From I to We: Group Formation and Linguistic Adaption in an Online Xenophobic Forum

From I to We: Group Formation and Linguistic Adaption in an Online Xenophobic Forum

Authors

Venue: Journal of Social and Political Psychology

Quick takeaway:

  • Linguistic study of a xenophobic online chat room using Pennebaker’s LIWC text analytic system. Users who stay in the group change from individual to group pronouns and align linguistically. Cognitive complexity also appears to reduce as users align with the group

Abstract:

  • Much of identity formation processes nowadays takes place online, indicating that intergroup differentiation may be found in online communities. This paper focuses on identity formation processes in an open online xenophobic, anti-immigrant, discussion forum. Open discussion forums provide an excellent opportunity to investigate open interactions that may reveal how identity is formed and how individual users are influenced by other users. Using computational text analysis and Linguistic Inquiry Word Count (LIWC), our results show that new users change from an individual identification to a group identification over time as indicated by a decrease in the use of “I” and increase in the use of “we”. The analyses also show increased use of “they” indicating intergroup differentiation. Moreover, the linguistic style of new users became more similar to that of the overall forum over time. Further, the emotional content decreased over time. The results indicate that new users on a forum create a collective identity with the other users and adapt to them linguistically.

Notes:

  • Social influence is broadly defined as any change – emotional, behavioral, or attitudinal – that has its roots in others’ real or imagined presence (Allport, 1954). (pg 77)
  • Regardless of why an individual displays an observable behavioral change that is in line with group norms, social identification with a group is the basis for the change. (pg 77)
  • In social psychological terms, a group is defined as more than two people that share certain goals (Cartwright & Zander, 1968). (pg 77)
  • Processes of social identification, intergroup differentiation and social influence have to date not been studied in online forums. The aim of the present research is to fill this gap and provide information on how such processes can be studied through language used on the forum. (pg 78)
  • The popularity of social networking sites has increased immensely during the last decade. At the same time, offline socializing has shown a decline (Duggan & Smith, 2013). Now, much of the socializing actually takes place online (Ganda, 2014). In order to be part of an online community, the individual must socialize with other users. Through such socializing, individuals create self-representations (Enli & Thumim, 2012). Hence, the processes of identity formation, may to a large extent take place on the Internet in various online forums. (pg 78)
  • For instance, linguistic analyses of American Nazis have shown that use of third person plural pronouns (they, them, their) is the single best predictor of extreme attitudes (Pennebaker & Chung, 2008). (pg 79)
  • Because language can be seen as behavior (Fiedler, 2008), it may be possible to study processes of social influence through linguistic analysis. Thus, our second hypothesis is that the linguistic style of new users will become increasingly similar to the linguistic style of the overall forum over time (H2). (pg 79)
  • This indicates that the content of the posts in an online forum may also change over time as arguments become more fine-tuned and input from both supporting and contradicting members are integrated into an individual’s own beliefs. This is likely to result (linguistically) in an increase in indicators of cognitive complexity. Hence, we hypothesize that the content of the posts will change over time, such that indicators of complex thinking will increase (H3a). (pg 80)
    • I’m not sure what to think about this. I expect from dimension reduction, that as the group becomes more aligned, the overall complex thinking will reduce, and the outliers will leave, at least in the extreme of a stampede condition.
  • This result indicates that after having expressed negativity in the forum, the need for such expressions should decrease. Hence, we expect that the content of the posts will change such that indicators of negative emotions will decrease, over time (H3b). (pg 80)
  • the forum is presented as a “very liberal forum”, where people are able to express their opinions, whatever they may be. This “extreme liberal” idea implies that there is very little censorship the forum is presented as a “very liberal forum”, where people are able to express their opinions, whatever they may be. This “extreme liberal” idea implies that there is very little censorship, which has resulted in that the forum is highly xenophobic. Nonetheless, due to its liberal self-presentation, the xenophobic discussions are not unchallenged. For example, also anti-racist people join this forum in order to challenge individuals with xenophobic attitudes. This means that the forum is not likely to function as a pure echo chamber, because contradicting arguments must be met with own arguments. Hence, individuals will learn from more experienced users how to counter contradicting arguments in a convincing way. Hence, they are likely to incorporate new knowledge, embrace input and contribute to evolving ideas and arguments. (pg 81)
