The Queue Transform

About the Author and the Reason for this Book

From decades of observing people in various cultures and locations around the world, two things in my opinion are common throughout. First, people will believe what they want to believe in an effort to reduce emotional discomfort. Second, they will not begin to change strongly held beliefs unless confronted with an immediate crisis having a direct, relevant, and negative impact on them as a result of their beliefs. Regarding the latter, if and when confronted with a reality that does not coincide with their beliefs, they will initially try to find someone or something to reinforce their beliefs or lessen their discomfort (Hogg & Adelman, 2013) in an effort to minimize any necessary changes in their beliefs. This is a fundamental part of Leon Festinger's (1957) cognitive dissonance theory. Those arguing against the facts supporting climate change are an example.

With a masters degree in operations research and 25 years of research and development as a national level analyst and technical program manager, my retirement has been spent crossing academic boundaries as a non-degree graduate student in an effort to develop a quantitative model of western social intragroup interaction within the most basic of western social systems. The purpose of this effort is to offer an approach for others in various cultures to build on, and one day to possibly identify data driven justifiable requirements which provide for a stable attractor in social space supporting maintenance of equitable societies.

Human history is full of chaotic periods, and understanding social requirements for a stable environment when rebuilding after such chaotic events would offer an opportunity for positive social change and a more sustainable governance process (Hubler & Pines, 1994, pp. 343-382). By applying cognitive dissonance theory and the concept of a planetary commons, based on the initial work of Elinor Ostrom (1990) and its subsequent development, this work begins to mathematically develop innate basic laws of social interaction to support development of a more equitable and stable political structure in social space.

The Author: Kurt Brintzenhofe

Abstract

Investigating Human Interaction through Mathematical Analysis: The Queue Transform is the result of four years of research over various academic disciplines to include probability theory, psychophysics, social psychology, information theory, detection theory, political economics, and history. Based on the data from field experiments conducted by Dr. Stanley Milgram and Dr. Bernd Schmitt, a closed form algebraic expression is derived starting with the concept of social impact theory introduced by Dr. Bibb Latane in 1981. The algebraic expression is then expanded using general information theory as presented by Dr. George Klir. This expanded expression is applied against existing independent social psychology field experiments to demonstrate the approach for transforming their various social structures into a closed form expression, resulting in the ability to predict results. With this, It is next argued that the social queue as a resource system, containing common-pool resources (time in particular), meets the eight design principles necessary to support stability within the queue. Making this link offers the potential to model more complex social systems. The importance being that If more complex social systems may eventually be evaluated for the purpose of identifying and validating stable social structures, then the opportunity exists to improve the stability of governments in our commons environment called Earth.

About the Book

Availability (1st Edition):

Chapter 1: Social Psychology and Psychophysics: Laying the Foundation

Availability (1st Edition):

Now available in print and digital open access by Taylor & Francis Publishing, Creative Commons, CC BY-NC-ND

URL: https://www.taylorfrancis.com/books/oa-mono/10.4324/9781003325161/investigating-human-interaction-mathematical-analysis-kurt-brintzenhofe

216 pages

Book Overview:

Chapter 1: Social Psychology and Psychophysics: Laying the Foundation

Availability (1st Edition):

Social science has been investigating human interaction for centuries, and yet the investigations have basically remained qualitative in nature. As such, and as Dr. Thomas Pettigrew (1986) has noted, this makes it difficult to quantitatively model and empirically test the various theories in social psychology for accuracy. It is the work of Dr. Stanley Milgram, Dr. Bibb Latane, and Dr. Bernd Schmitt which provide the concepts and data for quantitative modelling of social intragroup interaction as presented in this book. It is Dr. Latane’s social impact theory (Latane, 1981) concept that led to the ability to quantitatively predict basic group member mean probability of reaction as developed in Chapter 2. It is Dr. Milgram’s intrusion into a waiting line experiment (Milgram, et al., 1986) combined with the related experiment by Drs. Bernd Schmitt, Dube, and Leclerc (1992) that further develop in Chapter 3 the algebraic expression for investigating queue-like social group interactions. For demonstration, the algebraic expression is expanded further in Chapter 4 and applied to quantitatively model and explain various independent social psychology experiments taken from refereed journals involving basic social systems with an underlying queue-like structure. It is envisioned in Chapters 5-7 that if basic social systems as presented can be modelled, then with further development, more complex social systems may eventually be evaluated for the purpose of identifying and validating social structures which might eventually support stable governments in our commons environment called Earth. Where the Earth meets the definition of a commons environment as a bounded social system having subtractable resources (e.g.,. breathable air, drinkable water, productive land).

References:

Latane, B. (1981). The Psychology of Social Impact. American Psychologist, 36(4), 343-356. https://doi.org/10.1037/0003-066X.36.4.343

Milgram, S., Liberty, J., Toledo, R., & Wackenhut, J. (1986). Response to Intrusion into Waiting Lines. Journal of Personality and Social Psychology, 51(4), 683-689. Copyright American Psychological Association. https://doi.org/10.1037/0022-3514.51.4.683

Pettigrew, T.F. (1986). The Intergroup Contact Hypothesis Reconsidered. In M. Hewstone & R. Brown (Eds.), Contact & Conflict in Intergroup Encounters (pp. 169-195). New York: Basil Blackwell (John Wiley & Sons).

