In Collins’s theory,
“individuals, confronted with interactional situations, move towards those that give the highest payoff in emotional energy… Whether one is most attracted to a church service, a political rally, or an intimate conversation is determined by each individual’s expectations of the magnitude of EE flowing from that situation.” (Collins, 1993, p.214)
Thus for a model of agents with energy we must represent in some way not just the energy payoff from an interaction (see next section) but also the agent’s expectations
before an interaction. These expectations determine which of the various possible interaction rituals will actually be attempted.
In the base model, there is no representation of expectations. The decision to initiate an interaction employs no intelligence on the part of the agents (i.e. the initiator is selected with uniformly distributed chances). The decisions on who to attempt to interact with and which feature to compare first are likewise based on uniformly distributed chances. Concerning which trait to present in an interaction ritual, agents have no choice at all. Each has in its Cultural Capital just one trait for each feature. (We will later introduce agents with multiple traits for each feature – see section 6.5 below.) On a given topic, each agent has one and only one idea to offer. We might conceive of an agent’s trait as representing that agent’s view on which trait will deliver the best payoff, but this crude “expected value” is of the 1/0 type. A more realistic treatment of expectations will recognise that they come by degrees. The Baker-Quinn model, for example, models both “energy” and “energising relations” as continuous variables (Baker & Quinn, 2007).
Similarity relations do come by degrees – namely the proportion of features for which two agents share the same traits. But similarity is a reciprocal relation: if agent A shares 0.6 of its traits with agent B, then B shares 0.6 with A. There is nothing in the literature on energy to support the assumption that A will energise with B if and only if B will energise with A. Similarity relations can also be characterised by their transitivity. If A shares 0.7 of its relations with B, and B shares 0.7 with C, the possible sharing between A and C is now constrained to between 0.4 and 0.7. So
similarity relations will not provide us with a proxy for expectations concerning energy.
Energy models then need to record extra information for each agent - in addition to the cultural attributes modelled in the ACM. We can think of this information as representing expectations for the next energy payoff, or memories about past energy payoffs, from which expectations will be derived. Either way we have a numerical attribute that varies in value by degrees.
Modelling energy by degrees is essential to capture another important component of Collins’s theory - decay. Emotional energy is “highest at the peak intensity of an IR itself and leaves an energetic afterglow that gradually decreases over time.” (Collins, 1993, p.211) The rate of decay, he suggests, has not been measured but “a reasonable approximation may be that it has a ‘half life’ between a few hours and a few days”, unless experience of further IRs during that period alter it.
In our energy models energy levels are reduced over time. “Time” is taken to mean simulation iterations, and one social interaction is processed each iteration. Time is not modelled more realistically, since this seemed to call for the methods of discrete- event simulation (DES). Importing a DES engine into the base model was felt to complicate the programming too much, while reproducing the base model in a commercial DES package not designed for agent-based simulation seemed no easier. The interaction-iteration-timestep equation should be acceptable in an abstract model. Each iteration all energy levels are considered decayed by a fixed proportion of their levels in the previous timestep. The specification of this proportion controls the decay
rate, and the same proportion is assumed for all agents at all time. Thus decay rate - which we refer to in the results chapters by the “half life” - becomes a parameter to our model, and potentially an experimental factor.
Decay gives an explanation of why agents enter interactions - to recharge after their energy levels have decayed. Why do agents then exit IRs? Collins claims agents reach “emotional satiation” (Collins, 1993, p.210). It is “a physiological characteristic of emotions” that emotional arousal plateaus during the IR. This short-run satiation would also reduce the chance of repeated interactions running into one another, though he notes medium-run repetition of rewarding situations does tend to occur.
Our modelling of energy levels attempts to capture these interaction dynamics. For determining which IRs occur we use the difference between an energy level at time of IR and its current, decayed level. The level at time of satiation represents a peak in that agent’s experience of IRs. On the basis of that experience and the subsequent decay, an agent’s expectation of a repetition of an IR is that it will return the agent to the previous peak. Thus the difference between charged-up level and decayed level represents the size of an agent’s expectations - how much energy it expects to gain in IR. In summary:
Expected_Gain = Charged-Up_Level - Decayed_Level where
Decayed_Level = Charged-Up_Level *
We can then use this Expected Gain to stratify sampling of the components of the next IR event - for example, when selecting agents to initiate and receive interactions. Indeed, in the most sophisticated model (the Interaction Ritual Agents Model, or IRAM, of 6.5.4 and Chapter 10) this is how we will in fact select interaction participants. We build up to it, however, by sampling participants from a uniform distribution in the all the simpler models.
Another alternative to stratified sampling would be to always choose the IR opportunity with the maximum expected gain - or an arbitrary one of the opportunities with maximum gain, if more than one exists. This is seemingly Collins’s preferred option when he describes agents as boundedly rational optimisers of expected emotional energy return (Collins, 1993; 2004, p.158ff). Stratified sampling however reduces the contrast between energy-based selections and uniformly distributed chances. Agent energy-maximisers must wait for a future study.
Another alternative would have been to stratify by current energy level. As EE decays with time, this would make recency “an important feature of which IR has the strongest emotional attraction at a given time.” (Collins, 1993, p.214) But following Collins’s comment on satiation, we wish to avoid making the most likely event a repetition of the last successful IR. Also, low-EE agents would be less likely to enter IRs, and so being unable to recharge, their energy levels will get even worse. We therefore prefer to select agents by expected gain - representing their growing need or desire for interaction.
The modeller then faces decisions concerning the use of an energy attribute. As well as deciding how it determines IRs, he or she must also decide on how IRs affect energy levels. Given an energy payoff from a successful IR we update an energy level with the payoff level only if the payoff level is higher. If a payoff is lower than the current level, the agent is left with the same need as before. If the payoff is lower than that of the previous IR, but sufficient time has occurred since that IR for the energy level to decay below that of the payoff, then the agent acquires the new energy level (from the payoff), which represents that agent’s new, reduced, expectation.
This might seem to imply that agents with poor payoff opportunities interact more frequently than those with good ones - since poor opportunities will leave agents still with substantial need for interaction, or expected gain. However, decay means that even poor payoffs will have a chance to update an agent’s expectations eventually. Once an agent has been charged from a poor payoff, its expected gain is smaller, since decay is a fixed proportion of an energy level - whether that level was high or low. So of two agents interacting around the same time, one receiving poor payoff, the other a good one, the latter will soon have a much higher expected gain, and thus be likely to interact again sooner when we come to use sampling stratified by expected gain to select participants. Agents repeatedly receiving good payoffs will tend to enter IRs more frequently than those repeatedly receiving poor payoffs.
It is these repeating patterns of IRs - the “interaction ritual chains” (Collins, 2004) - that represent the relations making up social networks. Thus agents repeatedly receiving good payoffs will appear to have more reliable social contacts - and perhaps more of them.
So this concludes our introduction of energy, an attribute that decays over time, motivates agents to recharge it in IR events, and through determining their expectations for those IR events guides their decisions concerning which IRs to attempt or repeat.