    • Open debate can lead to the highest level of polarization (M&D)
    • There isn’t diverse opinion. The conversation is polarized, with opponents pushing towards the opposite pole. The question I’d like to see answered is has extremism increased in the forum?
  • Natural language analyses of anonymous social media forums also circumvent social desirability biases that may be present in traditional self-rating research, which is a particular important concern in relation to issues related to outgroups (Maass, Salvi, Arcuri, & Semin, 1989; von Hippel, Sekaquaptewa, & Vargas, 1997, 2008). The to-be analyzed media uses “aliases”, yielding anonymity of the users and at the same time allow us to track individuals over time and analyze changes in communication patterns. (pg 81)
    • After seeing “Ready Player One”, I also wonder if the aliases themselves could be looked at using an embedding space built from the terms used by the users? Then you get distance measurements, t-sne projections, etc.
  • Linguistic Inquiry Word Count (LIWC; Pennebaker et al., 2007; Chung & Pennebaker, 2007; Pennebaker, 2011b; Pennebaker, Francis, & Booth, 2001) is a computerized text analysis program that computes a LIWC score, i.e., the percentage of various language categories relative to the number of total words (see also www.liwc.net). (pg 81)
    • LIWC2015 ($90) is the gold standard in computerized text analysis. Learn how the words we use in everyday language reveal our thoughts, feelings, personality, and motivations. Based on years of scientific research, LIWC2015 is more accurate, easier to use, and provides a broader range of social and psychological insights compared to earlier LIWC versions
  • Figure 1c shows words overrepresented in later posts, i.e. words where the usage of the words correlates positively with how long the users has been active on the forum. The words here typically lack emotional content and are indicators of higher complexity in language. Again, this analysis provides preliminary support for the idea that time on the forum is related to more complex thinking, and less emotionality.
    • WordCloud
  • The second hypothesis was that the linguistic style of new users would become increasingly similar to other users on the forum over time. This hypothesis is evaluated by first z-transforming each LIWC score, so that each has a mean value of zero and a standard deviation of one. Then we measure how each post differs from the standardized values by summing the absolute z-values over all 62 LIWC categories from 2007. Thus, low values on these deviation scores indicate that posts are more prototypical, or highly similar, to what other users write. These deviation scores are analyzed in the same way as for Hypothesis 1 (i.e., by correlating each user score with the number of days on the forum, and then t-testing whether the correlations are significantly different from zero). In support of the hypothesis, the results show an increase in similarity, as indicated by decreasing deviation scores (Figure 2). The mean correlation coefficient between this measure and time on the forum was -.0086, which is significant, t(11749) = -3.77, p < 0.001. (pg 85)
    • ForumAlignmentI think it is reasonable to consider this a measure of alignment
  • Because individuals form identities online and because we see this in the use of pronouns, we also expected to see tendencies of social influence and adaption. This effect was also found, such that individuals’ linguistic style became increasingly similar to other users’ linguistic style over time. Past research has shown that accommodation of communication style occurs automatically when people connect to people or groups they like (Giles & Ogay 2007; Ireland et al., 2011), but also that similarity in communicative style functions as cohesive glue within a group (Reid, Giles, & Harwood, 2005). (pg 86)
  • Still, the results could not confirm an increase in cognitive complexity. It is difficult to determine why this was not observed even though a general trend to conform to the linguistic style on the forum was observed. (pg 87)
    • This is what I would expect. As alignment increases, complexity, as expressed by higher dimensional thinking should decrease.
  • This idea would also be in line with previous research that has shown that expressing oneself decreases arousal (Garcia et al., 2016). Moreover, because the forum is not explicitly racist, individuals may have simply adapted to the social norms on the forum prescribing less negative emotional displays. Finally, a possible explanation for the decrease in negative emotional words might be that users who are very angry leave the forum, because of its non-racist focus, and end up in more hostile forums. An interesting finding that was not part of the hypotheses in the present research is that the third person plural category correlated positively with all four negative emotions categories, suggesting that people using for example ‘they’ express more negative emotions (pg 87)
  • In line with social identity theory (Tajfel & Turner, 1986), we also observe linguistic adaption to the group. Hence, our results indicate that processes of identity formation may take place online. (pg 87)

