Consensus and Cooperation in Networked Multi-Agent Systems

Consensus and Cooperation in Networked Multi-Agent Systems

Journal: Proceedings of the IEEE

  • Proceedings of the IEEE is the leading journal to provide an in-depth review, survey, and tutorial coverage of the technical developments in electronics, electrical and computer engineering, and computer science. Consistently ranked as one of the top journals by Impact Factor, Article Influence Score and more, the journal serves as a trusted resource for engineers around the world

Authors:

Abstract:

  • This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with non-local information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small world effects on the speed of consensus algorithms and cooperative control of multi vehicle formations.

Notes:

  • In networks of agents (or dynamic systems), “consensus” means to reach an agreement regarding a certain quantity of interest that depends on the state of all agents. A “consensus algorithm” (or protocol) is an interaction rule that specifies the information exchange between an agent and all of its (nearest) neighbors on the network (pp 215)
    • In my work, this is agreement on heading and velocity
  • Graph Laplacians are an important point of focus of this paper. It is worth mentioning that the second smallest eigenvalue of graph Laplacians called algebraic connectivity quantifies the speed of convergence of consensus algorithms. (pp 216)
  • More recently, there has been a tremendous surge of interest among researchers from various disciplines of engineering and science in problems related to multi-agent networked systems with close ties to consensus problems. This includes subjects such as consensus [26]–[32], collective behavior of flocks and swarms [19], [33]–[37], sensor fusion [38]–[40], random networks [41], [42], synchronization of coupled oscillators [42]–[46], algebraic connectivity of complex networks [47]–[49], asynchronous distributed algorithms [30], [50], formation control for multi-robot systems [51]–[59], optimization-based cooperative control [60]–[63], dynamic graphs [64]–[67], complexity of coordinated tasks [68]–[71], and consensus-based belief propagation in Bayesian networks [72], [73]. (pp 216)
    • That is a dense lit review. How did they order it thematically?
  • A byproduct of this framework is to demonstrate that seemingly different consensus algorithms in the literature [10], [12]–[15] are closely related. (pp 216)
  • To understand the role of cooperation in performing coordinated tasks, we need to distinguish between unconstrained and constrained consensus problems. An unconstrained consensus problem is simply the alignment problem in which it suffices that the state of all agents asymptotically be the same. In contrast, in distributed computation of a function f(z), the state of all agents has to asymptotically become equal to f(z), meaning that the consensus problem is constrained. We refer to this constrained consensus problem as the f-consensus problem. (pp 217)
    • Normal exploring/flocking/stampeding is unconstrained. Herding adds constraint, though it’s dynamic. The variables that have to be manipulated in the case of constraint to result in the same amount of consensus are probably what’s interesting here. Examples could be how ‘loud’ does the herder have to be? Also, how ‘primed’ does the population have to be to accept herding?
  • …cooperation can be informally interpreted as “giving consent to providing one’s state and following a common protocol that serves the group objective.” (pp 217)
  • Formal analysis of the behavior of systems that involve more than one type of agent is more complicated, particularly, in presence of adversarial agents in noncooperative games [79], [80]. (pp 217)
  • The reason matrix theory [81] is so widely used in analysis of consensus algorithms [10], [12], [13], [14], [15], [64] is primarily due to the structure of P in (4) and its connection to graphs. (pp 218)
  • The role of consensus algorithms in particle based flocking is for an agent to achieve velocity matching with respect to its neighbors. In [19], it is demonstrated that flocks are networks of dynamic systems with a dynamic topology. This topology is a proximity graph that depends on the state of all agents and is determined locally for each agent, i.e., the topology of flocks is a state dependent graph. The notion of state-dependent graphs was introduced by Mesbahi [64] in a context that is independent of flocking. (pp 218)
    • They leave out heading alignment here. Deliberate? Or is heading alignment just another variant on velocity
  • Consider a network of decision-making agents with dynamics ẋi = ui interested in reaching a consensus via local communication with their neighbors on a graph G = (V, E). By reaching a consensus, we mean asymptotically converging to a one-dimensional agreement space characterized by the following equation: x1 = x2 = … = x (pp 219)
  • A dynamic graph G(t) = (V, E(t)) is a graph in which the set of edges E(t) and the adjacency matrix A(t) are time-varying. Clearly, the set of neighbors Ni(t) of every agent in a dynamic graph is a time-varying set as well. Dynamic graphs are useful for describing the network topology of mobile sensor networks and flocks [19]. (pp 219)
  • GraphLaplacianGradientDescent(pp 220)
  • algebraic connectivity of a graph: The algebraic connectivity (also known as Fiedler value or Fiedler eigenvalue) of a graph G is the second-smallest eigenvalue of the Laplacian matrix of G.[1] This eigenvalue is greater than 0 if and only if G is a connected graph. This is a corollary to the fact that the number of times 0 appears as an eigenvalue in the Laplacian is the number of connected components in the graph. The magnitude of this value reflects how well connected the overall graph is. It has been used in analysing the robustness and synchronizability of networks. (wikipedia) (pp 220)
  • According to Gershgorin theorem [81], all eigenvalues of L in the complex plane are located in a closed disk centered at delta + 0j with a radius of delta, the maximum degree of a graph (pp 220)
    • This is another measure that I can do of the nomad/flock/stampede structures combined with DBSCAN. Each agent knows what agents it is connected with, and we know how many agents there are. Each agent row should just have the number of agents it is connected to.
  • In many scenarios, networked systems can possess a dynamic topology that is time-varying due to node and link failures/creations, packet-loss [40], [98], asynchronous consensus [41], state-dependence [64], formation reconfiguration [53], evolution [96], and flocking [19], [99]. Networked systems with a dynamic topology are commonly known as switching networks. (pp 226)
  • Conclusion: A theoretical framework was provided for analysis of consensus algorithms for networked multi-agent systems with fixed or dynamic topology and directed information flow. The connections between consensus problems and several applications were discussed that include synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. The role of “cooperation” in distributed coordination of networked autonomous systems was clarified and the effects of lack of cooperation was demonstrated by an example. It was demonstrated that notions such as graph Laplacians, nonnegative stochasticmatrices, and algebraic connectivity of graphs and digraphs play an instrumental role in analysis of consensus algorithms. We proved that algorithms introduced by Jadbabaie et al. and Fax and Murray are identical for graphs with n self-loops and are both special cases of the consensus algorithm of Olfati-Saber and Murray. The notion of Perron matrices was introduced as the discrete-time counterpart of graph Laplacians in consensus protocols. A number of fundamental spectral properties of Perron matrices were proved. This led to a unified framework for expression and analysis of consensus algorithms in both continuous-time and discrete-time. Simulation results for reaching a consensus in small-worlds versus lattice-type nearest-neighbor graphs and cooperative control of multivehicle formations were presented. (pp 231)

