Mother Tigress’s Decision Choice: Navigating Stochastic Decision Making Under Risk and Uncertainty

Introduction

Tigers, as powerful territorial animals, are extremely dangerous to humans coming between her and her cubs. In the wild, a mother tigress confronts a multitude of decisions that directly impact her own survival and that of her vulnerable offspring. These choices unfold in an environment fraught with risk and uncertainty, where outcomes remain far from guaranteed.

Allow me to share a remarkable story to show how we can use a structured decision-making approach combining both intuition and available data to solve seemingly unstructured problems. A mother tigress found herself in a desperate situation when her cubs accidentally fell into a deep well. Remarkably, they managed to cling to a rock within the well. The tigress, driven by maternal instinct, sought help from an unlikely source—humans.

Now, the accuracy of this tale remains uncertain, but it serves as a good illustration of how even animals exhibit intelligent yet counterintuitive behavior when faced with extreme circumstances. In this article, I am discussing the details of the tigress’s behavior, analyzing her decisions within the framework of stochastic decision-making.

The narrative unfolds near an active Indian military camp, where the tigress inexplicably appeared. Despite the frequent gunshot sounds echoing through the camp, she approached without posing any threat. The camp commandant grappled with curiosity: Why would she risk her life by venturing so close to a military outpost?

Initially, the commandant’s instinct was to order the animal’s execution, safeguarding his team from potential danger. However, he reached out to a zoologist friend for insight. After days of careful observation, the zoologist determined that the tigress was attempting to communicate something urgent. With this revelation, he decided to follow her, accompanied by a small group of soldiers.

The tigress led them away from the base, into the forest. Eventually she approached and paused near a rock before moving away and giving space for the soldiers to approach. When they finally reached the rock, they discovered a deep well. They couldn’t believe their eyes when they saw the three tiny tiger cubs perched on a rock in the well, their lives hanging in the balance. The soldiers retrieved the tiger cubs from the well. From a safe distance, they witnessed the heartwarming reunion as the cubs rejoined their watchful mother.

This extraordinary encounter underscores the complexity of decision-making, even in the animal kingdom. Next, we’ll explore the tigress’s calculated choices, navigating risk and uncertainty in her quest to protect her cubs.

The Tigress’s Dilemma

As the tigress sat on top of the deep well, she probably realized that her cubs are going to die without help.? If she were to leap into the well, she understood that her own fate would be sealed alongside theirs.?? Probably, out of gut instinct she walked around looking for help.

In an extraordinary turn of events, the tigress found an unlikely ally—the soldiers stationed nearby. Her decision, guided by gut feeling rather than rational calculation, resulted in the best possible outcome. This outcome was nothing short of miraculous: her cubs were saved. However, this choice, while heroic, might not be the norm for most tigresses.

Now, let us delve into the tigress’s decision-making process through the lens of stochastic decision-making. This framework allows us to explore how such insights can inform strategic decision-making in various contexts.

Understanding Stochastic Decision Making

Stochastic decision making involves navigating choices when outcomes are influenced by chance or randomness. Here are some key concepts to consider:

1. Risk vs. Uncertainty: Risk?pertains to situations where all potential outcomes and their probabilities are known. Uncertainty?arises when outcomes and/or their probabilities remain shrouded in mystery.

Using the stochastic decision-making framework, we construct a decision tree—a visual representation of potential choices, their associated outcomes, and the value (utility) assigned to each outcome. Utility is measured on a scale from 0% (the worst outcome, where both mother and cubs perish) to 100% (the best outcome, where both survive). While estimating precise probabilities can be challenging, we focus on the most relevant options. For instance, consider the scenario where the tigress leaps into the well to rescue her cubs. In our simplified tree, we assign a 100% probability of death for both tigress and cubs. However, in reality villagers or forest officers could intervene and alter the course of events.

Fig 1: Tigress’s Stochastic Decision Tree

Using Expected Utility to Make Optimal Decisions

In the image provided,?option 2?stands out as the best choice, boasting a total expected utility of?20%, followed by?option 3?with an expected utility of?15%. Now, let’s delve into how expected utility aids us in making informed decisions.