Influence of augmented humans in online interactions during voting events

Influence of augmented humans in online interactions during voting events

  • Massimo Stella (Scholar)
  • Marco Cristoforetti (Scholar)
  • Marco Cristoforetti (Scholar)
  • Abstract: Overwhelming empirical evidence has shown that online social dynamics mirrors real-world events. Hence, understanding the mechanisms leading to social contagion in online ecosystems is fundamental for predicting, and even manouvering, human behavior. It has been shown that one of such mechanisms is based on fabricating armies of automated agents that are known as social bots. Using the recent Italian elections as an emblematic case study, here we provide evidence for the existence of a special class of highly influential users, that we name “augmented humans”. They exploit bots for enhancing both their visibility and influence, generating deep information cascades to the same extent of news media and other broadcasters. Augmented humans uniformly infiltrate across the full range of identified clusters of accounts, the latter reflecting political parties and their electoral ranks.
  • Bruter and Harrison [19] shift the focus on the psychological in uence that electoral arrangements exert on voters by altering their emotions and behavior. The investigation of voting from a cognitive perspective leads to the concept of electoral ergonomics: Understanding optimal ways in which voters emotionally cope with voting decisions and outcomes leads to a better prediction of the elections. (pg 1)
  • Most of the Twitter interactions are from humans to bots (46%); Humans tend to interact with bots in 56% of mentions, 41% of replies and 43% of retweets. Bots interact with humans roughly in 4% of the interactions, independently on interaction type. This indicates that bots play a passive role in the network but are rather highly mentioned/replied/retweeted by humans. (pg 2)
  • bots’ locations are distributed worldwide and they are present in areas where no human users are geo-localized such as Morocco.  (pg 2)
  • Since the number of social interactions (i.e., the degree) of a given user is an important estimator of the in uence of user itself in online social networks [1722], we consider a null model fixing users’ degree while randomizing their connections, also known as configuration model [2324].  (pg 2)
  • During the whole period, bot bot interactions are more likely than random (Δ > 0), indicating that bots tend to interact more with other bots rather than with humans (Δ < 0) during Italian elections. Since interactions often encode the spread of a given content online [16], the positive assortativity highlights that bots share contents mainly with each other and hence can resonate with the same content, be it news or spam.  (pg 2)
  • Differently from previous works, where the semantic content of bots and humans differs in its emotional polarity [12], in here we nd that bots mainly repeat the same political content of human users, thus boosting the spreading of hashtags strongly related to the electoral process, such as hashtags referring to the government or to political victory, names of political parties or names of influential politicians (see also 3). (pg 4)
  • Frequencies of individual hashtags during the whole electoral process display some interesting shifts, reported in Table III (Top). For instance, the hashtag #exitpoll, indicating the electoral outcome, becomes 10000 times more frequent on the voting day than before March 4. These shifts indicate that the frequency of hashtags reflects real-world events, thus underlining the strong link between online social dynamics and the real-world electoral process. (pg 4)
  • TABLE II. Top influencers are mostly bots. Hubs characterize influential users and broadcasters in online social systems [17], hence we use degree rankings for identifying the most in uential users in the network. (pg 5)
  • bots are mostly influential nodes which tend to interact mostly with other bots rather than humans and, when they interact with human users, they preferentially target the most influential ones. (pg 5)
  • we first filter the network by considering only pair of users with at least one retweet, with either direction, because re-sharing content it is often a good proxy of social endorsement [21]. However, Retweets alone are not sufficient to wash out the noise intrinsic to systems like Twitter, therefore we apply a more selective restriction, by requiring that at least another social action – i.e., either mention or reply – must be present in addition to a retweet [12]. This restrictive selection allows one to filter out all spurious interactions among users with the advantage of not requiring any thresholding approach with respect to the frequency of interactions themselves. (pg 5)
  • The resulting network is what we call the social bulk, i.e. a network core of endorsement and exchange among users. By construction, information ows among users who share strong social relationships and are characterized by similar ideologies: in fact, when a retweet goes from one user to another one, both of them are endorsing the same content, thus making non-directionality a viable approach for representing the endorsement related to content sharing. (pg 5)
  • Fiedler partitioning
  • The relevant literature has used the term “cyborg” for identifying indistinctly bot-assisted human or human-assisted bot accounts generating spam content over social platforms such as Twitter [5, 35]. Here, we prefer to use the term \augmented human” for indicating specifically those human accounts exploiting bots for artificially increasing, i.e. augmenting, their in uence in online social platforms, analogously to physical augmentation improving human performances in the real world [36]. (pg 8)
  • Baseline social behavior is defined by the medians of the two observables, like shown in Fig. 6c. This map allows to easily identify four categories of individuals in the social dynamics: i) hidden in uentials, generating information cascades rapidly spreading from a large small number of followers; ii) in uentials, generating information cascades rapidly spreading from a large number of followers; iii) broadcasters, generating information cascades slowly spreading from a large number of followers; iv) common users, generating information cascades slowly spreading from a small number of followers. (pg 9)
  • Hidden influentials, known to be efficient spreaders in viral phenomena [45], are mostly humans: in this category falls the augmented humans, assisted by social bots to increase their online visibility. (pg 10)
  • We define augmented humans as human users having at least 50% + 1 of bot neighbours in the social bulk. We discard users having less than 3 interactions in the social bulk. (pg 10)
  • The most central augmented human in terms of number of social interactions is Utente01, which interacts with 2700 bots and 55 humans in the social bulk. (pg 10)
  • The above cascade analysis reveals that almost 2 out 3 augmented humans resulted playing an important role in the flow of online content: 67% of augmented humans were either influentials or hidden influentials or broadcasters. These results strongly support the idea that via augmentation even common users can become social influencers without having a large number of followers/friends but rather by recurring to the aid of either armies of bots (e.g., Utente01, an hidden in uential) or the selection of a few key helping bots. (pg 11)

