This was the second consecutive day I was running late for office and while driving, I also noticed that my car was low on gas (petrol). I had enough gas to take me to the office and perhaps few more miles to drive to the nearest gas station (petrol bunk) for a refill. With the morning rush hour and many cars behind me at an intersection, I had to decide within a few seconds if I should go left and head to the office or go right and head to the gas station first for a refill before going to the office.

This happened to me last week and I made a decision (let’s keep my decision in suspense for a while). Later I started to examine why I made that decision, what were the reasons considered and given the circumstances, I wanted to know if I made the right decision. Obviously this is a trivial matter but in examining such a simple and binary decision, my intention was to refresh my understanding of the process, theory and models of ‘Decision-Making’.

Most of our daily decisions are driven by past experience, emotion, intuition, or made for us by somebody else (manager, subject matter expert, friends, parents, etc.). Few years back there was a trend in the management community to rely on intuition to make decisions and the book by Malcolm Gladwell – Blink: The Power of Thinking Without Thinking further reinforced that practice. It always intrigued me to think about corporate fates being decided by the intuition of few top-level decision makers. Agreed there is no perfect information and the decision makers have opinions and hypothesis as the starting point, nonetheless, any decision that does not involve some mindful effort seems just random and hence intuition driven decision-making feels counter-intuitive to me. My attempt here is to explore repeatable decision-making models that can be improved over time.

Barry Schwartz in his book The Paradox of Choice writes that a good decision-making process involves the following steps –

• Figure out your goal or goals
• Evaluate the importance of each goal
• Array the options
• Evaluate how likely each of the options is to meet your goals
• Pick the winning option
• As a consequence of your decision, modify goals

There are many other decision-making processes that define the process a bit differently but essentially, it boils down to three steps – if you are hungry and feel like eating Indian food, you go over to your favorite restaurant, look through the menu and order say palak paneer with roti. You have just gone through the three major steps in decision-making –

1. Need – Circumstances have arisen that necessitate decision-making (you are hungry)
2. Options – You lay out a bunch of alternatives (look through the menu)
3. Decision – Choose the best option that suits your need (order palak paneer with roti)

All of this seems quite natural and you may say we do not consciously think of these academic processes in making everyday decisions. However, in reading through decision-making literature it struck me that many of us miss out on the ‘Options’ part. When confronted with a problem, how many times have we asked “what are our options?”. Many times I am guilty of just choosing among what was available in front of me or opting for what worked earlier. We rarely pause to create and evaluate a set of options for the given situation.

Every major disciple such as Psychology, Management, Mathematics, Statistics, etc. have their own models for decision-making. Today I will attempt to apply a simple mathematical decision-making model in examining the situation we started off with. Let us capture the details –

• Running late for the office and the car is low on gas.
• Have enough gas to reach office but will need to refill on the way back home.
• Have to decide between Option 1. going to the office or Option 2. going to the gas station first.

Below are some more facts –

• If I choose to head to the office, I’ll be ‘On-Time’ and would feel good about myself.
• If I head to the gas station first, I’ll be 30 minutes late for the office. Other than feeling terrible about myself and having a low self-image for the rest of the day, there are no other dependencies (i.e. no meetings or anyone waiting for me during the 30 minutes delay).
• If for one in a million reason the gas station near my office is shut down, within a few miles I would be completely out of gas and cannot reach home.

Let’s capture this information within a Utility Table (a.k.a payoff matrix) and assign utility values.

Utility Value – is simply a number on a numerical scale that measures how much the decision maker values the outcome (it can be in terms of dollars, time, units, etc.).

	Self-Image Perception	Comfort from Gas Refill
Option 1 – Go to Office	8	3
Option 2 – Go to Gas Station	4	6

Across the top are attributes that I care about i.e. feeling good about myself (Self-Image Perception) and feeling of comfort from filling-up the gas tank and not worry about running out of gas (Comfort from Gas Refill).

Along the sides are the two available options.

The table cells contain utility value for each combination of option and attribute. All it means is for Option 1, I value showing up on-time and having a good self-image (8 units of utility) as compared to worrying a little about getting my tank filled up on the way back home (3 units of utility). Similarly for Option 2, since there is no immediate and known benefit from going to the gas station now vs. later in the day, I rate it relatively low on my utility-scale (6 units of utility). Going to the gas station and being late for office has adverse impact on my self-image hence lower rating (4 units of utility).

Now that we have captured everything we need to make the decision, lets analyze the data using different criteria –

Admissibility –  

“Eliminating inadmissible alternatives, those that have inferior utility value on a case-by-case basis when compared with another option”

As you can clearly see from the utility table above, for ‘Self-Image Perception’ attribute, Option 1 is superior evidenced by higher utility value (i.e. 8 vs. 4 ). For “Comfort from Gas Refill” attribute, Option 2 is a better choice (i.e. 6 vs. 3). There is no one option that is inferior to the other across the board and hence we cannot make decision using the Admissibility criterion without making compromises.

MaxiMax –

“Choosing the alternative that yields the largest possible payoff. This decision is either optimistic or desperate.”

If I am interested in maximizing the maximum benefit in the short-term and ignoring all other facts, perhaps I would value having a good self-image high on the scale. Accordingly Option 1 would be the winner.

MiniMax –

“Choosing the alternative that minimizes the maximum risk. This decision is cautious, conservative and pessimistic.”

Now the critical question to consider is what is the risk in this situation? Having a bad self-image or running out of gas? In the given situation, I would consider running out of gas as the bigger risk. I have had few bad experiences in the past from running out of gas and that is more ‘real’ risk to me than any self-image ‘perception’ issues. According to this criterion I would choose Option 2 and go to the gas station.

So to break the suspense, what did I actually do?

I took a right turn and went to the gas station. The thought that drove me to make that decision was similar to the MiniMax criterion. I thought about some unforeseen emergency/urgency that might require me to commute and I realized that having no gas in my car would completely handicap me and I would be ill-prepared for any such contingencies. Hence I opted to go to the gas station first before going to the office… in the flash of the moment, I just followed the old proverb “a stitch in time saves nine”.

You decide and save the World!

Here is another situation for you to apply the learning. This example is taken from one of my favorite books by James Stein and the models above are based off of this book – The Right Decision: A Mathematician Reveals How the Secrets of Decision Theory.

The U.S. government has just handed you, General Leslie Groves, the biggest blank check in history and with it a mission: to build the first atomic bomb. You’re going to have to find a physicist to be your second-in-command because only physicists can build an atomic bomb (if it can be built at all), and a general is about as popular with physicists as a fox at a chicken convention. However, you’ve finally narrowed your choice to three possibilities, and you’ve even pinned nicknames on them:

A. Slim: a chain smoker who could charm the birds out of the trees. Everybody in the physics community loves him, but can you trust him? The FBI thinks he might have Communist affiliations.

B. Sarge: a monomaniacal anti-Nazi who could probably lead a platoon of raw recruits to take an enemy machine-gun nest. An émigré from Hungary, even those who dislike him admire him.

C. Doc: winner of a Nobel Prize, he may be the brightest of the lot. A brilliant theorist and technician, he has only recently arrived from Italy, and he’s something of an unknown.

Nobody wants to think about the horrifying possibility that the Germans will get there first, so it is quite possible that Western civilization could be riding on your decision. Should you choose – A. Slim? B. Sarge? or C. Doc?

Feel free to leave your answers in the comments below and I will respond back.