Social networks, influence, and belief revision ` a la Girard, Liu & Seligman Pluralistic ignorance Our results on pluralistic ignorance A general framework: A hybrid dynamic network logic Conclusion and further research A Two-tiered Formalization of Social Influence e Christoff 1 Jens Ulrik Hansen 2 Zo´ 1 Institute for Logic, Language and Computation, University of Amsterdam 2 Department of Philosophy, Lund University Fourth International Workshop in Logic, Rationality and Interaction (LORI-IV) Hangzhou, October 10, 2013 . . . . . . 1 / 36
Social networks, influence, and belief revision ` a la Girard, Liu & Seligman Pluralistic ignorance Our results on pluralistic ignorance A general framework: A hybrid dynamic network logic Conclusion and further research Outline Social networks, influence, and belief revision ` a la Girard, Liu & Seligman The basics Social influence and belief revision Pluralistic ignorance A phenomenon from social psychology Limitations of the framework of Girard, Liu & Seligman Adding a layer Our results on pluralistic ignorance A formal language for social influence Robustness Fragility A general framework: A hybrid dynamic network logic The idea Dynamics Conclusion and further research . . . . . . 2 / 36
Social networks, influence, and belief revision ` a la Girard, Liu & Seligman Pluralistic ignorance The basics Our results on pluralistic ignorance Social influence and belief revision A general framework: A hybrid dynamic network logic Conclusion and further research Social networks, influence, and belief revision a la Girard, Liu & Seligman ` . . . . . . 3 / 36
Social networks, influence, and belief revision ` a la Girard, Liu & Seligman Pluralistic ignorance The basics Our results on pluralistic ignorance Social influence and belief revision A general framework: A hybrid dynamic network logic Conclusion and further research The basics Social networks ▶ Agents situated in a social network (a symmetric b graph) c k j ▶ The edges represent a “friendship” relation a i h d e f g . . . . . . 4 / 36
Social networks, influence, and belief revision ` a la Girard, Liu & Seligman Pluralistic ignorance The basics Our results on pluralistic ignorance Social influence and belief revision A general framework: A hybrid dynamic network logic Conclusion and further research The basics Social networks ▶ Agents situated in a social network (a symmetric B ¬ p graph) Bp Bp Up ▶ The edges represent a “friendship” relation Bp Simple beliefs Bp Bp Up The agents can be in 3 possible states: ▶ Bp Up B ¬ p ▶ B ¬ p Bp ▶ Up := ¬ Bp ∧ ¬ B ¬ p . . . . . . 4 / 36
Social networks, influence, and belief revision ` a la Girard, Liu & Seligman Pluralistic ignorance The basics Our results on pluralistic ignorance Social influence and belief revision A general framework: A hybrid dynamic network logic Conclusion and further research Social influence and belief revision Main assumptions ▶ Agents are influenced by their friends and only by their friends. ▶ Simple “peer pressure principle”: I tend to align my beliefs with the ones of my friends. ▶ Agents can “see” what their friends believe. ▶ I.e. an agent is “transparent” to all of his friends. . . . . . . 5 / 36
Social networks, influence, and belief revision ` a la Girard, Liu & Seligman Pluralistic ignorance The basics Our results on pluralistic ignorance Social influence and belief revision A general framework: A hybrid dynamic network logic Conclusion and further research Belief revision induced by social influence Strong influence When all of my friends believe that p , I (successfully) revise with p . When all of my friends believe that ¬ p , I (successfully) revise with ¬ p . B ¬ p Bp Bp B ¬ p . . . . . . 6 / 36
Social networks, influence, and belief revision ` a la Girard, Liu & Seligman Pluralistic ignorance The basics Our results on pluralistic ignorance Social influence and belief revision A general framework: A hybrid dynamic network logic Conclusion and further research Belief revision induced by social influence Strong influence When all of my friends believe that p , I (successfully) revise with p . When all of my friends believe that ¬ p , I (successfully) revise with ¬ p . B ¬ p Bp Bp B ¬ p ⇝ B ¬ p Bp Bp B ¬ p . . . . . . 6 / 36
