Communities, Anti-Communities, Pan-Community as Social Order

Transcription

1 Communities, Anti-Communities, Pan-Community as Social Order Yutaka NAKAI Faculty of Systems Engineering and Science, Shibaura Institute of Technology 307 Fukasaku, Minuma-ku, Saitama-City, Saitama, , Japan Abstract A society consisting of agents who can freely choose to attack or not to attack others inevitably evolves into a battling society (a war of all against all ). We investigated whether the strategies based on group s reputation ( Group s reputation-based Friend Selection Strategies : GFSSs) lead to the emergence and collapse of social order. GFSSs require an agent to evaluate whether others are his friends or enemies, based on whether others were peaceful or hostile to his group and whether others have the same attribute as him or not. We carried out evolutionary simulations on an artificial society with GFSSs agents etc. As a result, we found that three types pf social orders, what we call communities, anti-communities and pan-community, have emerged. For example, the communities consist of two mutually hostile communities, in each of which all members have the sane attribute and are friendly to other members. So, communities can remind us of the famous Max Weber s in-group / out-group morality. Keywords: community, public opinion club, reputation, a friend and an enemy, in-group morality, evolutionary simulation 1. Introduction How does social order emerge among individuals acting freely? This fundamental question in sociology was named the problem of order by T. Parsons (1937). For example, if people, as selfish individuals, can freely choose to attack or not to attack others, the society will inevitably change into a battling society. (Hobbesian state: a war of all against all ) However, real society is not in such a state and seems to have order. For another example, if people could freely choose whether to pay taxes or not, everyone would want to receive public services without paying taxes (so called free riders ), and as a result, nobody would receive public services. However, in real society, public services are maintained by tax revenues. As is well known, a variety of solutions to this problem have been proposed. Typical examples are central authority and social contract (Hobbes, T., 1651), institutionalization and internalization of norms (Parsons, T., 1937), system rationality and reduction of complexity (Luhmann, N., 1968), mutual understanding based on communicative reason (Habermas, J., 1981), and trust based

2 on rational expectation (Coleman, J., 1990). As well known, the Hobbesian state mentioned above can be described as a problem of generalized exchange (indirect reciprocity) under the 2-persons Prisoner s Dilemma (2PD). And, as solutions to the 2PD problem, a variety of reputation theories have been presented recently. These theories evaluate whether the other is good or bad on the basis of third party s reputations about the other, and intend to establish social order by taking revenge on bad persons or excluding them from the society. They can be interpreted as an altruistic strategy toward a selected good man, and are sometimes called discriminator strategies (DISC). As typical examples, we can see the following theories, in-group altruistic strategy (Takagi, E. 1996), imaging score strategy (Novak, M. A. and K. Sigmund 1998), standing strategy (Leimar, O. and P. Hammerstein 2001), and strict discriminator strategy (Takahashi, N. and R. Mashima, R. 2003). Especially, Nakai, Y. and Muto, M. (2005, 2008) studied an emergence of a community and social order. In the study, strategies evaluating who is a friend and who is an enemy are called Friend Selection Strategies (FSSs) and, as one of FSSs, Nakai & Muto proposed the strategy which requires agents to regard the other who attacked us as an enemy and the other who didn t as a friend, which they call us-tft strategy. They pointed out that us-tft leads to social order through the spontaneous formation of community like a collective security system. 2. Group s Reputation-based Friend Selection Strategies (GFSSs) In this study, we investigate whether the social perception of who is a friend and who is an enemy for a group leads to social order (peaceful state) through emergence of community. Here, a group means a collection of all persons who have a common attribute like a race, independently of whether they have relations among them or not. When people begin to be conscious about a concept of group, how do people evaluate others? From the sociological viewpoint, we pay attention to the following viewpoints. (VP1) whether the other attacked a group or not (VP2) whether the other has the same attribute or not Based on the viewpoints, we introduce four categories for the other, as follows. (OC1) The other who has the same attribute, and attacked a group in the previous turn (OC2) The other who has the same attribute, and didn t attack a group in the previous turn (OC3) The other who has the different attribute, and attacked a group in the previous turn (OC4) The other who has the different attribute, and didn t attack a group in the previous turn Because we can assign a friend ( f ) and an enemy ( e ) to each category, we have 16(=2 4 ) types of strategies, as theoretical strategies. And we express these strategies by the notation of G-XXXX, where X is f or e and each of four X corresponds to above (OC1) ~ (OC4) respectively.

