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Modeling sustainability in social networks

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Modeling sustainability in social networks

  1. 1. International Workshop on Complex Systems Dynamics, IIT Madras, August 2021. Modeling Sustainability in Social Networks Srinath Srinivasa Web Science Lab IIIT Bangalore sri@iiitb.ac.in
  2. 2. Web Science Lab Established in 2002 as Open Systems Lab focusing on modeling and analytics of Complex Network Structured Data Changed to Web Science Lab in 2015. Current strength: 6 PhD students, 1 postdoc, 3 MS Scholars, 22 MTech/iMTech project associates Research verticals: Digital Capabilities, Data Driven Governance, Social Cognition, Responsible AI 2
  3. 3. Artificial vs Natural Engineering Made of parts custom built for a specific purpose Well-defined functionality for each part Structure designed apriori into its present shape Imperative design Made of generic agents capable of playing several roles Autonomous actions by agents based on self- interest and utility maximization Structure a result of evolution and local adjustments Declarative design, Sense of Self 3
  4. 4. Machine vs “Being” Hermeneutics Machine hermeneutics: Models reality in terms of inanimate matter, and interactions between them Roots from Ancient Greece, greatly popularized by Newtonian models of physics Particle foundations for physical reality Great convergence: mass (matter) = energy Open question: Energy and Information Being Hermeneutics: Models reality as a “holistic” (system of) being, characterised by sustainable state of being, information content in different states of being, etc. Characteristic of Eastern “dharmic” civilizational thought Being: The unit of existence, modeled as a complex entity comprising of energy and information “Consciousness” foundations for reality 4
  5. 5. Postulates of “Being” Primary characteristic is to “be” (settle down in stable states or configurations) Under certain closed or boundedness conditions, collection of beings forms a (system of) being with its own stable states Sense of self (Sentient beings) Individual and collective sense of self Primary objective: Sustainability of the sense of self “Being” Oriented System Design 5 Image source: Google image search
  6. 6. “Being” Oriented System Design Postulate of sustainability: Any closed system of being settles down in a “low energy” stable state. Visible in physical systems as elasticity, inertia, ionic interactions, etc. and in biological systems as homeostasis. Sentience: Systems of being with a “sense of self”. Stable states are based on sustenance of the sense of self, rather than on just physical low-energy configurations. Being: A specific form of agency. We will be using the term “being” and “agent” interchangeably in this work. Being and its Environment: Consider agent a, having its sustainable state (w.l.o.g represented as a single state), as d(a) Any agent interacting with a bounded environment (called vidhi, represented as v(a)) over finitely many interaction choices, is guaranteed to have a state of equilibrium representing the “mutual best- response” function. (Nash’s Theorem: https://mathworld.wolfram.com/NashsTheorem.htm l) Let this equilibrium state be represented as e(a,v(a)). 6
  7. 7. “Being” Oriented System Design “Manageable” Complex Systems: 7 Tractabl e Mangeable Intractable Machines Linear Tractable / Predictable Dynamics by design Beings Non-Linear Ergodic / Bounded state space with invariants Intractable, but manageable due to invariant stable properties Chaos Non-Linear Non-Ergodic Intractable, may have no invariant / stable states
  8. 8. Networks of Beings Understanding emergence of classes of network topologies from individual decision-making Or Understanding underlying priorities of a population by their resultant network structure 8
  9. 9. Erdös-Renyi Networks Simplest formulation of social networks Assumes social network connections are formed in random Consider a set of n nodes. There can be a total of n(n-1)/2 undirected edges among them. Model 1: G(n,p): − Choose a set of m=p*n edges from this set in random and add them to the graph Model 2: H(n,p): − Each of the n(n-1)/2 edges is added to the graph with a probability p By Vonfrisch, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=3469734 9
  10. 10. Erdös-Renyi Networks Largest Connected Component (LCC): Most powerful community in the network With uniform probability of addition of edges, size of LCC undergoes an inflection when the number of edges is approximately n/2, growing rapidly till it start saturating approximately around 2n edges. Diameter of LCC increases with inflection, and starts reducing when the LCC size saturates. “With greater connectivity, world (LCC) grows bigger before it grows smaller.” 10
