Conditional Preferences In Strategic Thinking…From AskLewis.com

A practical approach to predictions and applied game theory

As a professional forecaster and predictive analyst, I have a true passion for applied game theory-based strategic thinking.

Here an individual studies how and why people make decisions. (Specifically, it is “the study of mathematical models of cooperation and conflict and between intelligent seemingly rational decision-makers”. Exploring this has helped me to understand aspects of science and politics. Another term suggested “as a more descriptive name for this way of thinking” is interactive decision theory.

Through the lens of applied game theory-based strategic thinking, it is easier for me to understand investing, entrepreneurship, the Israeli-Hamas War in Gaza, The Russian-Ukraine War, and even the MAGA movement in the United States.

In game theory, it soon becomes clear that some strategies of players are conditional on such factors as who certain key players are surrounded by and the time and space that exists between the application of particular strategies, (spatial distribution of strategies and patterns). For example, in a game where a player is compassionate or seeks fairness, they may make choices more concerned with compassion, empathy, and benefits to others ( higher social welfare) rather than to themselves. They may do this even if they may lose some benefits in doing so. In addition, social interaction may be conditional on the reputation of other players (agents). In the Middle East Hamas is considered to be a terrorist organization so they would have access to less sympathy.

All of these predictive questions have to do with aggregation (the formation of several things into a cluster), and the patterns formed there. This would be especially so in complex environments of decision science, strategizing, and organization theory. In these environments swarm optimization algorithms using AI may be of value.

All of these approaches represent important advances to our understanding of human and social interaction, and modifications to the strong assumptions made by traditional approaches in economics that assume categorical preferences.

However, our approach differs in syntax substance, and application from the above work in that we seek to develop a formal approach to conditional preferences, where extant social relations and ties give rise to both social and individual preferences.

In any exploration of decision-making and strategizing one must initiate a systematic inquiry into sociological and psychological factors of choice.

On the most basic level, the goal is to provide a rational (mathematical framework) to develop a formal model and structure of how extant social relations, modeled as conditional preferences, play a role in social interaction, aggregation, and applied game theory strategies.

Roughly speaking, conditional preferences arise when an individual (agent or player) has to choose options assuming that some event is given (the scenario and result are already defined).

The concept of conditional preferences leads to the idea of conditional beliefs, i.e., the beliefs of the individual conditioned by the fact that some event is given.

Before the development of game theory models, creating strategies on the formalization of conditional beliefs had proven to be a great challenge though it seemed like a fairly simple affair. Many of the variables needed to do this were hard to define and measure consistently. This has all changed with the advent of AI, NLP, and advanced ideas in game theory-based decision science.

When making decisions in a social environment, it is natural for an individual to take into consideration the opinions of others when forming her own opinions. In short, individuals may be influenced by the preferences of others for several reasons: they may like (or dislike, for that matter) the others involved, they may value others’ opinions, or they may have an existing relationship with others (familial, friendship, or professional).

My approach is to incorporate these extended interests into the game by endowing each player with a family of conditional utilities that enable it to account for the social influence that the preferences of other players have on its preferences. Conditional utilities provide social linkages among players that enable simultaneous consideration of both individual and social interests.

Graph Theory

In Graph theory, we study graphs, which are mathematical structures used to model specific relations between objects. Remember when you used graphs in school to measure and compare certain variables?

Today, applied game theory strategists use Graph theory to characterize the way preference relationships propagate through a collective to generate an emergent social model that characterizes the interdependence relationships that exist and which leads to solution concepts that account for both group and individual interests.

Our framework and formal model are general and thus it can readily be applied to a wide range of potential social contexts that feature extant social relations and influence, including geo and local politics.

Conditional preferences provide a natural way to account for social relations and influence, especially in hierarchical organizations where one person or group is in a superior position to another such as might occur in the military or an employer/manager-employee scenario.

The person “higher up the ladder” (HUTL) can choose either action “A1” or action “B1” and the individual “lower down the ladder” (LDTL) can choose either action “A2” or action “B2”. Under classical political and economic theory, each must determine their categorical preference ordering over the outcome space.

The priorities of the individual “lower down the ladder”, however, are likely to be influenced by the priorities of the person “higher up the ladder”.

One way to proceed is for the individual “lower down the ladder” to reason as follows: If the most preferred outcome for the person “higher up the ladder” were, say, “A1” then the person “lower down the ladder” could define his ordering given that hypothesis. But if the person “higher up the ladder” were to prefer “B 1” instead, the person “lower down the ladder” would define a different ordering. Continuing, the person LDTL could form a set of four different preference orderings, each one conditioned on a different hypothesized preference ordering by the person HUTL manager. This could be done without the person LDTL knowing the person HUTL’s actual preference ordering. The conditional preference orderings for the person LDTL are the consequents of hypothetical propositions whose antecedents are assumptions regarding the preferences of the person HUTL.

The Takeaway

There is an important difference in the interpretation of the person HUTL’s preference ordering and the person LDTL’s preference orderings. Whereas the person HUTL’s categorically orders his/her preferences over the possible joint actions of the two players, the person LDTL conditionally orders his/her preferences for joint action concerning the preferences for joint action of the person HUTL. Thus conditional preferences can provide a powerful approach to more formally modeling how extant social relations play a role in influencing the behavior of actors.

For advanced students of game theory, this line of reasoning is similar to the type of reasoning employed by multivariate probability theory (MPT). MPT is a graph-based probability measure (a function returning each event’s probability).

This story is an excerpt from my course “How to Become Really Wealthy”

©Lewis Harrison, all rights reserved.

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