Beyond Individual Choice

Beyond Individual Choice: Teams and Frames in Game Theory

  • Michael Bacharach
  • Natalie Gold
  • Robert Sugden
  • From Amazon.com: In the classical tradition of game theory, Bacharach models human beings as rational actors, but he revises the standard definition of rationality to incorporate two major new ideas. He enlarges the model of a game so that it includes the ways agents describe to themselves (or “frame”) their decision problems. And he allows the possibility that people reason as members of groups (or “teams”), each taking herself to have reason to perform her component of the combination of actions that best achieves the group’s common goal. Bacharach shows that certain tendencies for individuals to engage in team reasoning are consistent with recent findings in social psychology and evolutionary biology.
  • The following list of notes is oldest (bottom) to newest (top)
  • It is a central component of resolute choice, as presented by McClennen, that (unless new information becomes available) later transient agents recognise the authority of plans made by earlier agents. Being resolute just is recognising that authority (although McClennen’ s arguments for the rationality and psychological feasibility of resoluteness apply only in cases in which the earlier agents’ plans further the common ends of earlier and later agents). This feature of resolute choice is similar to Bacharach’ s analysis of direction, explained in section 5. If the relationship between transient agents is modelled as a sequential game, resolute choice can be thought of as a form of direction, in which the first transient agent plays the role of director; the plan chosen by that agent can be thought of as a message sent by the director to the other agents. To the extent that each later agent is confident that this plan is in the best interests of the continuing person, that confidence derives from the belief that the first agent identified with the person and that she was sufficiently rational and informed to judge which sequence of actions would best serve the person’s objectives. (pg 197)
  • The problem posed by Heads and Tails is not that the players lack a common understanding of salience; it is that game theory lacks an adequate explanation of how salience affects the decisions of rational players. All we gain by adding preplay communication to the model is the realisation that game theory also lacks an adequate explanation of how costless messages affect the decisions of rational players. (pg 180)
  • The fundamental principle of this morality is that what each agent ought to do is to co-operate, with whoever else is co-operating, in the production of the best consequences possible given the behaviour of non-co-operators’ (Regan 1980, p. 124). (pg 167)
  • Ordered On Social Facts
    • Are social groups real in any sense that is independent of the thoughts, actions, and beliefs of the individuals making up the group? Using methods of philosophy to examine such longstanding sociological questions, Margaret Gilbert gives a general characterization of the core phenomena at issue in the domain of human social life.
  • Schema 3: Team reasoning (from a group viewpoint) pg 153
    • We are the members of S.
    • Each of us identifies with S.
    • Each of us wants the value of U to be maximized.
    • A uniquely maximizes U.
    • Each of us should choose her component of A.
  • Schema 4: Team reasoning (from an individual viewpoint) pg 159
    • I am a member of S.
    • It is common knowledge in S that each member of S identifies
      with S.
    • It is common knowledge in S that each member of S wants the
      value of U to be maximized.
    • It is common knowledge in S that A uniquely maximizes U.
    • I should choose my component of A.
  • Schema 7: Basic team reasoning pg 161
    • I am a member of S.
    • It is common knowledge in S that each member of S identifies
      with S.
    • It is common knowledge in S that each member of S wants the
      value of U to be maximized.
    • It is common knowledge in S that each member of S knows his
      component of the profile that uniquely maximizes U.
    • I should choose my component of the profile that uniquely
      maximizes U.

