Abstract
This paper applies the theoretical criteria laid out by D’Arms et al. (1998) to various aspects of evolutionary models of signalling. The question that D’Arms et al. seek to answer can be formulated as follows: Are the models that we use to explain the phenomena in question conceptually adequate? The conceptual adequacy question relates the formal aspects of the model to those aspects of the natural world that the model is supposed to capture. Moreover, this paper extends the analysis of D’Arms et al. by asking the following additional question: Are the models that we use sufficient to explain the phenomena in question? The sufficiency question asks what formal resources are minimally required for the model to get the right results most of the time.
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Notes
There is, of course, a broader concern about modelling and simulations, in general, and their explanatory significance; however, as a first step toward a critical analysis of the ever-increasing literature on signalling games, I will here take a more narrow focus. However, for more general discussion of modelling see, e.g., Sugden (2000) and Humphreys and Imbert (2012).
Though the symmetric case is not stated explicitly, Lewis (2002) proves that, in an asymmetric signalling game with m states and n signals (\(n \ge m)\), there are \(\frac{n!}{(n-m)!}\) possible signalling systems. As such, when \(m=n\), as we have here, it follows immediately that there are n! possible signalling systems.
See Lewis’s formal definition of conventions (Lewis 2002, 78–79).
This ‘rational baggage’ is exemplified by Lewis’s discussion of higher-order expectations in the coordination game: “In order to figure out what you will do by replicating your practical reasoning, I need to figure out what you expect me to do. I know that, just as I am trying to figure out what you will do by replicating your reasoning, so you may be trying to figure out what I will do by replicating my reasoning. [...] So I may expect you to try to replicate my attempt to replicate your attempt to replicate my reasoning. So my own reasoning may have to include an attempt to replicate your attempt to replicate my attempt to replicate your attempt to replicate my reasoning. And so on” (Lewis 2002, 27–28). Without an excessive requirement on the rationality of the players, or a prior language already in place, it is not clear how Lewis’s notion of signalling can arise spontaneously.
See Skyrms (2014) for details of this model.
Note, however, that this is also true of fairness as a target phenomenon to be explained by an evolutionary model.
Sterelny (2012) highlights that the underlying problem that the vervet alarm-call system solves is decidedly not a coordination problem since a receiver vervet’s payoff for, e.g., running up a tree (upon hearing bark) does not in any way depend upon the sender vervet’s running up a tree. Thus, the vervets do not have mutually dependent rewards (Sterelny 2012, 76).
Proximate explanations are contrasted with (and complementary to) ultimate explanations. The latter would require detailing the evolutionary trajectory by which signalling arises in addition to the selective forces driving dynamic changes in the population, whereas the former would require describing the developmental and physiological mechanisms by which signalling is implemented. See Mayr (1961).
Here, Skyrms is referring to a definition in Jacob Bernoulli’s Art of Conjecture where he says that something is morally certain if its probability comes so close to complete certainty that the difference cannot be perceived. However, it should be noted that in light of subsequent work in this area, Skyrms weakened this claim in a later edition of the book. The claim itself is still true in a particular case; it is just not true generally.
The replicator equations capture the idea that an individual with higher-than-average fitness is more likely to reproduce; the composition of the population changes over time, resulting in corresponding changes to the fitness of a particular strategy relative to the average fitness of the population. See Taylor and Jonker (1978) for further details.
In this case, an individual in the (finite) population is selected proportional to its fitness; that individual produces an identical offspring which then replaces a randomly chosen individual in the population. Crucially, it is possible for a single mutant strategy that has a disadvantage with respect to relative fitness to generate a lineage that eventually takes over the entire population. See Nowak et al. (2004) and Nowak (2006) for further details.
Herrnstein reinforcement learning, based on the matching law (which, in turn, is a formalisation of the law of effect), supposes that the probability of selecting a particular action is proportional to the accumulated rewards for that action. See Thorndike (1905, 1911, 1927) and Herrnstein (1970) for further details.
More complex cases will be examined in Sect. 3.2.
To borrow a turn of phrase from John Woods.
Note that this question is also taken up in Crawford and Sobel (1982); their results suggest that “perfect communication is not to be expected in general unless agents’ interests completely coincide” (Crawford and Sobel 1982, 1450); however, Ahern and Clark show that when misalignment of preferences is not too strong, a ‘cyclic’ signalling system can evolve—they note a “range of behavior, from separating, to cycling, to collapse” as conflict increases (Ahern and Clark 2014, 31–32). See also Godfrey-Smith and Martínez (2013) and Martínez and Godfrey-Smith (2016).
Small-world network is a technical term characterised by a graph with a specific set of properties—e.g., high clustering coefficient (of nodes), short average path length (between nodes), etc. For example, many forms of the underlying architecture of the internet are small-world networks.
Mühlenbernd and Franke (2014) give a nice overview of how different network topologies shift the basin of attraction for signalling systems and pooling equilibria (by assuming non-equiprobable states).
Though, see Huttegger (2007c) for an analysis of robustness across different dynamics.
One such justification is got by analysing the payoffs or success rates for suboptimal pooling strategies. For example, in the \(4\times 4\) signalling game, the most efficient pooling strategy has an expected payoff of 0.75, and a success rate of 0.75. A cutoff of 0.80, in this case, is justified, since a suboptimal random walk may spend some time above the 0.75 success rate before settling into a partial-pooling equilibrium. However, the most efficient pooling strategy in an \(8 \times 8\) signalling game has an expected payoff (and success rate) of 0.875. As such, a cutoff of 0.80 is not warranted here, since this will include many runs that ended up with suboptimal conventions.
See also Skyrms (2010a).
Both Sterelny (2012) and Santana (2014) highlight that signalling in nature is often one-to-many or many-to-many, rather than the neat and tidy bijection that obtains in a signalling system. Thus, in targeting more complex signalling phenomena than merely the emergence of meaning, pooling should be expected.
For an extensive and systematic discussion of the problem of determining whether the right simplifications have been chosen, see Wimsatt (2007).
See also Schreiber (2001) for an analysis of the connection between the replicator dynamics and Pólya urns more generally.
For more details on this, see Sandholm (2010).
Note that a lot is being assumed here, so this may seem question-begging. However, Steinert-Threlkeld (2014) has shown that function words, such as ‘not’, may arise in signalling contexts.
Most researchers hold that the key distinction between language and animal communication systems is that the former utilises compositional syntax. See Progovac (2019) for an overview.
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Acknowledgements
This research was supported by the Social Sciences and Humanities Research Council of Canada, as well as a fellowship from the Department of Philosophy at Simon Fraser University. I would like to acknowledge the following people for their helpful comments and support during the writing of this paper: Nic Fillion, Matt DeVos, Holly Anderson, Jeffrey Barrett, Brian Skyrms, Louis Narens, Simon Huttegger, Cailin O’Connor, Aydin Mohseni, John Woods, Endre Begby, Gabriel Larivière, Nikolas Hamm, Sarah LaCroix. I would like to thank audiences at the IV Philogica Conference for Logic, Epistemology, and Philosophy of Science in Bogotà, Colombia and the Fall (2016) Social Dynamics Seminar at the Department of Logic and Philosophy of Science at UC Irvine. I would additionally like to thank the anonymous reviewers for extremely helpful comments and criticisms. Finally, thanks to Yoshua Bengio and the Québec AI Institute for providing generous resources.
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LaCroix, T. Evolutionary Explanations of Simple Communication: Signalling Games and Their Models. J Gen Philos Sci 51, 19–43 (2020). https://doi.org/10.1007/s10838-019-09481-7
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DOI: https://doi.org/10.1007/s10838-019-09481-7