  11. 11. Triadic Closure Informally: Two people who have a common friend are likely to become friends themselves. The more closer they are to their common friend, the more likely is it that they become friends themselves Triadic closure is not a property of how people behave-- it is a network property If “A is acquainted with B” implies “A spends time with B” then increasing amount of acquaintance between A, B and A,C within a given time period results in B and C spending time with each other (pigeon-hole principle) Entrenchment: Triadic closure property creates an effect of “entrenchment” in acquaintance networks (Image Source: [Easley and Kleinberg 2010]) Entrenched networks low in novelty, high in mutual familiarity (and hence, trust), thus lowering bookkeeping costs (at the expense of novelty) 11
  12. 12. Watts-Strogatz Model Refinement over the Erdos-Renyi random graph model to accommodate triadic closure 1) Consider N nodes to be on a ring lattice labeled [0, N-1] 2) Construct a (deterministic) graph having Nk/2 edges by connecting each node to k/2 neighbours each on its right and left. 3) For every node, choose one of the edges created in step 2, and break it with a probability ß (0 ≤ ß ≤ 1) 4) Rewire the broken edges and connect them randomly to any node in the graph 12
  13. 13. Watts-Strogatz Model When ß = 0, the graph is a deterministic graph with maximum possible triadic closure with k edges Creates a “resilient” network structure with a Hamiltonian circuit: diameter no greater than n/2, connectivity no lesser than 2, deterministic routing with local knowledge. Characteristic feature of entrenched communities in human societies: high trust, high familiarity, high resilience, low novelty. When ß = 1, the Watts-Strogatz model is equivalent to an Erdos-Renyi model G(n,p) where: When ß = 0, the graph has a deterministic regular or near-regular structure. With ß = 1, the degree distribution is known to be Poisson. Degree distributions in real-world social networks are known to be have a “hub and spoke” (power-law, log-normal, etc.) “scale- free” property, giving it short diameters (also known as “small world” networks). 13
  14. 14. Barabasi-Albert Model Generates a “hub-and-spoke” topology with a power-law degree distribution: “Scale-free” and “small-world” properties Resilient against random failures, but susceptible to “targeted attacks” (unlike WS networks with clustering links) De I, Keiono, CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=2459900 14
  15. 15. Barabasi-Albert Model Preferential Attachment Generative model for scale-free graphs: 1. Start with a small set of “seed” nodes connected randomly 2. For every subsequent incoming node: a. with probability γ connect to any existing node at random b. with probability 1-γ, connect to node k with probability π(k), where: where α > 0 Scale-free networks are known to be ubiquitous in nature and emergent human networks: Blood circulatory network, Global aviation network, Internet topology, etc. B-A networks are known to be resilient against “random failures” -- i.e. failure of any k nodes chosen at random will w.h.p. not partition the network. But they are not resilient against “targeted attacks”-- failure of a small set of key hubs can easily partition the network. R. Cohen, K. Erez, D. Ben-Avraham, S. Havlin (2000). "Resilience of the Internet to random breakdowns". Phys. Rev. Lett. 85: 4626. 15
  16. 16. Topology Breeding Human social networks exhibit properties of both entrenchment (WS network) and scale-free resilience (BA network), showing resilience against both random failures and targeted attacks. “Topology Breeding” an attempt to generate networks with properties of both BA and WS networks. Given a society of n agents (beings): Each agent has some “sustainability needs” which may be potentially met by other agent in the network. Each connection incurs a cost and brings some value The way connections are made across the network may give the network some “robustness” or resilience against failure of agents and edges Communication network has three optimization criteria: Efficiency Robustness Cost 16 Patil, Sanket, Srinath Srinivasa, Saikat Mukherjee, Aditya Ramana Rachakonda, and Venkat Venkatasubramanian. "Breeding diameter-optimal topologies for distributed indexes." Complex Systems 18, no. 2 (2009): 175. Patil, Sanket, Srinath Srinivasa, and Venkat Venkatasubramanian. "Classes of optimal network topologies under multiple efficiency and robustness constraints." In 2009 ieee international conference on systems, man and cybernetics, pp. 4940-4945. IEEE, 2009.