      • Bacharach notes to himself the ‘hunch’ that this schema is ‘the basic rational capacity’ which leads to high in Hi-Lo, and that it ‘seems to be indispensable if a group is ever to choose the best plan in the most ordinary organizational circumstances’. Notice that Schema 7 does not require that the individual who uses it know everyone’s component of the profile that maximizes U.
  • His hypothesis is that group identification is an individual’s psychological response to the stimulus of a particular decision situation. It is not in itself a group action. (To treat it as a group action would, in Bacharach’ s framework, lead to an infinite regress.) In the theory of circumspect team reasoning, the parameter w is interpreted as a property of a psychological mechanism-the probability that a person who confronts the relevant stimulus will respond by framing the situation as a problem ‘for us’. The idea is that, in coming to frame the situation as a problem ‘for us’, an individual also gains some sense of how likely it is that another individual would frame it in the same way; in this way, the value of w becomes common knowledge among those who use this frame. (Compare the case of the large cube in the game of Large and Small Cubes, discussed in section 4 of the introduction.) Given this model, it seems that the ‘us’ in terms of which the problem is framed must be determined by how the decision situation first appears to each individual. Thus, except in the special case in which w == 1, we must distinguish S (the group with which individuals are liable to identify, given the nature of the decision situation) from T (the set of individuals who in fact identify with S). pg 163
  • The psychology of group identity allows us to understand that group identification can be due to factors that have nothing to do with the individual preferences. Strong interdependence and other forms of common individual interest are one sort of favouring condition, but there are many others, such as comembership of some existing social group, sharing a birthday, and the artificial categories of the minimal group paradigm. (pg 150)
  • Wherever we may expect group identity we may also expect team reasoning. The effect of team reasoning on behavior is different from that of individualistic reasoning. We have already seen this for Hi-Lo. This has wide implications. It makes the theory of team reasoning a much more powerful explanatory and predictive theory than it would be if it came on line only in games with th3e right kind of common interest. To take just one example, if management brings it about so that the firm’s employees identify with the firm, we may expect for them to team-reason and so to make choices that are not predicted by the standard theories of rational choice.(pg 150)
  • As we have seen, the same person passes through many group identities in the flux of life, and even on a single occasion more than one of these identities may be stimulated. So we will need a model of identity in which the probability of a person’s identification is distributed over not just two alternatives-personal self-identity or identity with a fixed group-but, in principle, arbitrarily many. (pg 151)
  • The explanatory potential of team reasoning is not confined to pure coordination games like Hi-Lo. Team reasoning is assuredly important for its role in explaining the mystery facts about Hi-Lo; but I think we have stumbled on something bigger than a new theory of behaviour in pure coordination games. The key to endogenous group identification is not identity of interest but common interest giving rise to strong interdependence. There is common interest in Stag Hunts, Battles of the Sexes, bargaining games and even Prisoner’s Dilemmas. Indeed, in any interaction modelable as a ‘mixed motive’ game there is an element of common interest. Moreover, in most of the landmark cases, including the Prisoner’s Dilemma, the common interest is of the kind that creates strong interdependence, and so on the account of chapter 2 creates pressure for group identification. And given group identification, we should expect team reasoning.(pg 144)
  • There is a second evolutionary argument in favour of the spontaneous team-reasoning hypothesis. Suppose there are two alternative mental mechanisms that, given common interest, would lead humans to act to further that interest. Other things being equal, the cognitively cheapest reliable mechanism will be favoured by selection. As Sober and Wilson (1998) put it, mechanisms will be selected that score well on availability, reliability and energy efficiency. Team reasoning meets these criteria; more exactly, it does better on them than the alternative heuristics suggested in the game theory and psychology literature for the efficient solution of common-interest games. (pg 146)
