Skip to main content
SpringerLink
Log in

A DDL Approach to Pluralistic Ignorance and Collective Belief

  • Published:
Journal of Philosophical Logic Aims and scope Submit manuscript

Abstract

A group is in a state of pluralistic ignorance (PI) if, roughly speaking, every member of the group thinks that his or her belief or desire is different from the beliefs or desires of the other members of the group. PI has been invoked to explain many otherwise puzzling phenomena in social psychology. The main purpose of this article is to shed light on the nature of PI states – their structure, internal consistency and opacity – using the formal apparatus of Dynamic Doxastic Logic, and also to study the sense in which such states are “fragile”, i.e. to identify plausible conditions under which a PI state cascades into a state of shared belief as the result of announcement.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. The term ‘norm’ should here be understood in a descriptive sense as signifying a general tendency of behavioral conformity.

  2. According to a large scientific literature, this feature is also found in a number of equilibria and dynamics (e.g. informational cascades) that are grounded on a state of pluralistic ignorance (see [5, 6], and [11]), although some cases of PI reported in the litterature display a more robust behaviour.

  3. This is so in the case of a PI-scenario like that of Eq. 2. In the case of Eq. 1 it would instead dissolve into shared disbelief : everyone disbelieves that p and everyone believes that everyone disbelieves that p.

  4. See also [6] and [11]. Incidentally, we notice that this tale, published by Andersen in 1837, has a much longer tradition and many differing versions, the original plot going at least back to an older story from Juan Manuel de Villena (in El Conde Lucanor, 1335).

  5. Here “relatively few” means that in a group composed of n agents the process terminates in n rounds of communication between agents.

  6. By convention, non-labelled points are \(\neg N\)-states.

  7. Simple safety of \(\phi \) at w already guarantees such robustness for atomic proposition (as N) but is not in general preserved by update. For example the “moorean” \(p \wedge \neg K_{i}p\) may very well be safe at some state w but it is never preserved after a \(!p\)-update.

  8. Formal approaches to judgment aggregation (JA) and preference aggregation (PA) express individual opinions and preferences via an ordering among states. Aggregation policies can be represented as functions from the set of the individual orderings of the agents, having as value some other ordering among states, e.g. in the simple case where agent i is the dictator the output will simply consist in agent’s i ordering. Most literature in PA develops the theory of aggregation of total orders (or even linear ones), not of preorders such as the ones we are dealing with here, but there are exceptions (see [21]). The logical properties of different operators of preference aggregation have been largely investigated in [1] and, for what specifically concerns doxastic and proairetic logics based on plausibility frames, the reader may also refer to [8].

    An interesting issue, to be left for future work, is to develop this conceptual affinity into a technical one, integrating our framework with JA theories and studying how different policies of belief aggregation influence PI-scenarios. For example, the presence of a fashion leader or trendsetter, i.e. a person whose preference deserves bigger consideration than those of other agents, presumably has a big impact for creation and dissolution of PI. Here, for the sake of simplicity we treat all agents as epistemic peers.

  9. It is easy to verify that in the updated model \(B_{(1,2)}P_{\frac {1}{2}G(1,2)}N\) and \(B_{(2,1)}P_{\frac {1}{2}G(2,1)}N\).

  10. Several forms of belief revision are available in DDL, essentially as operations of order change among states (see [4] and [3] for examples). In our specific case two policies might be explored: (a) simple order upgrade where \(\neg B_{j}\phi \)-states become minimal in i’s information cell, and (b) addition of \(\neg B_{j}\phi \)-states in i’s information cell.

  11. Of course, nothing in this semantics prevents a group member from realizing at a later point that the group was at an earlier point in a state of PI.

  12. This semantics corresponds to a normal modal system KD45 for B, i.e. validates both \(B\phi \rightarrow BB\phi \) and \(\neg B\phi \rightarrow B\neg B\phi \) which are sufficient to derive a contradiction from Eq. 5 (see [3]). It is worth commenting, in this connection, on an alternative form of a PI scenario in which every member believes \(\phi \) and also that the others members, rather than failing to believe \(\phi \), believe \(\neg \phi \). From the assumption that a given member believes this to be so, we may easily derive a proposition expressing that this member believes all the other members to have contradictory beliefs.

References

  1. Andreka, H., Ryan, M., Schobbens, P.Y. (2002). Operators and Laws for combining preference relations. Journal of Logic and Computation, 12(1), 13–53.

    Article  Google Scholar 

  2. Bikhchandani, S., Hirshleifer, D., Welch, I. (1998). Learning from the behavior of others: conformity, fads, and informational cascades. Journal of Economic Perspectives, 12, 151–170.

    Article  Google Scholar 

  3. Baltag, A., & Smets, S. (2007). A qualitative theory of dynamic interactive belief revision, LOFT07. Texts in Logic and Games, 3, 13–60.