Schooling as a strategy for taxis in a noisy environment

Schooling as a strategy for taxis in a noisy environment

Journal: Evolutionary Ecology: Evolutionary Ecology is a conceptually oriented journal of basic biology at the interface of ecology and evolution. The journal publishes original research, reviews and discussion papers dealing with evolutionary ecology, including evolutionary aspects of behavioral and population ecology. The objective is to promote the conceptual, theoretical and empirical development of ecology and evolutionary biology; the scope extends to all organisms and systems. Research papers present the results of empirical and theoretical investigations, testing current theories in evolutionary ecology.

Author: Daniel Grunbaum: My research program seeks to establish quantitative relationships between short-term, small-scale processes, such as individual movement behaviors, and their long-term, large-scale population level effects, such as population fluxes and distributions.

Abstract

  • A common strategy to overcome this problem is taxis, a behaviour in which an animal performs a biased random walk by changing direction more rapidly when local conditions are getting worse.
    • Consider voters switching from Bush->Obama->Trump
  • Such an animal spends more time moving in right directions than wrong ones, and eventually gets to a favourable area. Taxis is ineffcient, however, when environmental gradients are weak or overlain by `noisy’ small-scale fluctuations. In this paper, I show that schooling behaviour can improve the ability of animals performing taxis to climb gradients, even under conditions when asocial taxis would be ineffective. Schooling is a social behaviour incorporating tendencies to remain close to and align with fellow members of a group. It enhances taxis because the alignment tendency produces tight angular distributions within groups, and dampens the stochastic effects of individual sampling errors. As a result, more school members orient up-gradient than in the comparable asocial case. However, overly strong schooling behaviour makes the school slow in responding to changing gradient directions. This trade-off suggests an optimal level of schooling behaviour for given spatio-temporal scales of environmental variations.
    • This has implications for everything from human social interaction to ANN design.