Social networks, influence, and belief revision ` a la Girard, Liu & Seligman Pluralistic ignorance The basics Our results on pluralistic ignorance Social influence and belief revision A general framework: A hybrid dynamic network logic Conclusion and further research Belief revision induced by social influence Strong influence When all of my friends believe that p , I (successfully) revise with p . When all of my friends believe that ¬ p , I (successfully) revise with ¬ p . B ¬ p Bp Bp B ¬ p B ¬ p Bp ⇝ ⇝ B ¬ p Bp Bp B ¬ p Bp B ¬ p . . . . . . 6 / 36
Social networks, influence, and belief revision ` a la Girard, Liu & Seligman Pluralistic ignorance The basics Our results on pluralistic ignorance Social influence and belief revision A general framework: A hybrid dynamic network logic Conclusion and further research Belief contraction induced by social influence Weak influence When none of my friends supports my belief in ¬ p and some believe that p , I (successfully) contract it. When none of my friends supports my belief in p and some believe that ¬ p , I (successfully) contract it. Bp Up B ¬ p B ¬ p . . . . . . 7 / 36
Social networks, influence, and belief revision ` a la Girard, Liu & Seligman Pluralistic ignorance The basics Our results on pluralistic ignorance Social influence and belief revision A general framework: A hybrid dynamic network logic Conclusion and further research Belief contraction induced by social influence Weak influence When none of my friends supports my belief in ¬ p and some believe that p , I (successfully) contract it. When none of my friends supports my belief in p and some believe that ¬ p , I (successfully) contract it. Bp Up Up Up ⇝ B ¬ p B ¬ p Up B ¬ p . . . . . . 7 / 36
Social networks, influence, and belief revision ` a la Girard, Liu & Seligman Pluralistic ignorance The basics Our results on pluralistic ignorance Social influence and belief revision A general framework: A hybrid dynamic network logic Conclusion and further research Influence dynamics The influence operator I For each agent a : ▶ If a is strongly influenced to believe p ( ¬ p ), then a will believe p ( ¬ p ). ▶ If a is only weakly influenced to believe p ( ¬ p ) and believes ¬ p ( p ), then a will become undecided. ▶ Otherwise, a keeps her current belief state. . . . . . . 8 / 36
Social networks, influence, and belief revision ` a la Girard, Liu & Seligman Pluralistic ignorance A phenomenon from social psychology Our results on pluralistic ignorance Limitations of the framework of Girard, Liu & Seligman A general framework: A hybrid dynamic network logic Adding a layer Conclusion and further research Pluralistic ignorance . . . . . . 9 / 36
Social networks, influence, and belief revision ` a la Girard, Liu & Seligman Pluralistic ignorance A phenomenon from social psychology Our results on pluralistic ignorance Limitations of the framework of Girard, Liu & Seligman A general framework: A hybrid dynamic network logic Adding a layer Conclusion and further research A phenomenon from social psychology Different takes on pluralistic ignorance ▶ Everyone believes the same thing, but mistakenly believes that everyone else believes something else. ▶ An error of social comparison: Individuals mistakenly believes that others are different from themselves (even though they might act similar). ▶ Everyone publicly supports a norm they privately reject. ▶ A discrepancy between private beliefs and public beliefs/behavior. . . . . . . 10 / 36
Social networks, influence, and belief revision ` a la Girard, Liu & Seligman Pluralistic ignorance A phenomenon from social psychology Our results on pluralistic ignorance Limitations of the framework of Girard, Liu & Seligman A general framework: A hybrid dynamic network logic Adding a layer Conclusion and further research A phenomenon from social psychology Different takes on pluralistic ignorance ▶ Everyone believes the same thing, but mistakenly believes that everyone else believes something else. ▶ An error of social comparison: Individuals mistakenly believes that others are different from themselves (even though they might act similar). ▶ Everyone publicly supports a norm they privately reject. ▶ A discrepancy between private beliefs and public beliefs/behavior. Examples ▶ The Emperor’s New Clothes ▶ A silent classroom ▶ Campus drinking . . . . . . 10 / 36
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