  • BIC_pg 149 (pg 149)
  • I think MB is getting at the theory for why there is explore/exploit in populations
  • We have progressed towards a plausible explanation of the behavioural fact about Hi-Lo. It is explicable as an outcome of group identification by the players, because this is likely to produce a way of reasoning, team reasoning, that at once yields A. Team reasoning satisfies the conditions for the mode-P reasoning that we concluded in chapter 1 must be operative if people are ever to reason their way to A. It avoids magical thinking. It takes the profile-selection problem by the scruff of the neck. What explains its onset is an agency transformation in the mind of the player; this agency transformation leads naturally to profile-based reasoning and is a natural consequence of self-identification with the player group. (pg 142)
  • Hi-Lo induces group identification. A bit more fully: the circumstances of Hi-Lo cause each player to tend to group-identify as a member of the group G whose membership is the player-set and whose goal is the shared payoff. (pg 142)
  • If what induces A-choices is a piece of reasoning which is part of our mental constitution, we are likely to have the impression that choosing A is obviously right. Moreover, if the piece of reasoning does not involve a belief that the coplayer is bounded, we will feel that choosing A is obviously right against a player as intelligent as ourselves; that is, our intuitions will be an instance of the judgemental fact. I suspect, too, that if the reasoning schema we use is valid, rather than involving falacy, our intuitions of reality are likely to be more robust. Later I shall argue that team reasoning is indeed nonfallacious. (pg 143)
    • I think this is more than “as intelligent as ourselves”, I think this is a position/orientation/velocity case. I find it compelling that people with different POVs regard each other as ‘stupid’
    • When framing tendencies are culture-wide, people in whom a certain frame is operative are aware that it may be operative in others; and if its availability is high, those in it think that it is likely to be operative in others. Here the framing tendency is-so goes my claim-universal, and a fortiori it is culture-wide. (pg 144)
    • But for the theory of endogenous team reasoning there are two differences between the Hi-Lo case and these other cases of strong interdependence. First, outside Hi-Los there are counterpressures towards individual self-identification and so I-framing of the problem. In my model this comes out as a reduction in the salience of the strong interdependence, or an increase in that of other features. One would expect these pressures to be very strong in games like Prisoner’s Dilemma, and the fact that C rates are in the 40 per cent range rather than the 90 percent range, so far from surprising, is a prediction of the present theory (pg 144)
      • This is where MB starts to get to explore/exploit in populations. There are pressueres that drive groups together and apart. And as individuals, our thresholds for group identification varies
  • Now it is the case, and increasingly widely recognized to be, that in games in general there’s no way players can rationally deliberate to a Nash equilibrium. Rather, classical canons of rationality do not in general support playing in Nash equilibria. So it looks as though shared intentions cannot, in the general run of games, by classical canons, be rationally formed! And that means in the general run of life as well. This is highly paradoxical if you think that rational people can have shared intentions. The paradox is not resolved by the thought that when they do, the context is not a game: any situation in which people have to make the sorts of decisions that issue in shared intentions must be a game, which is, after all, just a situation in which combinations of actions matter to the combining parties. (pg 139)
  • Turn to the idea that a joint intention to do (x,y) is rationally produced in 1 and 2 by common knowledge of two conditional intentions: Pl has the intention expressed by ‘I’ll do x if and only if she does y’, and P2 the counterpart one. Clearly P1 doesn’t have the intention to do x if and. only if P2 in fact does y whether or not Pl believes P2 will do y; the right condition must be along the lines of:
    (C1) P1 intends to do x if and only if she believes P2 will do y. (pg 139)