  17. 17. Topology Breeding Use of genetic algorithms to find optimal topologies under different constraints over efficiency, robustness and cost Infrastructure cost is bounded by giving each node exactly k edges to make connections with other nodes so as to minimize distance to all nodes, and maximize connectivity. Topologies generated from individual runs are combined using a cross-over function to overcome local minima. Topologies with lower fit functions are discarded. Fit calculated by a parameter α that trades between efficiency and robustness 17
  18. 18. Topology Breeding Star topology Emergent topology when α = 1 (100% importance to efficiency and 0% importance to robustness) Star has the smallest degree of separation for a network of n nodes and (k=1) edge per node. Ring topology Emergent topology when α = 0 (100% importance to robustness and 0% importance to efficiency) Circle is has highest resiliency (connectivity = 2) against targeted attacks under the cost constraints (k=1) 18
  19. 19. Emergent topology when α is set to some value between 0 and 1 (and cost factor k = 1) were a family of topologies combining the circle and star. Displayed properties of “hub and spoke” with a small diameter and a scale-free degree distribution, and connectivity of at least 2 for a large subset of the graph. Degree distribution in the hub and spoke resembles a power-law Topology Breeding 19
  20. 20. Topology Breeding With α = 1 (maximum emphasis on efficiency or diameter reduction, and minimum emphasis on resilience or connectivity), maximum permissible degree (p) and number of edges (e) were varied, with n=20 nodes. Result is a class of tree/star structured topologies until e=20, and then topologies with a core ring (connectivity ≥ 2) with spokes connecting to the core. Degree distributions approximated by a power law. 20
  21. 21. Topology Breeding With α = 0 (minimum emphasis on efficiency or diameter reduction, and maximum emphasis on resilience or connectivity), maximum permissible degree (p) and number of edges (e) were varied, with n=20 nodes. Result is uniformly a class of circular skip lists (CSL) (connectivity ≥ 2) with no spokes-- only chords. Degree distributions still approximated by a power law (unlike WS networks). CSL has properties of both WS and BA networks, and can be resilient to both random failures and targeted attacks while optimising on efficiency. Seems to appear in real world banking networks. 21 Lux, Thomas. "Emergence of a core-periphery structure in a simple dynamic model of the interbank market." Journal of Economic Dynamics and Control 52 (2015): A11-A23
  22. 22. Sense of Self Basic unit of sustainability. Agency is modeled as an optimization process of utility maximization, driven by “self-interest” While much research has focused on strategies for utility maximization, relatively little interest has gone into (computationally) modeling the “sense of self” that drives self interest. Classical model From the theory of games and rational choice, by von-Neumann and Morgenstern. Self-interest (and the idea of “Self” itself) modeled as a preference relation across pairs of choices: Strong preference (>), Weak preference (≥), Indifference (||) Valuation modeling: If A > B > C, and choice I returns B with probability 1, while choice II returns A with probability p, and B with probability 1-p. The choices are said to be indifferent when for some value of p, E(II) = E(I), or p v(A) + (1-p) u (C) = u(B) 22
  23. 23. Sense of Self Rational Fools: Critique of classical model by Amartya Sen. Argues that it is too simplistic to reduce “sense of self” Human sense of self contains at least the following extra elements: ● Rational Empathy ● Sense of fairness ● Basic level of trust If humans were strict rational maximizers, above kinds of interactions would be more commonplace. 23 Agents pursuing “Rational empathy” (Pareto improvements, rather than rational maximization), can agree to cooperate in a one- shot PD game.
