Mapping models to target systems

This brings us to the penultimate theoretical step: we need a plausible set of rules for how to apply signalling theory to religion. In general, such a theory would have to plausibly identify senders and receivers, any appropriate signal costs and cooperation benefits, and the means by which sender and receiver strategies are encoded and updated in an adaptive manner. The charge to avoid here is ……… it being so vague and ‘anything goes’ that it resembles an unfalsifiable Panglossian program (Gould and Lewontin 1978) – a charge that has been levelled at the Zahavis (Pomiankowski and Iwasa 1998). Vaguely, verbally shoe-horning religious rituals into signalling models shouldn’t be good enough. We need some sort idea of a procedure and set of standards for mapping signalling models to target systems.

6.3.1. Models and target systems

There are some theoretical resources to draw upon for this. Signalling models are just mathematical structures, and following Michael Weisberg’s picture of scientific modelling (Weisberg 2013), explanatory scientific models should also include an assignment mapping of the structure’s key features to features of a target system: the agents, the signal, the signified trait, the response, and the real-world mechanisms or institutions which correspond to game theoretic strategies and underpin their evolution. Taking the STR seriously therefore means not just appealing to signalling theory but also assigning the mathematical structures of signalling models to target systems in a plausible manner.

One of the simplest assignments would be a mapping for a public, mass religious ritual as follows:

Signal: participation in the ritual (whatever that entails),

Senders: the active ritual participants (plus those who decline, i.e. don’t signal),

Receivers: observing conspecifics (including fellow participants),

Response: subsequent treatment (with respect to cooperative assortment),

Mechanism: behavioural norms and practices (encoding strategies), inherited vertically from parent to offspring, or horizontally via some form of success-sensitive cultural learning.

This assignment provides the minimum level detail needed for a tractable hypothesis, when paired with an interpreted signalling model: for example differential cost-benefit with some type of payoff structure (i.e. actual costs and benefits for the people in the sender & receiver roles), or index-signalling based on some tractable signalling constraint. More complex target systems and assignments are of course possible if some of the above features are varied (e.g. with senders and receivers being elites and followers rather than peers), and some of these combinations will correspond to existing STR variations from the literature. But in any case there needs to be some level of interpretation and assignment. If the formal and theoretical distinctions between signalling models and payoff structures are complex, their application to real-world cases in religious signalling adds another layer of complexity.

The overall recipe for a viable evolutionary model of signalling would therefore look something like this: a) the costs and benefits of signalling and outcome must be able to be combined into overall payoffs which b) makes sense to feed into some plausible update mechanism, c) over an adaptive timescale that makes sense for that model and its interpretation in the target system.

In the stotting case the (tacit) adaptive mechanism and timeframe was natural selection over millions of years on the savanna. The (high type) gazelles and their predators are hypothesised to have a biologically evolved a signalling system, driven and maintained by the fitness incentives of sending and responding to a signal, kept honest by its genuine, significant, and differential fitness costs for the senders. The problem in this case was the leap from energy expenditure being costly in one objective respect to it constituting a fitness cost in the strategic environment.

In the case of extreme religious rituals, the modelling situation is even more messy. Consider the possession ritual as described in (Power 2017). To model the devotees as senders in signalling game we must identify costs and benefits which combine into payoffs that are fit to feed into some evolutionary update mechanism; and do likewise with the observers whose changed perception of the sender collectively deliver the mutual social benefit. Presumably, the update mechanism is a cultural one, either laid down in development or via more ephemeral learning, reinforcement, or success-following. Fitness/prosperity benefits from social connection, and whatever costs are associated with the possession ritual must be made commensurate somehow in the context of this update mechanism, and this will require some sort of plausible/validated rationale. The theoretical gaps here are not be impossible to fill, but they would require work.

6.3.2. Payoff-update system

Most of the generic assignment elements listed above have been discussed already in previous chapters. The last element is the most complex: the evolutionary mechanism whereby sender and receiver strategies are encoded/embodied, such that they have some form of heredity but also sensitivity to selection-like processes that update them over time and allow them to evolve. This therefore links the previously discussed currency problem with an update requirement: there needs to be an overall payoff-update system that is coherent and plausible. This deserves to be unpacked in greater detail in the human cultural context.

As previously argued, what is crucial is that payoffs can be ranked and compared. This is what would allow strategies to have something like meaningful variability of relative fitness. Payoffs may have cardinality (with a numerical value on some scale or other, as I am using here), or simply have an ordinal ranking, but to generate meaningful results the preference orderings of both sender and receiver must each be complete and (to some extent) determinate66. This formal requirement has implications which need to be kept in mind when mapping costs and benefits of signals and displays (ritual or otherwise) to formal models of signalling. Game theory and its solution concepts are just mathematical tools, but you cannot link signalling and

66 _{Agents can of course be indifferent between two or more outcomes, because their outcome payoffs at the nodes} are (determinately) approximately the same. Indeterminacy or incommensurably between them on the hand would be a systemic problem.

the cooperation problem without them, and this means that there must be ‘playing fields’ which determine what’s at stake for the players.