    • So this is in belief space, and belief is based on awareness and trust
  • There are two obstacles to showing this, one superable, the other not, I think. First, there are two Nash equilibria, and nothing in the setup to suggest that some standard refinement (strengthening) of the Nash equilibrium condition will eliminate one. However, I suspect that my description of the situation could be refined without ‘changing the subject’. Perhaps the conditional intention Cl should really be ‘I’ll do x if and only if she’ll do y, and that’s what I would like best’. For example, if x and y are the two obligations in a contract being discussed, it is natural to suppose that Pl thinks that both signing would be better than neither signing. If we accept this gloss then the payoff structure becomes a Stag Hunt – Hi-Lo if both are worse off out of equilibrium than in the poor equilibrium (x’ ,y’). To help the cause of rationally deriving the joint intention (x,y), assume the Hi-Lo case. What are the prospects now? As I have shown in chapter 1, there is no chance of deriving (x,y) by the classical canons, and the only (so far proposed) way of doing to is by team reasoning. (pg 140)
  • The nature of team reasoning, and of the conditions under which it is likely to be primed in individual agents, has a consequence that gives further support to this claim. This is that joint intentions arrived at by the route of team reasoning involve, in the individual agents, a ‘sense of collectivity’. The nature of team reasoning has this effect, because the team reasoner asks herself not ‘What should I do?’ but ‘What should we do?’ So, to team-reason, you must already be in a frame in which first-person plural concepts are activated. The priming conditions for team reasoning have this effect because, as we shall see later in this chapter, team reasoning, for a shared objective, is likely to arise spontaneously in an individual who is in the psychological state of group-identifying with the set of interdependent actors; and to self-identify as a member of a group essentially involves a sense of collectivity. (pg 141)
  • One of the things that MB seems to be saying here is that group identification has two parts. First is the self-identification with the group. Second is the mechanism that supports that framing. You can’t belong to a group you don’t see.
  • To generalize the notions of team mechanism and team to unreliable contexts, we need the idea of the profile that gets enacted if all the agents function under a mechanism. Call this the protocol delivered by the mechanism. The protocol is , roughly, what everyone is supposed to do, what everyone does if the mechanism functions without any failure. But because there may well be failures, the protocol of a mechanism may not get enacted, some agents not playing their part but doing their default actions instead. For this reason the best protocol to have is not in general the first-best profile o*. In judging mechanisms we must take account of the states of the world in which there are failures, with their associated probabilities. How? Put it this way: if we are choosing a mechanism, we want one that delivers the protocol that maximizes the expected value of U. (pg 131)
  • Group identification is a framing phenomenon. Among the many different dimensions of the frame of a decision-maker is the ‘unit of agency’ dimension: the framing agent may think of herself as an individual doer or as part of some collective doer. The first type of frame is operative in ordinary game-theoretic, individualistic reasoning, and the second in team reasoning. The concept-clusters of these two basic framings center round ‘I/ she/he’ concepts and ‘we’ concepts respectively. Players in the two types of frame begin their reasoning with the two basic conceptualizations of the situation, as a ‘What shall I do?’ problem, and a ‘What shall we do?’ problem, respectively. (pg 137)
  • A mechanism is a general process. The idea (which I here leave only roughly stated) is of a causal process which determines (wholly or partly) what the agents do in any simple coordination context. It will be seen that all the examples I have mentioned are of this kind; contrast a mechanism that applies, say, only in two-person cases, or only to matching games, or only in business affairs. In particular, team reasoning is this kind of thing. It applies to any simple coordination context whatsoever. It is a mode of reasoning rather than an argument specific to a context. (pg 126)
  • In particular, [if U is Paretian] the correct theory of Hi-Lo says that all play A. In short, an intuition in favour of C’ supports A-playing in Hi-Lo if we believe that all players are rational and there is one rationality. (pg 130)
    • Another form of dimension reduction – “We are all the same”
  • There are many conceivable team mechanisms apart from simple direction and team reasoning; they differ in the way in which computation is distributed and the pattern of message sending. For example, one agent might compute o* and send instructions to the others. With the exception of team reasoning, these mechanisms involve the communication of information. If they do I shall call them modes of organization or protocols. (pg 125)
  • A mechanism is a general process. The idea (which I here leave only roughly stated) is of a causal process which determines (wholly or partly) what the agents do in any simple coordination context. It will be seen that all the examples I have mentioned are of this kind; contrast a mechanism that applies, say, only in two-person cases, or only to matching games, or only in business affairs. In particular, team reasoning is this kind of thing. It applies to any simple coordination context whatsoever. It is a mode of reasoning rather than an argument specific to a context. (pg 126)
  •  .
    • BIC_102 (page 102)
    • BIC107 (pg 107)
    • BIC107b (pg 107)
  • Evolutionary reasons for cooperation as group fitness, where group payoff is maximized. This makes the stag salient in stag hunt.
  • Explaining the evolution of any human behavior trait (say, a tendency to play C in Prisoner’s Dilemmas) raises three questions. The first is the behavior selection question: why did this trait, rather than some other, get selected by natural selection? Answering this involves giving details of the selection process, and saying what made the disposition confer fitness in the ecology in which selection took place. But now note that ‘When a behavior evolves, a proximate mechanism also must evolve that allows the organism to produce the target behavior. Ivy plants grow toward the light. This is a behavior, broadly construed. For phototropism to evolve, there must be some mechanism inside of ivy plants that causes them to grow in one direction rather than in another’ (Sober and Wilson 1998, pp. 199-200). This raises the second question, the production question: how is the behavior produced within the individual-what is the ‘proximate mechanism’? In the human case, the interest is often in a psychological mechanism: we ask what perceptual, affective and cognitive processes issue in the behavior. Finally, note that these processes must also have evolved, so an answer to the second question brings a third: why did this proximate mechanism evolve rather than some other that could have produced the same behavior? This is the mechanism selection question. (pg 95)
    • These are good questions to answer, or at least address. Roughly, I thing my answers are
      • Selection Question: The three phases are a very efficient way to exploit an environment
      • Production Question: Neural coupling, as developed in physical swarms and moving on to cognitive clustering
      • Mechanism Question: Oscillator frequency locking provides a natural foundation for  collective behavior. Dimension reduction is how axis are selected for matching.
  • “We need to know, in detail, what deliberations are like that people engage in when they group-identify”. Also, agency transformationAgencyTransformation
  • Dimension reduction is a form of induced conceptual myopia (pg 89)? Conceptual Myopia
  • GroupIdentification
  • Group as Frame
  • Categorizatino and bias