  24. 24. Sense of Self Risk Aversion: Kahnemann and Tversky in their work on “prospect theory” show that the human sense of self does not treat the prospect of gains and losses symmetrically. Fund I, requires investment of Rs. 5000, and has a guaranteed return of Rs. 7500 at the end of its term. Fund II, requires investment of Rs. 5000, and returns either nothing or Rs. 15,000 with equal probability. Both funds have same expected utility in classical model, but humans shown to prefer Fund I over Fund II. Utility of prospects of gains saturate with more expected gains (diminishing value of returns), while utility of prospects of losses, grows with a high negative slope. 24
  25. 25. Sense of Self Elastic sense of identity: Human sense of self is not a monolithic entity. Humans often “identify” with external objects and concepts, by making it a part of their sense of self. Given agent a, sense of self S(a) given by: Sa = (I, da, γa), where I is the “identity set” comprising of objects (including ‘a’ itself) to which, the sense of self is attached, da: {a} xI → R represents “semantic distance” to each object in I, and 0 ≤ γa ≤ 1 represents the rate at which identification attenuates. Agent a identifies with object at distance d with an attenuation of γa d 25
  26. 26. Sense of Self Computational Transcendence: Modeling an elastic sense of identity, where an agent “identifies” with its neighbour to different extents. Modeled as a utility function that combines payoffs from oneself and neighbour, with attenuation factor. When both players “transcend” their sense of self to include their neighbour to an extent of (⅓) or more, it makes rational sense to corporate, rather than defect. 26
  27. 27. Sense of Self Regional and Global Identities: 27 HH HT TH TT H 6 6 6 6 1 6 1 6 6 10 10 2 T 6 6 1 2 10 10 10 2 10 0 0 0
  28. 28. Identity and Sustainability Regional and Global Identities: Social identities within communities in a population often conflict with interests of the population as a whole, leading to the “salad bowl” problem of diversity Ex: Regional vs national language conflicts, Religion versus nation loyalty conflicts, etc Homophily: Tendency of an agent to prefer other agents of the same regional identity, when establishing new connections Insularity: Tendency of an agent to distrust by default, agents belonging to another regional identity, and trust by default, agents belonging to the same regional identity. The extent of homophily and insularity within a population of regional identities may vary. 28 Jayati Deshmukh, Srinath Srinivasa, Sridhar Mandyam. What keeps a vibrant population together? Complex Systems journal. (to appear)
  29. 29. Identity and Sustainability Network evolution: Agents in a network adopt either one of several “regional” identities, or a “global” identity Agents play a game of Iterated Prisoners’ Dilemma (IPD) with their neighbours using the game matrix shown Global Agents: Global agents establish new connections with a probability in proportion to the degree of the target agent (preferential attachment) Network Formation: With a probability hp (homophily probability), regional agents connect to other regional agents of the same identity, and with a probability (1-hp) regional agents connect rationally, using preferential attachment. 29
  30. 30. Identity and Sustainability Network Dynamics: With probability ip a regional agent is flagged as “insular” and “non- insular” with a probability (1-ip). Non-insular regional agents, and global agents, adopt a cooperative TIT-FOR-TAT (TFT) strategy, that begins with offering cooperation, and reflecting the previous move from the other player, in subsequent iterations. Insular agents adopt a Distrustful TFT (DTFT) that begins with non-cooperation for agents not belonging to same identity. Network Evolution: A given network plays IPD for an “epoch” τ, after which, links giving a net negative payoff are discarded and new ones established according to Network Formation heuristics. Network reaches an equilibrium (Pareto optimality) when all links have positive payoffs. 30