Notes

  • Because limiting resources typically have `patchy’ distributions in which concentrations may vary by orders of magnitude, success or failure in finding favourable areas often has an enormous impact on growth rates and reproductive success. To locate resource concentrations, many aquatic organisms display tactic behaviours, in which they orient with respect to local variations in chemical stimuli or other environmental properties. (pp 503)
  • Here, I propose that schooling behaviours improve the tactic capabilities of school members, and enable them to climb faint and noisy gradients which they would otherwise be unable to follow. (pp 504)
  • Schooling is thought to result from two principal behavioural components: (1) tendencies to move towards neighbours when isolated, and away from them when too close, so that the group retains a characteristic level of compactness; and (2) tendencies to align orientation with those of neighbours, so that nearby animals have similar directions of travel and the group as a whole exhibits a directional polarity. (pp 504)
    • My models indicate that attraction isn’t required, as long as there is a distance-graded awareness. In other words, you align most strongly with those agents that are closest.
  • I focus in this paper on schooling in aquatic animals, and particularly on phytoplankton as a distributed resource. However, although I do not examine them specifically, the modelling approaches and the basic results apply more generally to other environmental properties (such as temperature), to other causes of population movement (such as migration) and to other socially aggregating species which form polarized groups (such as flocks, herds and swarms). (pp 504)
  • Under these circumstances, the search of a nektonic filter-feeder for large-scale concentrations of phytoplankton is analogous to the behaviour of a bacterium performing chemotaxis. The essence of the analogy is that, while higher animals have much more sophisticated sensory and cognitive capacities, the scale at which they sample their environment is too small to identify accurately the true gradient. (pp 505)
    • And, I would contend for determining optimal social interactions in large groups.
  • Bacteria using chemotaxis usually do not directly sense the direction of the gradient. Instead, they perform random walks in which they change direction more often or by a greater amount if conditions are deteriorating than if they are improving (Keller and Segel, 1971; Alt, 1980; Tranquillo, 1990). Thus, on average, individuals spend more time moving in favourable directions than in unfavourable ones. (pp 505)
  • A bacterial analogy has been applied to a variety of behaviours in more complex organisms, such as spatially varying di€usion rates due to foraging behaviours or food-handling in copepods and larval ®sh (Davis et al., 1991), migration patterns in tuna (Mullen, 1989) and restricted area searching in ladybugs (Kareiva and Odell, 1987) and seabirds (Veit et al., 1993, 1995). The analogy provides for these higher animals a quantitative prediction of distribution patterns and abilities to locate resources at large space and time scales, based on measurable characteristics of small-scale movements. (pp 505)
  • I do not consider more sophisticated (and possibly more effective) social tactic algorithms, in which explicit information about the environment at remote points is actively or passively transmitted between individuals, or in which individual algorithms (such as slowing down when in relatively high concentrations) cause the group to function as a single sensing unit (Kils, 1986, described in Pitcher and Parrish, 1993). (pp 506)
    • This is something that could be easily added to the model. There could be a multiplier for each data cell that acts as a velocity scalar of the flock. That should have significant effects! This could also be applied to gradient descent. The flock of Gradient Descent Agents (GDAs) could have a higher speed across the fitness landscape, but slow and change direction when a better value is found by one of the GDAs. It occurs to me that this would work with a step function, as long as the baseline of the flock is sufficiently broad.
  • When the noise predominates (d <= 1), the angular distribution of individuals is nearly uniform, and the up-gradient velocity is near zero. In a range of intermediate values of d(0.3 <= d <= 3), there is measurable but slow movement up-gradient. The question I will address in the next two sections is: Can individuals in this intermediate signal-to-noise range with slow gradient-climbing rates improve their tactic ability by adopting a social behaviour (i.e. schooling)? (pp 508)
  • The key attributes of these models are: (1) a decreasing probability of detection or responsiveness to neighbours at large separation distances; (2) a social response that includes some sort of switch from attractive to repulsive interactions with neighbours, mediated by either separation distance or local density of animals*; and (3) a tendency to align with neighbours (Inagaki et al., 1976; Matuda and Sannomiya, 1980, 1985; Aoki, 1982; Huth and Wissel, 1990, 1992; Warburton and Lazarus, 1991; Grunbaum, 1994). (pp 508)
    • * Though not true of belief behavior (multiple individuals can share the same belief), for a Gradient Descent Agent (GDA), the idea of attraction/repulsion may be important.
  • If the number of neighbours is within an acceptable range, then the individual does not respond to them. On the other hand, if the number is outside that range, the individual turns by a small amount, Δθ3, to the left or right according to whether it has too many or too few of them and which side has more neighbours. In addition, at each time step, each individual randomly chooses one of its visible neighbours and turns by a small amount, Δθ4, towards that neighbour’s heading. (pp 508)
  • The results of simulations based on these rules show that schooling individuals, on average, move more directly in an up-gradient direction than asocial searchers with the same tactic parameters. Figure 4 shows the distribution of individuals in simulations of asocial and social taxis in a periodic domain (i.e. animals crossing the right boundary re-enter the left boundary, etc.). (pp 509)
  • Gradient Schooling
  • As predicted by Equation (5), asocial taxis results in a broad distribution of orientations, with a peak in the up-gradient (positive x-axis) direction but with a large fraction of individuals moving the wrong way at any given time (Fig. 5a,b). By comparison, schooling individuals tend to align with one another, forming a group with a tightened angular distribution. There is stochasticity in the average velocity of both asocial and social searchers (Fig. 5c). On average, however, schooling individuals move up-gradient faster and more directly than asocial ones. These simulation results demonstrate that it is theoretically possible to devise tactic search strategies utilizing social behaviours that are superior to asocial algorithms. That is, one of the advantages of schooling is that, potentially, it allows more successful search strategies under `noisy’ environmental conditions, where variations on the micro-scales at which animals sense their environment obscure the macro-scale gradients between ecologically favourable and unfavourable regions. (pp 510)