Schmitt, B., Dube, L., & Leclerc, F. (1992). Intrusions Into Waiting Lines: Does the Queue Constitute a Social System? Journal of Personality and Social Psychology, 63(5), 806-815. https://doi.org/10.1037/0022-3514.63.5.806

Chapter 1: Social Psychology and Psychophysics: Laying the Foundation

Dr. Thomas Pettigrew (1986) posed the question as to whether the various theories in social psychology were exclusive to one another, whether they were accurate, or when combined, would they support a greater understanding of how we interact in society and why? He then went on to ask, if they do, how do we know? His commentary is the genesis of this book. To begin addressing his questions, many of the past greats in social psychology and psychophysics must be introduced, from Gustav Fechner, Pitirim Sorokin, Kurt Lewin, Leon Festinger, to Stanley Stevens. Building on the work of these pioneers, axioms for a social space are presented for consideration, primarily based on the work of Kurt Lewin combined with Leon Festinger’s cognitive dissonance theory (Festinger, 1957), followed by selected works of Milgram and Latane which are used to develop the basic algebraic expression for social intragroup member quantitative modelling. It is one of Latane’s theories, using data from a Milgram experiment that is of initial interest. The first step though is to derive a justifiable quantitative model supporting Latane’s theory using a form of Weber’s Law and Fechner’s Law that is developed in a methodical and justifiable manner. This derivation is accomplished using the sonar equation. The derived form of Weber’s Law and Fechner’s Law is not new, but only noted in published documents without explanation as seeming to provide a more accurate model of empirical results. The derivation in this chapter provides the explanation and the justification for their use.

References:

Festinger, L. (1957). A Theory of Cognitive Dissonance. Stanford, California: Stanford University Press. from http://www.sup.org/books/title/?id=3850

Chapter 2: Milgram’s Drawing Power of Crowds and Social Impact Theory

Chapter 3: Revisiting Milgram’s 1978 “Response to Intrusion into Waiting Lines” Experiment

Chapter 1: Social Psychology and Psychophysics: Laying the Foundation

As a means of introducing social impact theory, Bibb Latane made use of many previous experiments, including the data from the Milgram, Bickman, and Berkowitz (1969) “Drawing Power of Crowds” experiment. The quantitative approach Latane used to model the data was conceptual, but the idea was brilliant. To model Milgram’s experiment in a manner that Latane was attempting requires use of basic information theory as related to optimal encoding. Based on examples and argument, the necessary density function using Fechner’s sensation magnitude is derived with proofs. With the density function established, the kernel of the algebraic model under development emerges through use of “The Drawing Power of Crowds” data. Theorems are developed and proven to address how to obtain the two mean social situation random variables within the derived form of Fechner’s Law, and it is then shown, using both uniform encoding and exponential encoding, that the subsequent basic model accurately predicts the results of Milgram’s “Drawing Power of Crowds” experiment and supports Latane’s hypothesis that mean probability of reaction by group members is in fact impacted by the magnitude of the social stimulus, and more importantly, it is predictable on average. Another important result of the derived model is that for the same social situation, it is shown that Fechner’s Law under exponential encoding and Stanley Stevens Power Law demonstrate mathematical equivalency.

References:

Milgram, S., Bickman, L., & Berkowitz, L. (1969). Note on the Drawing Power of Crowds of Different Size. Journal of Personality and Social Psychology, 13(2), 79-82. http://dx.doi.org/10.1037/h0028070

Chapter 3: Revisiting Milgram’s 1978 “Response to Intrusion into Waiting Lines” Experiment

Summarized raw data from Milgram’s 1978 field experiment and documented in Milgram et al. (1986) “Response to Intrusion into Waiting Lines” experiment was obtained from the Stanley Milgram Papers held at the Manuscripts and Archives, Yale University Library and used with permission from his daughter Ms. Michelle Marques (a.k.a. Milgram) who now controls the estate. Combining this with critical data from a subsequent but related queue intrusion experiment by Schmitt, Dube, and Leclerc (1992) leads to expansion of the basic algebraic formulation derived in Chapter 2, allowing for accountability of how group pressure and group member reaction/non-reaction influence a member of interest’s mean probability of reaction. The derivation relies on Bayesian statistics, theorems developed in the previous chapters, and all six conditions of Milgram’s 1978 experiment which was conducted in various locations and social situations in New York City. The result is interesting in that Kurt Lewin’s general person-situation interaction equation is now validated and operationalized using data. It is also interesting that the Golden Ratio once again appears, possibly as a means to optimize identification of social norm violations (Benjafield and Adams-Weber, 1976, p. 14). With this expanded algebraic model in place, the next step taken in this book is to evaluate independent field experiments having social situations which are transformable into a queue-like structure.