  31. 31. Identity and ... Simulation runs were conducted for four extreme configurations: Low (20%)/High (80%) Insularity/Modularity and results calibrated when network reached equilibrium. Case 1: No global agents With no “global” agents, regional agents have no problem forming a melting pot at LILH, but break apart into separate clusters at HIHH. At LIHH or HILH, they form a “salad bowl” of segregated clusters, but still connected. 31
  32. 32. Identity and ... Case 2: Small number (20%) of global agents Global agents form the glue that keep the network connected, in all four cases. With low insularity, network is less segregated and has a smaller diameter. Despite playing a key role in keeping the network together, global agents neither have high payoffs, nor high bargaining power based on Dominance of Neighbours (DON) metric! 32
  33. 33. Identity and ... Average payoffs for global vs regional agents in all four configurations for Case - 2. Scatter plot of bargaining power (DON) and payoff for global and regional agents for Case - 2. 33
  34. 34. Identity and ... Case - 3: High number (80%) of global agents Global agents overwhelm the network and create a densely connected melting pot for LILH and LIHH configurations. When insularity is high (HILH and HIHH), insular regional agents are alienated, to the extent that they find it lucrative to break apart from the network altogether (HIHH). 34
  35. 35. Identity and Sustainability Average payoffs for global and regional agents in HIHH configuration, for variation in the percentage of global agents. Global agents’ payoffs lesser than that of regional agents, till their population reaches ~75% at which stage, they alienate insular regional agents anyway! Identity needs to be stronger than rationality to be a global agent! 35
  36. 36. Identity and Sustainability The dynamics of identity: Our sense of self is elastic, and can be attached to external concepts and ideas Identifying with an external entity, characteristically different from rationally associating with it Cooperative behaviour can emerge without long-term iteration and evolution, with elastic identity Regional and global identities: Global identities are critical to keep a diverse population of regional identities united No rational incentive for global identity-- global agents neither get most wealthy, nor most powerful Very large proportion global agents in the demographics, can alienate regional identities 36
  37. 37. Conclusions “Being-oriented computing” as a potential modeling paradigm for analyzing and building manageable complex systems Elements of being: Resilience (sustainability), Identity (sense of self) Current work: Introducing an elastic sense of self in RL agents for designing responsible AI Acknowledgments: Sanket Patil Aditya Ramana Rachakonda Prof. Venkatasubramanian (formerly Purdue) Jayati Deshmukh Prof. Sridhar Mandyam 37
  38. 38. Relevant Publications Sanket Patil, Srinath Srinivasa, and Venkat Venkatasubramanian. Classes of Optimal Network Topologies under Multiple Efficiency and Robustness Constraints. Proc. of the IEEE Int’l Conference on Systems, Man and Cybernetics (SMC 2009), San Antonio, Texas, USA, October 2009, pp. 4940 – 4945 Sanket Patil, Srinath Srinivasa. Theoretical Notes on Regular Graphs as applied to Optimal Network Design. Proceedings of the International Conference on Distributed Computing and Internet Technology (ICDCIT 2010), Bhubaneswar, India, February 2010. Patil, Sanket, Srinath Srinivasa, Saikat Mukherjee, Aditya Ramana Rachakonda, and Venkat Venkatasubramanian. "Breeding diameter-optimal topologies for distributed indexes." Complex Systems 18, no. 2 (2009): 175. Patil, Sanket, Srinath Srinivasa, and Venkat Venkatasubramanian. "Classes of optimal network topologies under multiple efficiency and robustness constraints." In 2009 ieee international conference on systems, man and cybernetics, pp. 4940-4945. IEEE, 2009. Jayati Deshmukh, Srinath Srinivasa. Evolution of Cooperation with Entrenchment Effects. Proceedings of the International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS 2015), Istanbul, Turkey, ACM Press, May 2015. Jayati Deshmukh, Srinath Srinivasa. Cooperation and the Globalization-Localization Dilemmas. Complex Systems journal. (to appear) Jayati Deshmukh, Srinath Srinivasa, Sridhar Mandyam. What keeps a vibrant population together? Complex Systems journal. (to appear) 38
  39. 39. Thank You! 39

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