  • School-size effects must depend to some extent on the tactic and schooling algorithms, and the choices of parameters. However, underlying social taxis are the statistics of pooling outcomes of independent decisions, so the numerical dependence on school size may operate in a similar manner for many comparable behavioural schemes. For example, it seems reasonable to expect that, in many alternative schooling and tactic algorithms, decisions made collectively by less than 10 individuals would show some improvement over the asocial case but also retain much of the variability. Similarly, in most scenarios, group statistics probably vary only slowly with group size once it reaches sizes of 50-100. (pp 514)
  • when group size becomes large, the behaviour of model schools changes in character. With numerous individuals, stochasticity in the behaviour of each member has a relatively weaker effect on group motion. The behaviour of the group as a whole becomes more consistent and predictable, for longer time periods. (pp 514)
    • I think that this should be true in belief spaces as well. It may be difficult to track one person’s trajectory, but a group in aggregate, particularly a polarized group may be very detectable.
  • An example of group response to changing gradient direction shows that there can be a cost to strong alignment tendency. In this example, the gradient is initially pointed in the negative y-direction (Fig. 9). After an initial period of 5 time units, during which the gradient orients perpendicularly to the x-axis, the gradient reverts to the usual x-direction orientation. The school must then adjust to its new surroundings by shifting to climb the new gradient. This example shows that alignment works against course adjustment: the stronger the tendency to align, the slower is the group’s reorientation to the new gradient direction. This is apparently due to a non-linear interaction between alignment and taxis: asymmetries in the angular distribution during the transition create a net alignment flux away from the gradient direction. Thus, individuals that pay too much attention to neighbours, and allow alignment to overwhelm their tactic tendencies, may travel rapidly and persistently in the wrong direction. (pp 516)
    • So, if alignment (and velocity matching) are strong enough, the conditions for a stampede (group behavior with negative outcomes – in this case, less food) emerge
  • The models also suggest that there is a trade-off in strengthening tendencies to align with neighbours: strong alignment produces tight angular distributions, but increases the time needed to adjust course when the direction of the gradient changes. A reasonable balance seems to be achieved when individuals take roughly the same time to coalesce into a polarized group as they do to orient to the gradient in asocial taxis. (pp 518)
    • There is something about the relationship between explore and exploit in this statement that I really need to think about.
  • Social taxis is potentially effective in animals whose resources vary substantially over large length scales and for whom movements over these scales are possible. (pp 518)
    • Surviving as a social animal requires staying in the group. Since belief can cover wide ranges (e.g. religion), does there need to be a mechanism where individuals can harmonize their beliefs? From Social Norms and Other Minds The Evolutionary Roots of Higher Cognition :  Field research on primate societies in the wild and in captivity clearly shows that the capacity for (at least) implicit appreciation of permission, prohibition, and obligation social norms is directly related to survival rates and reproductive success. Without at least a rudimentary capacity to recognize and respond appropriately to these structures, remaining within a social group characterized by a dominance hierarchy would be all but impossible.
  • Interestingly, krill have been reported to school until a food patch has been discovered, whereupon they disperse to feed, consistent with a searching function for schooling. The apparent effectiveness of schooling as a strategy for taxis suggests that these schooling animals may be better able to climb obscure large-scale gradients than they would were they asocial. Interactive effects of taxis and sociality may affect the evolutionary value of larger groups both directly, by improving foraging ability with group size, and indirectly, by constraining alignment rates. (pp 518)
  • An example where sociality directly affects foraging strategy is forage area copying, in which unsuccessful fish move to the vicinity of neighbours that are observed to be foraging successfully (Pitcher et al., 1982; Ranta and Kaitala, 1991; Pitcher and Parrish, 1993). Pitcher and House (1987) interpreted area copying in goldfish as the result of a two-stage decision process: (1) a decision to stay put or move depending on whether feeding rate is high or low; and (2) a decision to join neighbours or not based upon whether or not further solitary searching is successful. Similar group dynamics have been observed in foraging seabirds (Porter and Seally, 1982; Haney et al., 1992).
  • Synchrokinesis depends upon the school having a relatively large spatial extent: part of a migrating school encounters an especially favourable or unfavourable area. The response of that section of the school is propagated throughout the school by alignment and grouping behaviours, with the result that the school as a whole is more effective at route-finding than isolated individuals. Forage area copying and synchrokinesis are distinct from social taxis in that an individual discovers and reacts to an environmental feature or resource, and fellow group members exploit that discovery. In social taxis, no individual need ever have greater knowledge about the environment than any other — social taxis is essentially bound up in the statistics of pooling the outcomes of many unreliable decisions. Synchrokinesis and social taxis are complementary mechanisms and may be expected to co-occur in migrating and gradient-climbing schools. (pp 519)
  • For example, in the comparisons of taxis among groups of various sizes, the most successful individuals were in the asocial simulation, even though as a fraction of the entire population they were vanishingly small. (pp 519)
    • Explorers have the highest payoff for the highest risks

