The Math on Why ‘Never Trump’ Never Had a Chance


With all the #NeverTrump hype on social media, my inner Nate Silver wanted to learn how likely it would be for Donald Trump to get the first ballot nomination at the upcoming RNC convention. Could Trump actually be ousted as the presumptive nominee? The math says no. Let’s explore how.

First, a little background.

GOP Rules Committee member Kendal Unruh planned to contest Donald Trump’s presumptive nomination at the RNC convention. Her ultimate plan rested on the notion that delegates are allowed to vote their conscience instead of being bound by state law or RNC rules.

In order to promote this idea, Unruh’s playbook is as follows:

  1. Conscience Clause play: Codify the notion that delegates are unbound by inserting a ‘Conscience Clause’ amendment to Rule 38 of the Republican National Convention rules.
  2. Brokered Convention-conscience play: Educate delegates that it is their right to vote their conscience based on hundreds of years of legal precedents.
  3. Brokered Convention-abstain play: Whip the delegation to abstain from voting.

Conscience Clause Play

In order for a conscience clause to be inserted, half of the 112 Rules Committee members would be needed to adopt the clause. If this failed (which it has), Unruh would need 28 signatures to file a minority report to push the vote to the entire delegation on the convention floor.

Free the Delegates Plan

Here’s the math on why it’s likely she’ll have trouble getting even 28 members to file a minority report.

Conscience Clause Parameters

  • 112 Rules Committee members made up of two chairs and two delegates from each state/territory
  • 57 Rules Committee members are needed to adopt or change a rule
  • If adoption fails, 28 Rules Committee members are needed to file a minority report to send vote to convention floor


  1. National polls reflect preferences for Rules Committee members in play
  2. All Rules Committee members will be present (whether they abstain or not)
  3. Elected RNC officials will vote pro-Trump
  4. Chair and co-chair may vote

Conscience Clause Analysis

Rules Committee Minority Report Waterfall

With 39 in play, you have to wonder how many Rules Committee members are willing to publicly vote against the will of the people. Unruh needs at least 72% willing to vote against the will of the people to garner 28 signatures: a highly unlikely proposition.


On July 14th 2016 evening, Rules Committee members voted to bind the delegates by 87-12 vote. Only 21 delegates voted to continue the debate for Unruh’s Conscience Clause amendment. Unruh still has until Monday to file a minority report. As we’ve learned from the math, garnering 28 signatures for a minority report, while not impossible, is highly unlikely.

A deeper dive could include developing a list of preferences that indicate propensity to vote against #NeverTrump via polling, mapping social networks, and of course Google.

Will the GOP Convention be contentious? Cartoonist Gary Varvel: 2016 GOP Convention

Brokered Convention Plays

A contested convention takes places when a candidate doesn’t emerge with over half (>1236) the delegate vote. By RNC party rules, Trump won 1543 delegates effectively clinching the nomination. If 306 of those delegates abstain or vote for someone other than Trump, the nomination could be contested on the first ballot leading to a brokered convention.

Assuming that binding delegates wasn’t codified last night, did Unruh ever have a chance of getting a brokered convention by getting delegates to vote their conscience? Not in the slightest and here’s why.

 Brokered Convention Parameters


  1. National polls reflect preferences for delegate members in play
  2. All delegates will be present (whether they abstain or not)
  3. Delegates can vote their conscience without fear

Brokered Convention Analysis

Trump needs at least 347 delegates out of the 902 in play to win the nomination on the first ballot. What are the chances that nearly a third of the available delegates will vote Trump? If 45% are satisfied with Trump, then the odds are pretty good. However, polls have been known to be wrong and do not necessarily reflect the preferences of the RNC delegation.

I wondered what ‘satisfaction with Trump’ threshold would be needed for a brokered convention to be probable. Accordingly, I plotted the expected value of a binomial distribution for at least 347 delegates against the likelihood that a delegate would vote for Trump. Here is the result.

NeverTrump Math

From this chart, we see that if the ‘satisfaction with Trump’ threshold (or likelihood that delegates would vote Trump) was at 35% then there is only a 1.62% probability that Trump would win the nomination on the first ballot. As long as at least 44.9% of delegates are satisfied with Trump, the possibility of a brokered convention is ZERO.

61.6% of the delegation would need to be dissatisfied with Trump for a brokered convention to even have a 50/50 shot. Noting that most members of the delegation fall within Trump’s core demographic, the idea that the #NeverTrump movement had any or will have any chance of getting a brokered convention is mathematically laughable.

Should Kendal Unruh have raised the issue despite the mathematical odds? — Absolutely.