Three views of the Odyssey

  • I’ve been thinking of ways to describe the differences between information visualizations with respect to maps, diagrams, and lists. Here’s The Odyssey as a geographic map:
  • Odysseus'_Journey
  • The first thing that I notice is just how far Odysseus travelled. That’s about half of the Mediterranean! I thought that it all happened close to Greece. Maps afford this understanding. They are diagrams that support the plotting of trajectories.Which brings me to the point that we lose a lot of information about relationships in narratives. That’s not their point. This doesn’t mean that non-map diagrams don’t help sometimes. Here’s a chart of the characters and their relationships in the Odyssey:
  •  odyssey
  • There is a lot of information here that is helpful. And this I do remember and understood from reading the book. Stories are good about depicting how people interact. But though this chart shows relationships, the layout does not really support navigation. For example, the gods are all related by blood and can pretty much contact each other at will. This chart would have Poseidon accessing Aeolus and  Circe by going through Odysseus.  So this chart is not a map.
  • Lastly, is the relationship that comes at us through search. Because the implicit geographic information about the Odyssey is not specifically in the text, a search request within the corpora cannot produce a result that lets us integrate it
  • OdysseySearchJourney
  • There is a lot of ambiguity in this result, which is similar to other searches that I tried which included travelsail and other descriptive terms. This doesn’t mean that it’s bad, it just shows how search does not handle context well. It’s not designed to. It’s designed around precision and recall. Context requires a deeper understanding about meaning, and even such recent innovations such as sharded views with cards, single answers, and pro/con results only skim the surface of providing situationally appropriate, meaningful context.

Some thoughts on alignment in belief space. 

Murmuration

A nagging question for me is why phase locking, a naturally occurring phenomenon, was selected for to produce collective intelligence instead of something else. My intuition is that building communities using rules of physical and cognitive alignment takes advantage of randomness to produce a good balance of explore/exploit behaviors in the population.

Flocking depends on the ability to align, based on a relationship with neighbors. The ease of alignment is proportional to two things (I think).

  1. A low number of dimensions. The fewer the dimensions, the easier the alignment. It is easier to get a herd of cattle to stampede in a slot canyon than an open field. This is the fundamental piece.
  2. A contributing factor to the type of collective behavior is the turning rate with respect to velocity. The easier it is to turn, the easier it is to flock. It’s no accident that starlings, a small, nimble bird, can produce murmurations. Larger birds, such as geese, have much less dynamic formations.

This applies to belief space as well. It is easier for people to agree when a concept is simplified. Similarly, the pattern of consensus will reflect the groups’ overall acceptance or resistance to change. I think this is a critical difference between a progressive and a reactionary. 

Within an established population that exhibits collective behavior, there should be two things then:

  1. A shared perception of a low-dimension physical/belief space
  2. A similar velocity and turning rate between individuals

I’m going to assume that like in most populations, these qualities have a normal distribution. There will be a majority that have very common dimension perception, velocity, and turning rates. There will also be individuals at either tail of the population. At one end, there will be those who see the world very simply. At the other, there will be those who see complexity where the majority don’t. At one end, there will be those who cannot adapt to any change. At the other, there will be those who hold no fixed opinion on anything.

Flocking depends, on alignment. But the individuals at the extremes will have difficulty staying with the relative safety of the flock. This means that there will be selection pressures. Those individuals who oversimplify and are unable to change direction should be selected against. When it’s more important to attend to your neighbors that find food, things don’t end well. What happens at the other end?

There is one tail of this population that produces nimble individuals that perceive a greater complexity in the world. They also have difficulty staying with the flock, because their patterns of behavior are influenced by things that they perceive that the rest of the flock does not. In cooperative game theory, this ‘noticing too much’ disrupts the common frames (alignment) that groups use to make implicit decisions (page 14).

I believe that these individuals become explorers. Explorers are also selected against, but not as much. The additional perception provides a better understanding of potential threats. Nimbleness helps to prevent getting caught. These explores provide an extended footprint for the population, which means greater resilience if the primary population encounters problems.

A population can rebuild from an explorer diaspora. Initially, the population will consist of too many explorers, and will have poor collective behaviors, but over time, selection pressures will push the mean so that there is sufficient alignment for flocking, but not so much that there is regular stampeding.

A final thought. There is no reason that these selection pressures exist only on populations that use genes to control their evolution. Looked at, for example, a machine learning context, the options can be restated (loosely) in statistical language:

  1. Nomadic: Overfit to the environment terms and underfit to the social term
  2. Flocking: Fit with rough equivalence to the environmental and social terms
  3. Stampede: Overfit to the social term and underfit to the environmental term

Since it is always computationally more efficient to align tightly with a population that is moving in the right direction (it’s copying your answers from your classmates), there will always be pressure to move towards stampedes. The resiliency offered by nomadic exploration is a long term investment that does not have a short term payoff. The compromise of flocking gives most of the benefits of either extreme, but it is a saddle point, always under the threat of unanticipated externalities.

When intelligent machines come, they will not be tuned by millions of years of evolution to be resilient, to have all those non-optimal behaviors that “even the odds”, should something unforeseen happen. At least initially, they will be constructed to provide the highest possible return on investment. And, like high-frequency trading systems, stampedes, in the form of bubbles and crashes will happen.

We need to understand this phenomena much more thoroughly, and begin to incorporate concepts like diversity and limited social influence horizons into our designs.

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