    Google Scholar 

  4. van Benthem, J.F.A.K. (2007). Dynamic logic for belief revision. Journal of Applied Non-Classical. Logics, 2, 129–155.

    Article  Google Scholar 

  5. Bicchieri, C., & Fukui, Y. (1999). The great illusion: ignorance, informational cascades and the persistence of unpopular norms. Business Ethics Quarterly, 9, 127–155.

    Article  Google Scholar 

  6. Centola, D., Willer, R., Macy, M.V. (2005). The emperor’s dilemma: a computational model of self-enforcing norms. American Journal of Sociology, 110, 1009–1043.

    Article  Google Scholar 

  7. van Ditmarsch, H., van der Hoek, W., Kooi, B. (2007). Dynamic epistemic logic: Synthese library (Vol. 337). Springer.

  8. Girard, P., & Seligman, G. (2009). An analytic logic of aggregation. Logic and its Applications. Lecture Notes in Computer Science, 5378, 146–161.

    Article  Google Scholar 

  9. Hansen, J.U. A logic-based approach to pluralistic ignorance, online paper. http://www.academia.edu/1894486/A_Logic-Based_Approach_to_Pluralistic_Ignorance.

  10. Hansen, J.U. (2011). A logic toolbox for modeling knowledge and information in multi-agent systems and social epistemology. PhD Thesis Roskilde University. Computer Science Research. Report no. 133, ISSN 0109-9779.

  11. Hendricks, V.F. (2010). Knowledge transmissibility and pluralistic ignorance. Metaphilosophy, 41(3), 279–291.

    Article  Google Scholar 

  12. Hintikka, J. (1962). Knowledge and belief: An introduction to the logic of the two notions. Cornell: Cornell University Press.

    Google Scholar 

  13. Hoek, W.v.d., & Lomuscio, A. (2004). A logic for ignorance. Electronic Notes in Theoretical Computer Science, 85(2), 117–133.

    Article  Google Scholar 

  14. Katz, D., & Allport, F.H. (1931). Student attitudes. Syracuse, New York: Craftsman.

    Google Scholar 

  15. Krech, D., & Crutchfield, R.S. (1948). Theories and problems of social psychology. New York: McGraw-Hill.

    Book  Google Scholar 

  16. Latane, B., & Darley, J. (1969). Bystander Apathy. American Scientist, 57, 244–268.

    Google Scholar 

  17. Leitgeb, H., & Segerberg, K. (2007). Dynamic doxastic logic: why, how and where to. Synthese, 155, 167–190.

    Article  Google Scholar 

  18. Malcolm, N. (1958). Ludwig Wittgenstein: A memoir. London: Oxford University Press.

    Google Scholar 

  19. Matz, D.C., & Wood, W. (2005). Cognitive dissonance in groups: the consequences of disagreement. Journal of Personality and Social Psychology, 88(1), 22–37.

    Article  Google Scholar 

  20. Noelle-Neumann, E. (1974). The spiral of silence: a theory of public opinion. Journal of Communication, 24(2), 43–51.

    Article  Google Scholar 

  21. Pini, M.S., Rossi, F., Venable, K.B., Walsh, T. (2009). Aggregating partially ordered preferences. Journal of Logic and Computation, 19(3), 475–502. doi:10.1093/logcom/exn012.

    Article  Google Scholar 

  22. Prentice, D.A., & Miller, D.T. (1993). Pluralistic ignorance and alcohol use on campus: some consequences of misperceiving the social norm. Journal of Personality and Social Psychology, 64(2), 243–256.

    Article  Google Scholar 

  23. Segerberg, K. (1995). Belief revision from the point of view of doxastic logic. Bulletin of the IGPL, 3, 535–553.

    Article  Google Scholar 

  24. Segerberg, K. (2006). Moore problems in full dynamic doxastic logic In J. Malinowski & A. Pietruszczak (Eds.), Essays in logic and ontology (poznan studies in the philosophy of the sciences and the humanities, 91) (pp. 95–110). Amsterdam, New York: Rodopi.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy, Lund University, Kungshuset, Lundagård, 222 22, Lund, Sweden

    Carlo Proietti & Erik J. Olsson

Authors
  1. Carlo Proietti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erik J. Olsson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Carlo Proietti.

Additional information

We would like to especially thank Davide Grossi for many highly useful comments and suggestions on earlier versions of this paper. We are also indebted to the referees for several valuable remarks that helped improve the final version. We also wish to thank Rasmus Rendsvig, Vincent Hendricks, Frank Zenker, Jens Ulrik Hansen, Bengt Hansson and the participants to the Lund-Copenhagen Workshop on Social Epistemology as well as audiences in Bologna (EEN meeting 2012), Lund, Paris and Bochum for many helpful observations.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Proietti, C., Olsson, E.J. A DDL Approach to Pluralistic Ignorance and Collective Belief. J Philos Logic 43, 499–515 (2014). https://doi.org/10.1007/s10992-013-9277-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10992-013-9277-3

Keywords

Search

Navigation