UPDATE (7/20/2016 13:18): Bound votes accounted for 65.61% of the delegation. Delegate reported votes accounted for 62.62% of the delegation (76 delegate votes bound to Trump opted for someone else and 2 delegates bound to someone else switched their vote for Trump for a net difference of 74 delegates).

A Mathematical Solution to Choosing the Right Spouse?

I’ve always been a fan of how math and science can be applied to romance (see related articles here). So when a friend linked me to Krulwich’s article “How To Marry The Right Girl: A Mathematical Solution” on NPR, I was immediately intrigued. To summarize, Krulwich describes a dilemma in which Johannes Kepler is troubled with choosing the right wife among eleven potential mates. For the best decision-making process, Krulwich introduces ‘The Marriage Problem’ solution as explained by Alex Bellos.

The Rules

Here are the rules of the game. You have a finite number of choices. Each mate is evaluated sequentially one by one. Once you pass on a mate you cannot go back to that person. Once you’ve made an offer, the game ends. While this is a simple example of an optimal stop model, (i.e. it’s missing transaction costs for each evaluation), the results are interesting nonetheless.

The Strategy

The strategy that Krulwich highlights is relatively easy. Pass on the first 36.8% of potential mates. Next, when you meet a potential mate that’s better than ones in the first group, propose marriage. Note that you may run into a problem if the best potential mate was in the first group. Krulwich says if that happens you will at least get the second best pick (but that is untrue). Think about it, you will keep passing on people until you reach the nth potential mate in your queue. The nth mate may be riddled with character flaws or hideous (to you at least– everyone’s beautiful to someone, right?) Right. Anyhoo, what is true is you will indeed optimize your decision-making.

A Simulation

I decided to simulate the model for myself to determine the probability of outcomes. I ran the simulation for 1000 trials. The probability of landing at least an 8 hovers near 71.8% with a median score of 9.75 (see histogram above). Feel free to review or enhance my code here (myGithub).

A few caveats to my model (pardon any technical jargon): First, I used a random uniform distribution when in reality a lognormal curve would be a better fit. Thus I imagine a more precise estimated median will be closer to an 8. Second, I used the strategy described in the NPR article and didn’t go into the nuances for a complex optimal stop. The model also assumes attraction levels and other ranked traits stay constant (obviously not ideal assumptions). Finally, realize that this model illustrates optimal choice and not optimal outcome as there is a bit of game theory involved when you figure the preferences of whom you’ve chosen.


How about other applications to this model? Should you accept the first offer on your home? B-School? Job? Figure out the average amount of offers for your specified timescale and you’re on your way to optimized decision-making.


“Trust Me I’m a Doctor” – Are Doctors As Smart As You Think They Are?

Are doctors smart?

The odds to becoming a doctor are incredibly low. Let’s take a look at the credentials required to become one:

  1. You need a bachelor’s degree (only 479 million people or 6.7% of the world population have one)
  2. You believe you’ll do well on the MCAT (86,181 people took the MCAT in 2011)
  3. You believe your GPA and MCAT scores are competitive (45,266 people applied to U.S. medical schools in 2012)
  4. You are accepted into an M.D. program (only 19,517 matriculated into a U.S. program in 2012)

While the figures in the list above don’t tell the whole story (people who delay or decide against medical school or those who pursue alternative pathways to practice in the U.S.), they give you a general idea of the selectivity surrounding the profession. Given this tough selection process, it’s no wonder why so many people assume that doctors are really smart; it’s pretty likely that they are smarter than the average person.

But how smart are doctors really? Doctors can’t possibly know everything about everything. It’s unreasonable, for example, to quiz them on how to rebuild the engine on your Volkswagen Jetta. Yet so many people trust doctors with non-medical related advice all the time. Pretty much anything that is said can be qualified if it is coming from a doctor.

Camel Life

But you my friend think critically and realize how audacious it is to believe everything a doctor says. How critical should you be though, when it comes to your doctor’s medical advice? The majority of people, 70%, trust the accuracy of their doctor’s advice without the need for additional research or opinions. That figure is especially surprising when as much as 42% of the public report having experience with doctors making diagnostic errors. The error rate is so high that the International Journal of Healthcare Management is labeling misdiagnosis an epidemic. And rightfully so, 220,000 Americans die each year from preventable harm due to medical errors (with some estimates reaching 400,000).  To put that into context, doctors are killing 25 to 45 people every hour.

