Trump, Modi as Brand Archetypes: Can we predict their next moves for their nations?

At the recently held Cambridge Union debate on conflicts, American economist, Public Policy analyst, and Professor, Jeffrey Sachs spoke about present-day geopolitics and geo-economics through the prism of Merill Flood, Melvin Dresher, and Albert W. Tucker's 'Prisoner's Dilemma' and Friedman's 'Folk Theorem'. He specifically focused on the US's tumultuous relationships with Russia and China. And, with the return of President-elect Donald Trump, these dynamics are expected to become more interesting, if not entirely unpredictable!

For the uninitiated, the Prisoner's Dilemma is a very interesting page from game theory that delves into the costs and benefits of any two individuals in a situation/event where they have to choose between acting selfishly or selflessly. This theory is a metaphor for how self-interest can damage the pursuit of the common good. Folk Theorem, on the other hand, postulates that when the same two individuals (as stated in the Prisoner's Dilemma) participate in repeated situations/events and choose to be patient and far-sighted, they drive stable, less damaging outcomes, based on the prospect of future interactions. Over time, a Nash equilibrium could be achieved if each individual chose the best strategy based on the other's actions, with no individual having any incentive to change their approach.

In this write-up, I am going to explore the idea and theory of predicting relationship outcomes (relationship being some function of multivariate factors across defense, trade among others) between the US (constant) and key nations (variable). For brevity, I will focus my demonstration on the US and India!

However, before I begin, we need to understand that while the two 'individuals' in question are nations, they are led by leaders who influence situations beyond the strategic operating spaces provided by their think tanks during negotiations. People leading nations are supreme commanders with executive powers who often bring their personalities and egos to bear on outcomes. Ergo, we will outline/plot the leader personalities on a measurable framework before we can war-game situations.

Brand Archetypes are a good starting point. The Brand Archetype Wheel is a derivative of Carl Jung's personality wheel that allows us to plot individuals on a 360-degree character spectrum.

Whether brands or people, usage of the Jungian Archetype Wheel has largely been a qualitative exercise. Quant-plotting, based on coordinates, rarely follows qualitative approximation! And while that is not an issue, it does not augur well for building predictive models, further downstream. Therefore, what if we turned Jung's Archetype Wheel into a mathematical framework where we could plot, say, President-elect, Donald Trump and India's Prime Minister, Modi, followed by using both the Prisoner's Dilemma and the Folk Theorem as confusion matrices of arrays 2*2?

Specifically, I'd like to introduce a 'personality distance' between any two leaders, mapped on the Jung wheel. But before that, in analyzing U.S.-India relations through the archetypes of President Trump and Prime Minister Modi, let us place them on Jung's archetype wheel based on their leadership styles, motivations, and public personas.

In the absence of any survey data, I will place President-elect Trump and PM Modi on the wheel in the following manner:

President-elect Trump: Archetype: Outlaw (Yellow segment)

• Traits: Trump’s leadership aligns with the "rebel" or "revolutionary" elements, focusing on challenging established norms and pushing "America First/America Great" policies. His approach to international relationships is transactional and unpredictable, often aiming to disrupt traditional alliances or arrangements if they don’t align with U.S. interests.

Prime Minister Modi: Archetype: Ruler and Caregiver (Blue segment)

• Traits: Modi often emphasizes India’s rise as a structured, responsible global power. His vision aligns with the “leader” and “politician” sub-archetypes, emphasizing structure, order, and national pride. Modi also carries a “Caregiver” persona, promoting policies to uplift India’s socioeconomic status.

However, on what multi-variate factors would we base these positions? Possible and measurable factors could include...

• Power Quotient: Measures influence, authority, and dominance (high for “Ruler,” low for “Innocent”).
• Risk Threshold: Indicating willingness to take risks (high for “Outlaw,” low for “Caregiver”).
• Innovation: Measures openness to new ideas (high for “Creator,” low for “Traditionalist”).
• Empathy Quotient: Assesses compassion and concern for others (high for “Caregiver,” low for “Jester”).

All factors above could be Likert Scale columns, based on historical actions, policies, and public speeches (This could be done through a sentiment analysis where positive, negative, and neutral responses are categorically coded and turned into a column).

Assigning coordinates to each of the multivariate factors

Each archetype on the Jungian wheel could then be assigned a position in a multi-dimensional space based on the defined dimensions. For example:

• Outlaw (Trump): Power Quotient = 8, Risk Threshold = 7, Innovation = 5, Empathy Quotient = 3.
• Ruler (Modi): Power Quotient = 7, Risk Threshold = 4, Innovation = 6, Empathy Quotient = 8.

Choice of 'DISTANCE'

For simplistic calculations, the go-to option would be 'Euclid Distance'. However, the problem with using Euclidian distance is the 'straight-forward' nature of the psychological measurement between the two archetypes that circumvents the correlation between traits/ignores the dependency of variables. A slightly better, more accurate version of the Euclidian Distance measurement could be KNN or K-Nearest Neighbors but we will park that aside for now.

Other distance measurement options include Cosine Similarity and Manhattan Distance among others. However, given the possibility of a correlation between the Power Quotient and Risk Threshold, Mahalanobis Distance is a more effective candidate.

Calculating Mahalanobis Distance between President-elect Trump and PM Modi Archetypes

Here,

• X is Trump’s multivariate vector: [8,7,6,3]
• Y is Modi’s multivariate vector: [7,4,5,8]
• S is the covariance matrix of multivariate correlations

Next, assume that S, the covariance matrix has values as seen in the 4*4 order below...

Plugging X, Y, and S^{-1} into the formula (assuming S^{-1} (transposed) is calculated):

1. We first compute X?Y=[1,3,1,?5]
2. We then apply the formula to find d, giving us a hypothetical distance of approximately 5.42.

