19 cases in January 2020. As the outbreak continued, our R0 stayed well below 1. We took some comfort in this, and attributed it to assiduous contact tracing. But we were also acutely aware that this was a global figure for Singapore, and that the R0 could be much higher in specific settings if the virus spread there. And so it turned out. We have 300,000 migrant workers living in communal dormitories, where the transmission potential is high. A few undetected cases there snowballed into a major outbreak. The R0 in the dormitories was estimated to be between 2 and 3.
However, another heterogeneity has kept our death rates very low. As of the time of writing, our fatality rate is around 0.05 percent, 34 deaths out of about 60,000 COVID-19 cases so far. This may be because many of our cases were migrant workers, who are younger and healthier than our general population. The vast majority have had mild or no symptoms, and only a handful needed ICU care. A similar sized outbreak among our elderly population or nursing homes in those early days would have been quite a different story. Fortunately, now that we have vaccines, we have prioritized the vaccination of the elderly and vulnerable, which has hopefully reduced this risk.”
POSITIVE COMPLEMENTARITIES IN MARRIAGE
PhD student in Public Policy at the Harvard Kennedy School
“I took Richard’s class when I was about a year into a relationship with the person who would become my wife. My wife and I are extremely different in many ways: she likes to make decisions immediately, I like to collect more information and spend time pondering; she loves meat, I am a vegetarian; she is from the U.S., I am from the UK.
Initially these differences caused a fairly large amount of difficulty, but when I learned from Richard that cross-partial derivatives are important I realized I needed to think about our differences as complementarities. When hosting a dinner party, it’s fantastic to have someone who can cook a delicious meat dish and another person who can make vegetables shine: the dinner party is much better than it would be if you had two people who could only cook meat. Similarly, it’s good to have someone to make the quick decisions for decisions where that’s suitable, and someone who can tap the brakes and make sure the important decisions have been properly analyzed.
For me, the essence of cross-partial derivatives is that despite the cost of trans-Atlantic flights, marrying someone quite different from you can be an excellent choice."
WHEN TRYING TO UNDERSTAND A COMPLEX REAL-WORLD SITUATION, THINK OF AN EVERYDAY ANALOGUE
Adjunct Lecturer in Public Policy at Harvard Kennedy School
Vice President at Analysis Group, Inc.
“In my work as a consultant and a statistics instructor, I find it valuable to illustrate complex statistical problems using the familiar example of political polling, which many people (at least in my social and professional circles) know well. For example, when trying to convey the concept of sampling error, say when sampling mortgages to evaluate the performance of mortgage-backed securities, I’ll analogize to the inherent uncertainties when polling for an upcoming presidential race.”
GOOD DECISIONS SOMETIMES HAVE POOR OUTCOMES
A. J. Meyer Professor of Energy and Economic Development
Harvard Kennedy School
“One of my greatest frustrations when reading the newspaper is when someone explicitly or implicitly judges the quality of a decision on the basis of its outcomes, rather than judging the quality of the decision in the context of information that was available at the time. A related pet peeve is when politicians and others claim that an improved economy, or decreased pollutant emissions, or some other raw change, is evidence of a policy success. The comparison that ought to be made is not how things have changed from time A to time B, but rather how things are at time B, compared with how they would have been without the policy.”
GOOD DECISION, BAD OUTCOME
Albert J. Weatherhead III and Richard W. Weatherhead Professor of Public Management
Harvard Kennedy School
“What bad things can happen if we don't realize that good decisions can have bad outcomes? From an individual point of view, not understanding this maxim produces inappropriate blaming of ourselves -- or others – for situations where we were just unlucky. And people waste time diagnosing "what went wrong" when nothing went wrong, luck was just bad. Also, concerns about regret one will feel if things turn out badly lead many simply to stick with the status quo, meaning we lose the benefits of gaining from change. Understanding that good decisions can produce bad outcomes will thus improve the average quality of our decisions.” To read more by Steven Kelman, please visit his blog post here.