References:

Benjafield, J., & Adams-Weber, J. (1976). The Golden Section Hypothesis. British Journal of Psychology, 67(1), 11-15. https://doi.org/10.1111/j.2044-8295.1976.tb01492.x

Chapter 4: Applying the Queue Transform to Experiments Outside the Queue

Chapter 3: Revisiting Milgram’s 1978 “Response to Intrusion into Waiting Lines” Experiment

Seven previously performed independent social psychology field experiments are selected based on the criteria that they have a queue-like underlying structure. These experiments are analyzed using the derived algebraic model from Chapter 3.

In analyzing these more general queue-like experiments, the generalized information theory nomenclature and concepts developed by George Klir (2006) are applied. To quantitatively model and evaluate the results requires at least two cases within each of the experiments. A base case to establish values for the critical social situation variables, and one or more test cases to model against empirical results, for the same social situation, but with different stimulus intensities compared to the base case. Two of the experiments had insufficient information, which in itself is useful as feedback for data collection design in any future field experiments. The resultant test case results are compared to empirical results, then combined with the previous queue test cases and plotted. The resultant Pearson correlation coefficient value of the cumulative test case results is r(26)=0.9754, p<0.00001.

References:

Klir, G. (2006). Uncertainty and Information – Foundations of Generalized Information Theory. John Wiley & Sons, Inc. https://doi.org/10.1002/0471755575

Chapter 5: From the Queue to the Commons

Chapter 6: Defining an Algebraic Group in Social Space

With mathematical model development having been demonstrated on simple queue-like social systems, it remains to consider how this may be applied to more complex social systems in future efforts. It is argued the queue represents a commons environment having boundaries and subtractable resources (either time in queue or the resource sought, or both). Of the eight design principles required to support a stable social commons, as developed by Elinor Ostrom in her ground-breaking work (Ostrom, 1990), four of those principles are considered critical as evaluated by Cox, Arnold, and Tomas (2010) and subsequently approved by Elinor Ostrom in a 2013 paper published shortly after her death (Wilson, Ostrom, & Cox, 2013).

All eight design principles and their relation to the queue are addressed, with focus on the critical four. With this potential capability for use in more complex social systems, an algebraic group structure is proposed in the next chapter that may allow for further theoretical development of a quantifiable social space which then has the potential to be further operationally tested.

References:

Cox, M., Arnold, G., & Tomas, S. (2010). A Review of Design Principles for Community-based Natural Resource Management. Ecology and Society. 15(4):38. https://doi.org/10.5751/ES-03704-150438

Ostrom, E., (1990). Governing the Commons. New York: Cambridge University Press. https://doi.org/10.1017/CBO9781316423936

Wilson, D., Ostrom, E, & Cox, M. (2013). Generalizing the Core Design Principles for the Efficacy of Groups. Journal of Economic Behavior & Organization, 90S, S21-S32. https://doi.org/10.1016/j.jebo.2012.12.010

Chapter 6: Defining an Algebraic Group in Social Space

Based on Leon Festinger’s cognitive dissonance theory and mathematical development up to this point, an algebraic Abelian group is developed which also takes into account the effects of time. If time were not a factor, then it may be argued that people would eventually go insane from the cumulative effects of the various social stimuli leading to emotional discomfort that all of us encounter in varying degrees on a daily basis. With an Abelian group now established and clearly defined, there is now a structure for further theoretical development allowing the possibility to quantitatively predict certain measures in social space, a space that Pitirim Sorokin and Kurt Lewin could only qualitatively discuss in their time.

Chapter 7: History as Data

Chapter 6: Defining an Algebraic Group in Social Space

Chapter 7: History as Data

With the analytical and theoretical foundations of a subspace (queue-like structures) in social space established, this final chapter introduces the concept of using history as data. We often like to say that if you do not learn from history, then you will repeat it. With that, it seems we do not learn from history as it is currently taught. If we can view history in a more structured manner, where cause and effect are more clearly defined, then maybe that would facilitate our understanding of how certain present actions in social space relate to past social scenarios, scenarios that do not lead to desirable outcomes. Using the German Confederation’s revolution of 1848 as an example current political sensitivities are avoided, but the lessons learned through the build up to their 1848 revolution have many similarities to present day social conditions existing in numerous countries around the world. After presenting events leading up to the revolution in the German Confederation, relationships to the Queue Transform and the commons environment are considered. As one of the many examples, absence of a free press facilitates actions by those who would take advantage of the social commons environment for personal gain, at the expense of others in that same social environment. The free press is similar to those members in queue who react to an intrusion, thus providing information to the other queue members as to the severity and importance of the intrusion. If those queue members closest to the intrusion point were to not react, or in other words to provide inaccurate or misleading information (McMullen, 2022, July, 23), the remaining queue members would be much less likely to react as was demonstrated in Milgram’s intrusion experiment.

Reference:

McMullen, J. (2022, July, 23). The Audacious PR Plot that Seeded Doubt About Climate Change. BBC, https://www.bbc.com/news/science-environment-62225696