Alignment in social interactions

Alignment in social interactions (2016)

Journal: Consciousness and Cognition, an International Journal, provides a forum for a natural science approach to the issues of consciousnessvoluntary control, and self. The journal features empirical research (in the form of articles) and theoretical reviews. The journal aims to be both scientifically rigorous and open to novel contributions.

Mattia Gallotti (Scholar):  Manager of The Human Mind Project at the School of Advanced Study of the University of London. I have a keen interest in academic management and governance, and I now consult on aspects of social innovation in the public sector.

Merle Theresa Fairhurst-MenuhinMerle is equally driven by a passion for art and science. Her days are split between work in cognitive neuroscience and exploring the rich repertoire of art song.

Chris Frith (Scholar):  I have been trying to delineate the mechanisms underlying the human ability to share representations of the world, for it is this ability that makes communication possible and allows us to achieve more than we could as individuals. We think that there are two major processes involved. The first is an automatic form of priming (sometimes referred to as contagion or empathy), whereby our representations of the world become aligned with those of the person with whom we are interacting. The second is a form of forward modelling, analogous to that used in the control of our own actions.

Abstract:

  • According to the prevailing paradigm in social-cognitive neuroscience, the mental states of individuals become shared when they adapt to each other in the pursuit of a shared goal. We challenge this view by proposing an alternative approach to the cognitive foundations of social interactions. The central claim of this paper is that social cognition concerns the graded and dynamic process of alignment of individual minds, even in the absence of a shared goal. When individuals reciprocally exchange information about each other’s minds processes of alignment unfold over time and across space, creating a social interaction. Not all cases of joint action involve such reciprocal exchange of information. To understand the nature of social interactions, then, we propose that attention should be focused on the manner in which people align words and thoughts, bodily postures and movements, in order to take one another into account and to make full use of socially relevant information.