Consider the following examples of payoff-update systems.

1. Pricing behaviour of two corporations in a duopoly. The stakes for the players are monetary, the motives are maximising profit, so we can draw predictions from pricing equilibria (assuming the players are free enough and clever enough to price accordingly) as the players adjust rationally to each other’s pricing moves.

2. Two human beings are able to subject each other to painful electrical shocks in a sadistic, 2-way variation on the Milgram experiments. The payoffs are comfort or discomfort, the motivation in minimising discomfort, and we can predict behaviour to the degree that the players actions are driven by hedonic self-interest (instead of anger or sadomasochism, for example).

Now imagine a version of (2) where the players can trade off money for electric shocks. The problem now isn’t just how to convert the ‘currencies’, it is also how to select the paradigm of rational strategy update. We could imagine (as economists do) a more abstract notion of utility evidenced by (or constituted by) the preferences revealed in action and decision, which monetary value and hedonic value can both serve as proxies for in cleaner cases like (1) and (2). But is there a principled way of combining both hedonic and monetary payoffs in a single utility scale, prior to running the experiment? Probably not, at least not in any simple or usefully general manner67, which is probably why prudent experimental economists stick to a single measurable quantity (usually money) as a proxy for utility.

However, this is very similar to what seems to be going on in many verbal models of costly religious signalling. The costs of an extreme ritual are said to be pain and discomfort, whereas the benefits are such things as improved standing in the community and improved prospects for cooperation opportunities, and not much thought is given to how and why signalling strategies might be being composed and modified over time. Comfort, money, respect, and social standing are all ‘good’, in some sense, but more is needed. It’s very plausible to imagine

67 _{We can imagine an experiment designed to reveal what the preference trade-off functions between comfort and} money might look like. What are the marginal costs of pain avoidance? Is there a level of agony that no amount of money will compensate? Ethics committees alone make this epistemically inaccessible.

that financial burdens, the respect of your peers, and your standing in society might all have an impact on eventual reproductive success: they might imply indirect costs or benefits to fitness. However, they are indeed quite indirect, and there will be no simple, linear mapping between any of these into fitness. Furthermore, how does the pain inflicted by an extreme ritual, experienced a few times a year over a few hours or days, impact on fitness? Probably not a great deal at all, especially if the norms surrounding rituals encourage the participation of supporters to take care of the main participant, as they generally do for initiation ceremonies. Perhaps we should instead see these costs and benefits as feeding into a utility maximisation or decision theoretic framework: we avoid pain and seek social and material benefit, and so at that level of abstraction we can indeed assign some sort of value. This must be the case to some extent: people act on a variety of motivations without suffering agential incoherence. But this has two problems. The first is as already mentioned: costs and benefits are being passed through a highly subjective filter before behaviour is generated, so differing proxy measures require conversion (somehow) before they can be useful in modelling that behaviour. E.g. pain is aversive, but is it aversive in the same way as going into debt is aversive? No, and it is reasonable to think that the cognitive systems which underpin pain avoidance work differently from those relating to debt avoidance (the modern literature on behavioural economics also shows that framing effects can make a huge difference in terms of which cost is acted on in any particular occasion). Second, if costs and benefits are translated into utilities, it becomes harder to link them to anything like a paradigmatic evolutionary, population-level feedback mechanism. Of course, this is only a problem with respect to a dependence on the biological signalling paradigm. As briefly mentioned in chapter four, signalling theory in economics takes its own form with analogous (but often distinct) modelling options, and there may well be tools there that can be co-opted instead.

Perhaps this is the direction that religious signalling theory should go, but that is not a question for this dissertation. I will simply assume that (at least some of) the lessons of more biologically attuned signalling models will be general enough to carry over. In any case, there are other adaptive paradigms available. As suggested in chapter 1, behavioural traits can also be transmitted both horizontally and vertically by mechanisms such as social learning and ‘follow success’ rules; and there are some plausible ways that these might approximate the effects of selective mechanisms (cultural fitness, Heyes-style cognitive gadgets, etc). Some sort of payoff-update system along these lines might be a viable option as well, though I will not

further elaborate on this either. Of course, there is also natural selection of traits transmitted via genic inheritance, though this may be more plausible for broader ‘reactive’ causal components of signalling strategies, such as temperament and basic social and aesthetic capacities or biases that can facilitate ritual displays and their reception.

Whatever the payoff-update system might be for a putative signalling system or signalling mechanism, we needn’t be pedantic in insisting on a complete, independently validated story. But a coherent one is required. There will also be peculiarities to take account of; each possibility will imply its own scales of what constitutes success or failure, and therefore the features of the situation which correspond to costs and benefits. One other thing to bear in mind here (regarding the potential multiplicity of mechanisms) is that different evolutionary update mechanisms (natural selection, cultural processes, etc) will have corresponding differences in evolutionary timeframe. The consequences of this will be investigated further in chapters 7 and 8.