...once complex meanings could be formed by the combination of words, and once the referents of those words ceased to be directly observable objects and actions, magical beliefs having a powerful effect on behavior could have emerged.
- Manuel DeLanda, Philosophy and Simulation
One of the things that I'm most interested in exploring / simulating is social emergence. By this, I mean patterns and events that occur as a direct result of social interactions but are not pre-ordained by those interactions.
A feud between two families over multiple generations is a prime example. While there is (presumably) a catalyzing event, it's only through the tit-for-tat actions and reactions (a slight, a fistfight, a slashed tired) that it continues to be carried over time. A feud itself isn't reducible to any single event, place, actor, or object (or even a group of those). But it is continually maintained by actors, their relationships between and within groups, and their material circumstances (one might guess that if one family suddenly gains a lot of power, the feud would be squashed somehow).
Another example is group decision-making. This assumes some external circumstance that must be responded to in a binary way (or, assume if there's many ways of responding — say responses A, B, C, etc. that it can be reduced to a binary decision, e.g. A or not A, B or not B...) and that the response requires the involvement of the whole or a significant part of the group. From a game theory perspective, the cases that are interesting to consider are those where taking action benefits the group but harms the individual, or harms the group but benefits the individual. In a long-running simulation, it's better for individuals to take those actions that benefit the group but harm themselves, but individual decision-making is heavily weighted against harm to one's self (or close associations). Agent-based modeling, in contrast to a game theoretical framework, would allow for varying degrees of altruism or foresight, network effects and relationships between individuals, and disparate external circumstances to which groups must respond.
A more interesting question than the mechanics of group decision-making might be the emergence of the realization of the need for a group-based decision, although this seems possibly more a question of individual psychology than a group/social one, or else a question of communication and persuasion among group members.
The (extended) family, religion, government, politics, the educational system, the arts, science, media, agriculture and industry, currency and exchange and finance, are all socially emergent. I have no idea how to categorize or organize them among one another.
Earlier this year I read Ellen Meiksins Wood's The Emergence of Capitalism: A Longer View. Wood is a Marxist scholar with a decidedly critical view of capitalism, but this book is focused on refuting classical economist's view of capitalism as naively arising out of simple exchange ("propensity to truck and barter"), which had been going on for thousands of years. Wood argues that something specific and historically contingent happened in Europe (specifically England) a few centuries ago that created the ripe conditions for capitalist modes of production, and that once those took hold, they were carried forward by distinct "laws of motion" that caused the phenomenon to spread across the globe. This metaphor is useful in thinking about social emergence, as it's never an identifiable 'thing' that emerges, but shifts in relations and behavior that reproduce themselves more or less successfully, needing both internal and external (re-) sources to survive and evolving and adapting over time.