Visualizing the Mahalanobis Distance between President-elect Trump and PM Modi using the DESMOS Graphing Calculator

To summarize, using qualitative research, followed by quantitative mapping can help us lock positional coordinates on the Jungian Archetype Wheel for any context, brand, or geopolitics.

Now that we found a way to pin the archetypes of both Trump and Modi, let us now talk about how the rendering of the Prisoner's Dilemma and the Folk Theorem on a two-dimensional confusion matrix can help us war-game negotiation scenarios between the US and India on parameters such as Defense and Trade.

To recap...

The Prisoner's Dilemma is a fundamental concept in game theory that highlights how rational individuals might not cooperate, even if it appears to be in their best interests. Here’s a simplified scenario:

The Scenario: Two individuals (prisoners) are arrested and accused of a crime. Each prisoner can either cooperate with the other by staying silent or betray the other by confessing and testifying.

Outcomes:

a. If both prisoners cooperate (remain silent), they each receive a moderate sentence.

b. If one betrays while the other cooperates, the betrayer goes free, and the cooperator receives a heavy sentence.

c. If both betray each other, both receive a harsh sentence.

The Dilemma: Rationally, each prisoner is tempted to betray to minimize their sentence. However, if both betray, they end up worse off than if they had both cooperated.

The Folk Theorem builds on this concept in the context of repeated games. It suggests that in an indefinitely repeated prisoner's dilemma, cooperation can be sustained as a Nash equilibrium. This means that if the game is played multiple times, players might adopt a cooperative strategy, recognizing that the long-term benefits of cooperation outweigh the short-term gains from betrayal. This theorem allows for the possibility of maintaining cooperative behavior over time, as players factor in the consequences of future interactions

Let us now render both the game theories into a confusion matrix for model building. This will help us game and structure potential outcomes.

Confusion Matrix for U.S.-India relations with Trump and Modi as players

Let us simulate the Prisoner’s Dilemma and Folk Theorem matrices across two critical issues: Defense Purchases and Trade.

Both sides benefit from cooperation, but if the U.S. becomes restrictive (defects), India may retaliate by diversifying its defense sources. Cooperation yields stronger defense ties and Indo-U.S. alignment.

This scenario shows that cooperation benefits both sides by increasing bilateral trade. Defection from either side could lead to economic strain or retaliation.

Folk Theorem Analysis

• Repeating Cooperation: According to the Folk Theorem, repeated interactions over time would ideally lead both the U.S. and India to cooperate, especially if future benefits are prioritized over immediate gains.
• Incentive Structure: For the U.S.: The potential of India as a strategic partner in the Indo-Pacific and as a large defense market creates a strong incentive for cooperation. For India: Access to advanced U.S. technology, economic growth through trade, and security support against regional threats incentivize India to cooperate.

Through the lens of the Folk Theorem, the U.S. and India could potentially build a sustainable, mutually beneficial relationship if they embrace long-term cooperative strategies. However, both leaders' archetypes (Outlaw and Ruler - assumed for this simulation) mean that short-term nationalistic interests might occasionally lead to defection, especially on contentious issues like trade. The outcome depends on whether both leaders value the future benefits of cooperation over immediate domestic or international (regional) geopolitical gains.

Predictive Model Building for wargaming the 2x2 Matrices

Lastly, to build a predictive model to wargame the confusion matrices I put out, we could use historical data across defense deals, trade deals, and the Indo-Pacific relationship outcomes. Here’s an outline:

Data Collection: Historical data on U.S.-India decisions regarding:

a. Defense Deals: Historical occasions where both nations cooperated (e.g., joint purchases, favorable defense terms) or defected (e.g., sanctions, competing alliances).

b. Trade: Trade agreements and tariffs — cooperative decisions (mutual tariff reductions) vs. defecting decisions (tariff increases, trade restrictions).

Features for Prediction:

a. Leader’s Decision History: Record past decisions by each country in the two domains.

b. Economic and Strategic Payoffs: Quantify the outcomes in terms of economic gains, security benefits, or diplomatic influence.

Classification Model Choice:

a. Supervised Learning Model: A classification model (like logistic regression or decision trees) to predict “Cooperate” or “Defect” based on historical features.

b. Reinforcement Learning: Another approach is a Q-learning model, where both players (U.S. and India) learn optimal strategies through repeated interactions, maximizing long-term payoffs.

Demonstration (Conceptual Example): Imagine having the following historical data on decisions and outcomes in each domain:

a. Features: U.S. decision history, India decision history, historical payoffs.

b. Label: Cooperative or Defective outcome for each interaction.

Recorded and taxonomized data as suggested above could help us train a model to predict future cooperative or defective outcomes in defense, trade, and other factors, allowing for a more scientific and accurate scenario analysis under different strategies.

By organizing historical data on defense deals, trade agreements, and other important relationship pivots, we can see how geopolitical diplomacy operates. The matrices above, combined with the Jungian archetype distances can help us build models predicting likely scenarios based on past behavior.

The Unpredictability of Nash Equilibrium in Diplomacy

in geopolitics, achieving a stable Nash Equilibrium isn’t guaranteed. Diplomatic interactions are subject to unpredictable elements such as domestic pressures, sudden policy shifts, or changes in global alliances. Thus, models and wargaming strategies can sit pretty on abundant historical data and accurate statistics but they will always miss the outlier outcome window.

A Word of Caution

I am not trying to oversimplify geopolitics. The “Archetype Distance” metric is just an attempt to fix conviction, and the Prisoner’s Dilemma and Folk Theorem offer strong frameworks, not guarantees. Geopolitical interactions will always have an element of unpredictability, influenced by unique cultural, political, and economic factors. While one can model and predict outcomes, the real world doesn’t always play by the rules of game theory.