The fact of the matter is our knowledge of medicine and how we practice it is still fairly primitive. Doctors are human and humans are sometimes irrational decision makers who are prone to making mistakes. Adding to these limitations, there are few mechanisms to tackle issues that contribute to diagnostic errors. For one, the current culture at hospitals is to sweep mistakes under the rug, making it incredibly difficult to share and learn from them. Two, HIPAA regulations restrict access to medical records making it extremely difficult for the public to scrutinize. Three, very few hospitals will voluntarily publish or come forth with their error rates. The amalgamation of these problems, among others, leads to information asymmetry which leaves patients to either rely on geographic availability or word of mouth recommendations from friends, family, and insurance companies. This happens despite patients knowing what information should be most influential in their decision-making framework to choosing a healthcare provider.

While companies such as HealthGrades are hoping to solve the information asymmetry bit, current privacy regulations limit what they can do. Other attempts to eliminate the root causes of misdiagnosis are still challenging endeavors. To answer the question in the title, doctors are smart but not as smart (or competent) as you think they are. It is in your best interest to do your homework when you choose your doctor and vet his or her advice.

*For more reading, here is a behavioral economics approach to study potential root causes of medical errors by researching physician overconfidence and its influence on misdiagnosis drafted by my colleagues Rachelle Lee, Seungwook Moon, and myself Robin Kabir.


Speed-Watching: Download information straight to your brain (Matrix-style)


Remember the movie Matrix where Trinity instantly learned how to fly a helicopter by downloading the program straight to her brain? While we’re not there yet (see perceptual learning via neurofeedback), it is possible to learn things in half the time by listening to lectures at double speed. I call it speed-watching.

If you’ve ever taken a class on Coursera, you’ve likely noticed the +/- buttons that allow you to do this. If you feel overwhelmed by 2x speeds, watch a lecture at 2x for one minute and then reduce to 1.75x. Sooner or later your brain will adjust to faster speeds and you’ll be blazing through lectures in no time. In fact, 2x will even start to feel slow at times.

I also ‘speed-watch’ my news, recipe videos, and topics on Khan Academy. The only time I don’t speed-watch is if I’m listening to music videos or learning a language. To access this speed feature in YouTube, you will need to enable HTML5. Do it here:

Beyond saving time, speed-watching also keeps your mind engaged, thereby increasing comprehension. Lack of engagement is why many in classrooms let their minds wander, doodle, or catch up on email. Now that education can be customized to ‘your’ learning curve, what will education be like in the future?

If you can see the bigger picture, you recognize that we are at the verge of exciting times. 

For those interested in accelerated learning, here’s a link that compiles a few resources to help your endeavor:


The Behavioral Economics of Hospital Acquired Infections (HAI)


According to the CDC, hospital acquired infections (HAI) in the US is a $35 billion problem infecting 1.7 million while killing roughly 99,000 people each year. In other words, HAI kills more people than breast cancer and prostate cancer combined. The main culprit leading to incidences of HAI is doctors and other healthcare providers forgetting or refusing to wash their hands. The reason for these failures may be explained using behavioral economic notions prospect theory, mental accounting, and decoupling effects that lead to hyperbolic discounting.

Prospect Theory

First, consider that each time healthcare providers wash their hands a transaction cost is incurred. In essence, the current system is set to disaggregate losses and aggregate gains (which is not a happy combination). As a result, this system is not optimized to produce the intended effect of compliance. In addition, all things equal, the marginal benefit of each subsequent hand wash can be minimal or even negative. A snapshot of the hand-washing utility model below shows how utility is negative after the first hand-washing using anti-microbial soap that kills 99.9% of germs against a microbe that replicates itself every 15 minutes. Note: Putting more weight to costs (losses) may produce a more accurate graph.

Hand-washing Utility Model
X-axis: Number of hand-washings
Y-axis: Utility

Mental Accounting

Infection control at hospitals is a serious matter. According to the World Health Organization (2002), infection control protocols call for several preventative measures such as hand-hygiene, use of surgical drapes, cold temperatures in operating rooms, minimizing operating times and length of hospital stay, and the use of anti-microbial prophylaxes. It isn’t too difficult to imagine that physicians may bundle all infection control protocol costs into one mental account. If so, this phenomenon may explain why physicians may abstain from hand washing. Instead of paying the immediate costs1 related to hand-washing efforts, physicians may be balancing costs in the infection control account by thinking other measures such as prescribing prophylaxes will cover the costs. In the cases described, decisions are being made piecemeal and are topical suggesting the use of a mental account.

Hyperbolic Discounting

            Moreover, the effects of not washing your hands are not as immediate as, say, the effect of ‘forgetting’2 to use anesthesia. Thus, not washing hands becomes decoupled from the costs of future outbreaks. In turn, this effect reduces the salience of the outcome. Likewise, the perception of future benefits from washing hands is also minimized due to hyperbolic discounting.

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