3 We call these strategies Group s Reputation-based Friend Selection Strategies (GFSSs). For example, a G-feee agent regards those who have the same attribute as him and attacked his group as enemies and anybodies who have the different attribute from him as enemies, independently of whether they attacked his group or not. And a G-fefe agent regards anybodies who attacked his group as enemies, independently of whether they have the same attribute as him or not. Friend or Enemy? Me Other Definition of 2 4 GFSS strategies Action Attribute Attack (C) No Attack (D) Same Different friend or friend or friend or friend or enemy enemy enemy enemy Group Me C or D? Blue or Red? Action Attribute Attack (C) No Attack (D) Same Different Ex. G-feee strategy f e e e Figure 1. Group s Reputation-based Friend Selection Strategies (GFSSs). 3. Group as Public Opinion Club (POC) Now, we assume a theoretical concept of a club, where members share their own experiences and make reputations about others. The characteristics of the club are as follows. (POC1) All members of a club share their own experiences of who attacked them and who didn t attack them. (POC2) A member is assumed not to inform other members of false information. (POC3) Based on the experiences, all members make and share reputations about others of who were peaceful and who were hostile to their club, like public opinions. That is, a club can be seen as a kind of exchange field of information including reputations about others. And a club holds all members meetings as an exchange field of information. So, hereafter, we call it public opinion club (POC). In this study, we assume that a group forms a public opinion club (a group = a public opinion club). All members of a group are always members of the same POC, and they can t change their POC. That is, members don t leave from and new members don t participate in POC, and so POC can be seen as a fixed club, where people with common race or religion etc make reputations about others. People communicate as POC s members and, at the same time, they are forced to decide who is a friend and who is an enemy. And, at last, they come up with the strategies to evaluate who is a friend and

4 who is an enemy on the basis of their own group s (POC s) reputations. Such strategies are GFSSs mentioned above. Let us compare POC with Nakai & Muto s us. Here, it should be noted that each us-tft agent s us (me plus friends) is mutually different and an us-tft agent evaluates the other on the basis of the other s actions toward the agent s us. Therefore, an us-tft agent has to watch others actions toward him and his friends. And the larger his us becomes, the more difficult it is to watch all his friends experiences, because of his limited capability. That is, us-tft strategy has such a weak point that it doesn t work well in a large-scale society. In contrast, a POC member doesn t have to watch what happened to other members and, instead, he just informs other members of his own experiences and participates in discussion of reputations about others. Therefore, GFSSs don t require members a lot of effort even in a larger society and so they don t suffer from the us-tft s problem. In sum, GFSSs may work well in such a large society, compared to us-tft. 4. Evolutionary Simulation of Peace In order to examine whether GFSSs result in social order (peaceful state), we constructed an artificial society and carried out evolutionary simulations. In the artificial society, agents play the following battle game. Let us note that the battle game can be described as generalized exchanges under 2PD problem. (BG1) N agents play the game. (BG2) Each agent has a social perception of who is a friend and who is an enemy. (BG3) In one battle game, each agent (agent A) meets M other agents at random. (M stands for the matching number of one agent in one game.) Each agent (agent A) interacts with the other agent (agent B) one by one. (BG4) Agent A (as a performer) attacks or doesn t attack agent B (as a performed) on the basis of A s social perception of B. A attacks B if B is A s enemy, and A doesn t attack B if B is A s friend. (BG5) If A attacks B, A obtains a payoff of 0.5 and B loses a payoff of 3.0. Conversely, if A doesn t attack Performer B, both obtain and lose nothing (Figure 2). No Attack Performed C = 0 = 0 Attack D = +0.5 =-3.0 person Action No Attack (C) Attack (D) Performed Performer Agent A No Attack (C) Attack (D) No Attack (C) Attack (D) Figure 2. Performer s and Performed s Payoffs. Figure 3. Battle Game s Payoff Matrix. A B C or D C or D Agent B Nash Solution: (D, D)