Notes:

  • The concept of alignment has since evolved and is used to describe the multi-level, dynamic, and interactive mechanisms that underpin the sharing of people’s mental attitudes and representations in all kinds of social interactions (Dale, Fusaroli, & Duran, 2013). (pp 253)
  • The underlying justification for subsuming all these cases under the same mechanism is that cognition and action cannot be separated. The sharing of minds and bodies can then be conceptualized in terms of an integrated system of alignment, defined as the dynamic coupling of behavioural and/or cognitive states of two people (Dumas, Laroche, & Lehmann, 2014). (pp 253)
  • we are interested in the explanatory significance of alignment for a more general theory of social interaction, not in instrumental behaviour and/or alignment per se. (pp 254)
  • The central claim of this paper is that the alignment of minds, which emerges in social interactions, involves the reciprocal exchange of information whereby individuals adjust minds and bodies in a graded and dynamic manner. As these processes of alignment unfold, interacting partners will exchange information about each other’s minds and therefore act socially, whether or not a shared goal is in place. (pp 254)
  • In particular, in recent theoretical and empirical work on social cognition, reciprocity is increasingly recognized as a useful resource to capture the ‘‘jointness” of a joint action.Interpersonal understanding can be achieved by reading into one another’s mind reciprocally (Butterfill, 2013), and an explanation of the processes whereby the alignment of minds and bodies unfolds in space and time should involve an account of reciprocity (Zahavi & Rochat, 2015). In the process of a reciprocal exchange of information, individuals may adapt to varying degrees to one another. This is certainly the case in instances of temporal synchronisation and coordination in which physical alignment in time and space has been theorized to depend on cognitive models of adaptation (Elliott, Chua, & Wing, 2016Hayashi & Kondo, 2013Repp & Su, 2013) and thus on reciprocal interactions (D’Ausilio, Novembre, Fadiga, & Keller, 2015Keller, Novembre, & Hove, 2014Tognoli & Kelso, 2015). The behaviour of one player results in a change in behaviour of the other in a reciprocal way so as to achieve temporal synchrony. Interestingly, though not surprisingly, this reciprocal exchange of information results in physical alignment, which in turn has also been shown to result in greater degrees of affiliation and greater mental alignment (Hove & Risen, 2009Rabinowitch & Knafo-Noam, 2015Wiltermuth & Heath, 2009). Specifically, we suggest that, rather than a focus on the sharedness of the intended goal, we should attend to the graded exchange of information that creates alignment. The most social of interactions, in our formulation, are those in which ‘‘live” (‘‘online”, see Schilbach, 2014) information is exchanged dynamically (i.e. over time, across multiple points) bidirectionally and used to adapt behaviour and align with another (Jasmin et al., 2016). (pp 255)
  • Indeed, it is possible to have reciprocity and thus social interaction without cooperation. This would be the case, for example, in a competitive scenario in which the minds of the subjects are aligned at the appropriate level of description, and the sharing is essential to solve social dilemmas involving antagonistic behaviour (Bratman, 2014). In these exchanges, what is needed for the minds of the agents to attune to one another is that they adapt thoughts, bodily postures and movements, to take one another into account and reason as a team, even though the team might consist of competitive actors where none is aware that they are acting from the perspective of the same group and in the pursuit of some common goal (Bacharach, 2006). (pp 255)
  • fundamentally social nature has to do with the process whereby systems reciprocate thoughts and experiences, rather than with the endpoint i.e. the goal. It turns out that two features are often taken to be central to the process whereby interacting agents align minds and bodies. First, the interacting agents must be aware that they are doing something together with others. Second, the success of their joint performance is taken as a measure of how shared the participants’ goals are. (pp 255)
  • our suggestion is that what matters for the relevant alignment of minds and bodies to occur is the reciprocal exchange of information, not awareness of the reciprocal exchange of information. (pp 255)
    • This is all that is needed for flocking to happen. It is the range of that exchange that determines the phase change from independent to flock to stampede. Trust is involved in the reciprocity too, I think
  • Becoming mutually aware that we are sharing attitudes, dispositions, bodily postures, perhaps goals, does not mean that the ‘jointness’ of our actions has become available to each of us for conscious report. Reciprocity of awareness is emphatically not the same as awareness of reciprocity. The process of reciprocally exchanging information and mutually adapting to one another need not necessarily result in any degree of shared awareness. (pp 256)
  • In animals, a signal, for example about the source of food, that is too weak for an individual fish to follow can be followed by a group through the simple rules of bodily alignment that create shoaling behaviour (Grunbaum, 1998). Shoaling behaviour can also be observed in humans (Belz, Pyritz, & Boos, 2013), who can achieve group advantage through more complex forms of adjustment than just bodily alignment. Pairs of participants trying to detect a weak visual signal can achieve a greater group advantage when they align the terms they use to report their confidence in what they saw (Fusaroli et al., 2012). Indeed, linguistic alignment at many levels can be observed in dialogue (Pickering & Garrod, 2004) and can improve comprehension (Adank, Hagoort, & Bekkering, 2010; Fusaroli et al., 2012). (pp 256)