Understanding Expected Utility

When we flip a coin, there’s a?50% chance?of getting heads and a?50% chance?of getting tails. However, this doesn’t imply that if the first toss results in heads, the next will necessarily be tails. Instead, it means that over a large number of repetitions, the proportion of heads and tails will converge toward the expected 50%.

For organizations to consistently make successful decisions, they must adopt a culture of decision-making grounded in a?scientific framework. This ensures that, on average, decisions yield favorable outcomes, as indicated by their expected values.

Applying Expected Utility: An Example

Let’s consider the scenario outlined above. We have three options:

1. Option 1: Jump into the well - outcome “Mother and Cubs will Die.”
2. Option 2: Seek help - two outcomes 2a and 2b broken down below.
3. Option 3: Abandon the cubs - outcome “Cubs die, but the mother survives.”

Now, let’s break down the expected utilities for each option:

1. Option 1: Jump into the well. I assumed a?0% utility?for the outcome of “Mother and Cubs will Die.” Assuming?100% probability?for this outcome, choosing option 1 results in an expected utility of?0%.
2. Option 3: Abandon the cubs. Assigned 15% utility?since the cubs die, though the mother survives. Assuming?100% probability, option 3’s expected utility is?15%.
3. Option 2: This option has two possible outcomes: Outcome 2a: Mom is executed, so mom and cubs die (utility:?0%). Assuming 80% probability for this outcome, expected utility is 0%. Outcome 2b: Cubs are rescued so everyone survives (utility:?100%). With 100-80=?20% probability, expected utility is?20%?* 100% = 20%.

Combining the utilities for option 2 (0% + 20%), we arrive at a total utility of?20%, making it the winning choice. It’s important to note that the specific values assigned to probabilities and utilities significantly impact the outcome.

In summary, the value of this exercise lies in systematically evaluating options based on their expected utilities, leading to more informed and optimal decisions.

Value of the Approach Amid Uncertainties

In our decision-making process, we’ve assigned probabilities and utilities to various outcomes. While some aspects are universally agreeable, others remain subject to interpretation. Let’s explore this further:

1.??? Option 1: The probability and utility assigned to this option are generally accepted. However, for?outcome 2a, where the tigress approaches the military camp, the?probability (P)?of just 80%?for execution by the soldiers might raise questions. Nevertheless, most people concur that the utility of?0%?for the tigress if executed is reasonable. Interestingly, regardless of the specific value of?P, the expected utility for outcome 2a remains?0%.

2.??? Our final decision hinges on the values associated with?outcome 2b?for option 2 and?option 3. Here’s where we stand:

1. Outcome 2b: If soldiers intervene and save the cubs, both the mother and cubs survive. We assign a?probability (P)?of around?20%?and a?utility of 100% for this being the best outcome. The expected utility for outcome 2b is?20% * 100% = 20%. This makes probability the key variable for 2b.
2. Option 3: The cubs will die, but the mother will survive. We assume a?probability (P)?close to?100%?and a?utility of 15%. Hence, the expected utility for option 3 is?15%, making utility the key variable for option 3.

3.??? Challenges and Subjectivity: Critics may question the validity of this approach, especially when our recommended decision relies on two values that can be arbitrarily assigned. For instance:

1. If we set?P?to approximately?10%?for outcome 2b while maintaining a?15% utility?for option 3, suddenly?option 3?becomes the optimal choice.

4.??? The True Value: The strength of this approach lies in understanding the driving factors behind decisions and identifying limiting values. In our example, the utility assigned to?option 3?is inherently personal. The tigress, driven by maternal instincts, might deem any decision leading to her cubs’ demise as?unacceptable, assigning it a utility of?0%. Consequently, even if the tigress perceives a tiny probability for soldiers to save her cubs in outcome 2b, the expected utility for?option 3?being?0%, makes it less favorable than the expected value of?2b.