5 A typical instance of the battle game is a burglary. The performer obtains a payoff of 0.5 by stealing the performed s property, while the performed loses the same amount. The performed also suffers a loss of 2.5 due to physical and/or mental damages. To examine the ending state of the battle game, we assume two agents who interact reciprocally. The payoffs in Figure 2 result in the two-agent payoff matrix shown in Figure 3, which is just a typical payoff matrix for the 2PD problem. This means that a battle game society has to fall into a battling state. Here, we should note that the game s definition is incomplete it doesn t include how to determine who is a friend and who is an enemy. Without this piece, an agent cannot interact with anybody at all. Then, agents adopt a friend selection strategy like GFSSs etc and play the battle game. Regarding simulations we carried out, it should be noted that strategies to be investigated were not limited to only GFSSs. The reason is as follows. Even if we found out a peaceful state due to a formation of community in simulations with only GFSSs, it can t be interpreted as the emergence of community, because GFSSs are made based on a concept of group a prior. We should add other strategies to GFSSs. Then, let us remember that our essential interest is the effect of code of a friend and an enemy on the emergence of social order. And, the code of a friend and an enemy for me seems the most simple and essential one. Nakai & Muto proposed what they called My experienced-based Friend Selection Strategies (MFSSs), as follows. (MFS1) : the agent regards anybody as an enemy. (MFS2) me-tft: the agent regards anybody who attacked himself as an enemy and anybody who did not as a friend. (MFS3) me-cwd: the agent regards anybody who attacked himself as a friend and anybody who did not as an enemy. (CWD stands for a coward. ) (MFS4) ALL_C: the agent regards anybody as a friend. As we can see easily, GFSSs can be interpreted as extended variants of MFSSs. So, we carried out the basic simulations with only MFSSs, and did also another simulation by adding GFSSs to MFSSs. In the latter simulations, the existence of MFSSs gives agents the chance to select strategies except GFSSs. They are free to use group s reputations and adopt any strategy from MFSSs and GFSSs. For example, an agent participates in his own group s communication, including his report of who attacked him and who didn t attack him. And he knows just the existence of foreigners groups making similar communications. He understands these facts well, and decides to attack anybody who he meets. Besides, G-ffff and G-eeee are not different from ALL_C and respectively. (The former strategies take part in group s communication, but they don t use reputations finally.) In sum, we adopted 18 strategies except G-ffff and G-eeee in our simulations. The society is composed of a number of agents. Each agent has his own strategy and inherent

6 attribute (blue or red). Each simulation run is composed of a sequence of iterated turns, and each turn consists of four phases: perception, action, selection, and mutation. In the perception phase, each agent updates his social perception of who is a friend and who is an enemy, on the basis of his own strategy and information about others like group s reputations, with an occasional error noted by the perception error rate (μ p ). In the action phase, each agent plays the battle game in accordance with his updated perception. In the selection phase, the lower R% agents in payoffs abandon their strategies and adopt that of agents whose results were superior (We call R the reflection ratio ). In the mutation phase, a few agents are selected at random based on the strategy s mutation rate (μ s ). They abandon their strategies and adopt one of the 18 strategies at random. At the 0th turn, all agents are assumed to have the strategy and to perceive that all other agents are enemies, which expresses the state of war of all against all. After many iterated turns, the superior strategies survive and the inferior ones fade away. Our interest is in finding out what strategy survives and whether it leads to social order. me-tft G-eefe G-???? G-???? G-fefe G-???? G-???? G-ffef G-???? G-???? 0th generation No friends From Battling Society to Peaceful Society? One Turn Future Community & Many friends? Perception Social Perceptions (P i ) updated Based on Strategy (S i ) with an error Action Actions (C or D) Based on Social Perception (P i ) Selection Inferior Strategies are abandoned Superior Strategies are adopted Mutation Mutation of a few agents strategies Iterated Turns What What strategy strategy leads leads to to a a peaceful peaceful society society?? Figure 4. Evolutionary Simulation of Peace. 5. Emergence of three types of Social Order We carried out two simulations to investigate the effect of code of a friend and an enemy for group on the emergence of social order. As mentioned earlier, one simulates what society evolves from only MFSSs and the other simulates what society evolves from MFSSs and GFSSs. The conditions of the two simulations are exactly the same, except for the strategies. The number of agents is 40 (N=40) which are divided into 30 blue and 10 red agents, and the perception error rate is (μ p =). The matching

7 Friend Ratio Friend Ratio number is 20 (M=20). The reflection ratio is 1 (R=1). The strategy s mutation rate is 1% (μ s =1%). Typical results are seen in Figure 5, which shows the friend ratio over turns. This friend ratio is the average of all agents friend ratios. The friend ratio of 1.0 corresponds to a perfectly peaceful society. The upper diagram shows the result of the MFSSs simulation and the lower does the result of the MFSSs and GFSSs simulation. From the upper diagram, it is concluded that only MFSSs results in an instable society. We can find out a lot of battles in almost all turns while we can see some peaceful turns. In the lower diagram, in contrast, we can find out three types of social orders as noted by A, B, C in the diagram. So, we have such a finding that GFSSs can lead to some social orders and the code of a friend and an enemy for group has an effect on the emergence of peace to some extent. Society with MFSSs Turns Turns Society with MFSSs & GFSSs Turns A B C B C Figure 5. Friend Ratio vs. Turns (Upper: MFSSs, Lower: MFSSs and GFSSs). * Number of Agents: N=40 agents (Blue agents: 30, Red agents: 10),Matching Number of Agent in One Battle Game: M=20 agents, Reflection Ratio: R=1,Perception Error Rate: μ p =, Strategy s Mutation Rate: μ s =1% Next, in order to examine what the three states are, we observed the change in relationships among agents. For this purpose, we observed the network structure as the matrix form shown in Figure 6. One line of a matrix is an agent s social perception. When agent i regards agent j as a friend, the element (i, j) is expressed as a white dot. A square on a diagonal is important, because it indicates the emergence of a friendly community where each member sees all other members as friends. We have Figure 7 as a result. Regarding the social order noted by B, for example, we can see that