  • Much research has been driven, so far, by the implicit goal of identifying optimal group performance as a proxy for mental alignment (Fusaroli et al., 2012), however, there is conceptual room and empirical evidence for arguing that optimal task performance is not a good index of mental alignment or ‘optimal sociality’. In other words, taking achievement of a shared goal as the paradigm of a social interaction leads to the binary conception of sociality according to which an interaction is either (optimally) social, or it is not. (pp 256)
    • This is a problem that I have with opinion dynamics models. Convergence on a particular opinion isn’t the only issue. There is a dynamic process where opinions fall in and out of favor. This is the difference between the contagion model, which is one way (uninfected->infected) and motion through belief space. The goal really doesn’t matter, except in a subset of cases (Though these may be very important)
  • Two systems can interact when they have access to information relating to each other (Bilek et al., 2015). There are different ways of exchanging information between systems and hence different types of interaction (Liu & Pelowski, 2014), but in everycase some kind of alignment occurs (Coey, Varlet, & Richardson, 2012Huygens, 1673). (pp 257)
  • Such offline interaction can be contrasted with the case of online social interactions, where both participants act. The distinction between offline and online social interaction tasks is now acknowledged as crucial for advancing our understanding of the cognition processes underlying social interaction (Schilbach, 2014). (pp 257)
  • In contrast to salsa, consider the case of tango in which movements are improvised and as such require constant, mutual adaptation (Koehne et al., 2015; Tateo, 2014). Tango dancers have access to information relating to each other and, by virtue of the task, they exchange information with one another across time in a reciprocal and bidirectional fashion. The juxtaposition of tango with salsa highlights a spectrum of degrees of mutual reciprocity, with a richer form of interaction and greater need for alignment in tango compared with salsa.
  • we will take reciprocity to be the primary requirement for social interactions. We suggest that reciprocity can be identified with a special kind of alignment, mutual alignment, involving adjustment in both parties to the interaction. However, not all cases of joint action lead to mutual alignment. It is important to distinguish this mutual alignment from other types of alignment, which do not involve a reciprocal exchange of information between the agents. (pp 257)
  • In contrast to salsa, consider the case of tango in which movements are improvised and as such require constant, mutual adaptation (Koehne et al., 2015Tateo, 2014). Tango dancers have access to information relating to each other and, by virtue of the task, they exchange information with one another across time in a reciprocal and bidirectional fashion. The juxtaposition of tango with salsa highlights a spectrum of degrees of mutual reciprocity, with a richer form of interaction and greater need for alignment in tango compared with salsa. (pp 257)
  • AlignmentInSocialInteractions(pp 258)
  • The biggest challenge currently facing philosophers and scientists of social cognition is to understand social interactions. We suggest that this problem is best approached at the level of processes of mental alignment rather than through joint action tasks based on shared goals, and we propose that the key process is one of reciprocal, dynamic and graded adaptation between the participants in the interaction. Defining social interactions in terms of reciprocal patterns of alignment shows that not all joint actions involve reciprocity and also that social interactions can occur in the absence of shared goals. This approach has two particular advantages. First, it emphasises the key point that interactions can only be fully understood at the level of the group, rather than the individual. The pooling together of individual mental resources generates results that exceed the sum of the individual contributions. But, second, our approach points towards the mechanisms of adaptation that must be occurring within each individual in order to create the interaction (Friston & Frith, 2015). (pp 259)
  • This picture of social interaction in terms of mental alignment suggests two important theoretical developments. One is about a possible way to characterize the idea that types of social interaction lie on a continuum of possible solutions. If we focus on the task or the shared goal being pursued by agents jointly, as the current literature suggests, then only limited subdivisions of types of interaction will emerge. If, however, our focus extends so as to integrate the nature of the interaction, conceived of in terms of information exchange, then we can arrive at a higher degree of resolution of the space in which social interaction lie. This will define a spectrum of types of interaction (not just offline versus online social cognition), suggesting a dimensional rather than a discrete picture. After all, alignment comes in degrees and a spectrum-like definition of sociality implies that there is a variety of forms of alignment and hence of interactions. (pp 269)
    • My work would indicate that meaningful transitions occur for Unaligned (pure explore), Complex (flocking), and Total (stampede).