In summary, while uncertainties persist, this method allows us to dissect decisions, recognize critical variables, and navigate the delicate balance between probabilities and utilities.

Corporate Leadership’s Reliance on Intuition

In a thought-provoking 2022 LinkedIn article titled “Do The Best Leaders Rely On Their Intuition?”, Jayce Grayye highlighted the following quote:

“Bill Gates has been spotted saying that there are quite a lot of times when one has to rely on intuition.”

Jayce emphasizes that not everyone possesses complete information at all times. Consequently, many of the most effective leaders lean on their intuition to navigate complex decisions.

The Ever-Evolving Thoughts about Using Intuition for Decision Making

Let’s explore these viewpoints:

1. A?2003 Harvard Business Review article? cautioned against relying solely on intuition in high-stakes decision-making3.
2. A 2015 Harvard Business Review article shared thoughts about when it’s safe to rely on intuition (and when it’s not) 4.
3. Nolen reported that according to a 2016 KPMG study, only?one-third?of the?2,200 CEOs surveyed?fully trusted their data and resulting analytics2.
4. A 2023 Harvard Business Review article argued in favor of using both data and intuitions for making good decisions4.

Defining Intuition

Informed by insights from neuroscientists, let’s explore the concept of intuition:

What Is Intuition?

Intuition?emerges as the productive utilization of?unconscious information?to enhance decision-making and guide actions. Dr. Joel Pearson, a neuroscientist and founder of the?Future Minds Lab?at the University of New South Wales, describes it as follows:

“We can feel information even though it’s unconscious, and people often describe these feelings in their gut, stomachs, or back of the throat.”

Our brains process an?immense volume of data daily, yet our conscious awareness only grazes the tip of the iceberg. Beneath the surface lies a vast network of associations—information we often overlook as we navigate our lives.

The Hidden Associations

Despite our lack of conscious awareness, these associations persist. When you experience a hunch or gut feeling, it may stem from connections your brain has quietly forged. These intuitive nudges draw upon a wealth of accumulated knowledge, even if we can’t explicitly pinpoint their origins.

Practical Applications

Consider situations where intuition plays a crucial role:

• Tigress and Soldiers: In complex scenarios, like the tigress approaching soldiers, intuition guides decisions that defy explicit reasoning. Communication challenges, potential danger, and minuscule success probabilities often lead people away from such options.
• Supply Chain Safety Stock: Even in business, intuition influences choices. For instance, estimating probabilities (such as service levels) in supply chain safety stock calculations involves uncertain values like goodwill and future salvage value.

In summary, intuition bridges the gap between conscious and unconscious realms, allowing us to harness hidden wisdom for better decisions.? However, it is likely to be driven by the decision makers unconscious personal experiences.?

Conclusion

In contemplating the tigress’s hypothetical decision-making process, we uncover valuable lessons applicable to our own lives, particularly in intricate and uncertain scenarios. While intuition remains a trusted ally for many leaders, it’s essential to recognize its limitations:

1.??? Intuition’s Role: Leaders often rely on intuition when faced with decisions where quantitative data is scarce. Our unconscious minds draw upon past experiences, shaping our intuitive responses. However, intuition alone does not guarantee success.

2.??? The Multifaceted Approach: The framework discussed earlier provides a more robust decision-making process. By dissecting each variable’s impact, we gain clarity and make informed choices.

In the dynamic interplay between intuition and data-driven analysis, leaders navigate uncharted waters. As we forge ahead, let’s embrace both our gut feelings and empirical evidence, striving for optimal outcomes.

References:

1. Grayye, J. (2022). Do The Best Leaders Rely On Their Intuition?
2. Nolen, M. C. (2016). New Research Says CEOs Should Follow Their Intuition
3. Harvard Business Review. (2003). Don’t Trust Your Gut
4. Harvard Business Review. (2015). When It’s Safe to Rely on Intuition (and When It’s Not)
5. Harvard Business Review. (2023). Data and Intuition: Good Decisions Need Both