8 two communities have emerged. That is, almost all blue (red) agents form what we call a blue (red) community, where each blue (red) agent sees all other blue (red) agents as friends. In sum, GFSSs result in the following social orders. (RLT1-1) Communities : In the state, a community consists of all persons with the same attribute, where all members are mutually friends, while two different communities are hostile to each other. (RLT1-2) Anti-Communities : In the state, an anti-community consists of all persons with the same attribute, where all members are mutually hostile, while two different communities are peaceful toward each other. (RLT1-3) Pan-Community : In this state, all persons are mutually friends, independently of their attributes. There aren t communities and anti-communities, and a whole society becomes one community. Agent 3, 7, 8 are agent 1 s Agent 3, 4, 5, 6 see each other as friends. friends. - Friendly In-Group C C C C 5 C C C C C C C C 10 Figure 6. Observation of Relationships among Agents. 6 Figure 7. Communities, Anti-Communities, Pan-Community.

9 Friend Ratio Proportion of G-feee Friend Ratio Proportion of G-feee Friend Ratio Proportion of G-feee Finally, in order to investigate what strategies cause the three states, we observed proportions of strategies among all agents as shown in Figure 8, which were described together with a friend ratio over turns. And we have three types of diagrams in Figure 8. From these diagrams, we have the following findings. (RLT2-1) G-feee agents hold communities. We call them G-feee communities. (RLT2-2) G-eefe agents hold anti-communities. We call them G-eefe anti-communities. (RLT2-3) G-fefe agents hold a pan-community. We call it G-fefe pan-community. (In some simulations, we found out that G-fefe agents can hold not only pan-community but also communities or anti-communities.) G-eefe strategy frd_ratio G-eefe_ratio Turns G-feee strategy frd_ratio G-feee_ratio Turns G-fefe strategy frd_ratio G-fefe_ratio Turns Figure 8. Prevailing Strategies vs. Turns. (Upper: G-eefe strategy, Middle: G-feee strategy, Lower: G-fefe strategy)

10 6. Discussions Firstly, let us point out characteristics of a G-feee community, as follows. (D1) G-feee community shows the in-group reciprocity. In the community, every member who attacked his own group is always regarded as a common enemy. Therefore, a group has changed from just an exchange field of information to the practical institution to take revenge on members cheating to fellows. (D2) G-feee community shows the out-group hostility. In the community, every member unconditionally attacks anybody who belongs to a different group. Therefore, a group has changed from just an exchange field of information to the practical institution to exclude aliens unconditionally. Therefore, G-feee community can be interpreted as the institution showing the in-group reciprocity and out-group hostility using the group s common attribute as a symbol of community. Previous studies pointed out that group identification increases cooperation under NPD situation (Messick, D. M. and M. B. Brewer 1983; Kerr, N. L. 1995; Brewer, M. B. and S. K. Schneider 1990). Especially, minimal manipulation of group identification with abstract and vague similarities can increase cooperation rather than discussions among members (Brewer, M. B. and R. M. Kramer 1986). These indicate that group identification using a common symbol can foster cooperation. Although the previous studies interest and ours are different (the former is NPD and the latter is 2PD), their findings have a degree of similarity to ours. In addition, our results have also a similarity to Max Weber s in-group and out-group morality. As well known, Max Weber derived the concept from considerations on religious communities, while G-feee communities don t result from religion. So it is difficult to see Weber s findings as just a good example of G-feee community. But it seems interesting that both Weber s community and G-feee community have the common characteristic of unconditional hostility to aliens, which reminds us of a narrow-minded nationalism. Secondly, G-fefe pan-community shows indiscriminative reciprocity, which means that a G-fefe agent never pay attention to others attributes and sees others hostile to him as enemies and others peaceful to him as friends. In other words, attributes lose a practical meaning in G-fefe pan-community. In this sense, G-fefe pan-community reminds us of a kind of liberalism. In the end, G-eefe anti-community shows the in-group hostility and out-group reciprocity, opposite to G-feee community s case. But it seems difficult to regard anti-communities as usual phenomena in real world. And a war of all members against all members in an anti-community may destruct our assumption that members share information. Therefore, G-eefe anti-communities can be interpreted as just a theoretical state, like an imaginary solution of cubic equation.

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