I submitted for habilitation in **Computational Social Science** at Jacobs University Bremen with a cumulative habilitation work on

## Systemic Effects in Models of

Opinion Dynamics, Societal Growth, and the Wisdom of Crowds

This (click the title above for download) is an 88 page booklet presenting the results of twelve published papers focusing on systemic effects in opinion dynamics and societal growth and on the wisdom of crowd phenomenon in group guesstimation games. Read a short summary with a focus on the new results here.

**Chapter 1: Introduction
**This chapter outlines what systemic effects are and how they can be studied through agent-based modeling, referring to these two publications:

- P. Groeber, J. Lorenz, and F. Schweitzer, “Dissonance minimization as a microfoundation of social influence in models of opinion formation,” Journal of Mathematical Sociology, vol. 38, iss. 3, pp. 147-174, 2014. [Abstract]

Models of opinion formation are used to investigate many collective phenomena. While social influence often constitutes a basic mechanism, its implementation differs between the models. In this paper, we provide a general framework of social influence inspired by the concept of cognitive dissonance. We only premise that individuals strive to minimize dissonance resulting from different opinions compared to individuals in a given social network. Within a game theoretic context, we show that our concept of dissonance reduction exhibits basic properties of a coordination process. We further show that different models of opinion formation can be represented as best response dynamics within our framework. Thus, we offer a unifying perspective on these heterogeneous models and link them to rational choice theory.

`@Article{Groeber.Lorenz.ea2014Dissonanceminimizationas, Title = {Dissonance minimization as a microfoundation of social influence in models of opinion formation}, Author = {Patrick Groeber and Jan Lorenz and Frank Schweitzer}, Journal = {Journal of Mathematical Sociology}, Year = {2014}, Number = {3}, Pages = {147-174}, Volume = {38}, Abstract = {Models of opinion formation are used to investigate many collective phenomena. While social influence often constitutes a basic mechanism, its implementation differs between the models. In this paper, we provide a general framework of social influence inspired by the concept of cognitive dissonance. We only premise that individuals strive to minimize dissonance resulting from different opinions compared to individuals in a given social network. Within a game theoretic context, we show that our concept of dissonance reduction exhibits basic properties of a coordination process. We further show that different models of opinion formation can be represented as best response dynamics within our framework. Thus, we offer a unifying perspective on these heterogeneous models and link them to rational choice theory.}, Doi = {10.1080/0022250X.2012.724486}, Jlprojects = {continuous_opinion_dynamics, evolution_of_norms}, Owner = {janlo}, Timestamp = {2011.03.08} }`

- J. Lorenz, “Zur Methode der agenten-basierten Simulation in der Politikwissenschaft am Beispiel von Meinungsdynamik und Parteienwettstreit,” in Jahrbuch für Handlungs- und Entscheidungstheorie. Band 7: Experiment und Simulation, T. Bräuninger, A. Bächtiger, and S. Shikano, Eds., VS Verlag für Sozialwissenschaften, 2012, pp. 31-58.
`@InCollection{Lorenz2012ZurMethodeder, Title = {{Zur Methode der agenten-basierten Simulation in der Politikwissenschaft am Beispiel von Meinungsdynamik und Parteienwettstreit}}, Author = {Jan Lorenz}, Booktitle = {Jahrbuch f\"ur Handlungs- und Entscheidungstheorie. Band 7: Experiment und Simulation}, Publisher = {VS Verlag f\"ur Sozialwissenschaften}, Year = {2012}, Editor = {Thomas Br\"auninger and Andr\'e B\"achtiger and Susumu Shikano}, Pages = {31--58}, Doi = {10.1007/978-3-531-19606-0_2}, Keywords = {emmyown}, Owner = {janlo}, Timestamp = {2012.01.24} }`

**Chapter 2: Opinion Dynamics
**This chapter presents four different models of opinion dynamics, which are the result of theory- or data-driven modeling attempts. The evolving opinion landscapes (= distribution of opinions, represented by histograms) can be plotted on the vertical axis against the core parameter of the model on the horizontal axis. This delivers an

**opinion pattern diagram**where the coloring represents the frequency of agents’ opinions in that region of the [core parameter] x opinion space. The opinion landscapes are the one which appear after stabilization. See the four opinion pattern diagrams here:

- J. K. Shin and J. Lorenz, “Tipping Diffusivity in Information Accumulation Systems: More Links, less Consensus,” Journal of Statistical Mechanics: Theory and Experiment, vol. 2010, iss. 06, p. P06005, 2010. [Abstract]

Assume two different communities each of which maintain their respective opinions mainly because of the weak interaction between them. In such a case, it is an interesting problem to find the necessary strength of inter-community interaction in order for the two communities to reach a consensus. In this paper, the information accumulation system (IAS) model is applied to investigate the problem. With the application of the IAS model, the opinion dynamics of the two-community problem is found to belong to a wider class of two-species problems appearing in population dynamics or in the competition of two languages, for all of which the governing equations can be described in terms of coupled logistic maps. Tipping diffusivity is defined as the maximal inter-community interaction such that the two communities maintain different opinions. For a problem with a simple community structure and homogeneous individuals, the tipping diffusivity is calculated theoretically. As a conclusion of the paper, the convergence of the two communities to the same value is less possible the more overall interaction, intra-community and inter-community, takes place. This implies, for example, that the increase in the interaction between individuals caused by the development of modern communication tools, such as Facebook and Twitter, does not necessarily improve the tendency towards global convergence between different communities. If the number of internal links increases by a factor, the number of inter-community links must be increased by an even higher factor, in order for consensus to be the only stable attractor.

`@Article{Shin.Lorenz2010TippingDiffusivityin, Title = {Tipping Diffusivity in Information Accumulation Systems: More Links, less Consensus}, Author = {Jae Kyun Shin and Jan Lorenz}, Journal = {Journal of Statistical Mechanics: Theory and Experiment}, Year = {2010}, Number = {06}, Pages = {P06005}, Volume = {2010}, Abstract = {Assume two different communities each of which maintain their respective opinions mainly because of the weak interaction between them. In such a case, it is an interesting problem to find the necessary strength of inter-community interaction in order for the two communities to reach a consensus. In this paper, the information accumulation system (IAS) model is applied to investigate the problem. With the application of the IAS model, the opinion dynamics of the two-community problem is found to belong to a wider class of two-species problems appearing in population dynamics or in the competition of two languages, for all of which the governing equations can be described in terms of coupled logistic maps. Tipping diffusivity is defined as the maximal inter-community interaction such that the two communities maintain different opinions. For a problem with a simple community structure and homogeneous individuals, the tipping diffusivity is calculated theoretically. As a conclusion of the paper, the convergence of the two communities to the same value is less possible the more overall interaction, intra-community and inter-community, takes place. This implies, for example, that the increase in the interaction between individuals caused by the development of modern communication tools, such as Facebook and Twitter, does not necessarily improve the tendency towards global convergence between different communities. If the number of internal links increases by a factor, the number of inter-community links must be increased by an even higher factor, in order for consensus to be the only stable attractor.}, Collaborationtags = {JL publicationlist}, Doi = {10.1088/1742-5468/2010/06/P06005}, Eprint = {0909.1252}, Keywords = {emmyown}, Owner = {janlo}, Timestamp = {2009.09.08} }`

ODP-tipping-1

Opinion pattern diagram for increasing number of links (diffusivity) under a constant ratio of intra-vs-inter-community links. A phase of coexistence of different ideological camps appears with increasing diffusivity.

- T. Metz and J. Lorenz, “Become who you are: The homing pattern in partisanship as a self-reinforcing stochastic process,” SSRN Preprint, 2013. [Abstract]

Partisanship is characterized by a homing pattern in which individuals pick a party and alternate between supporting and not supporting it. We present a stochastic model in which the probability to announce an attachment depends on an initial propensity to support the party and the number of times support has been announced before. The model reproduces the empirical distributions of the total number of utterances of party preferences in German panel data holding the longest and most dense measurement of Partisanship worldwide.

`@Article{Metz.Lorenz2013Becomewhoyou, Title = {Become who you are: The homing pattern in partisanship as a self-reinforcing stochastic process}, Author = {Metz, Thomas and Lorenz, Jan}, Journal = {SSRN Preprint}, Year = {2013}, Abstract = {Partisanship is characterized by a homing pattern in which individuals pick a party and alternate between supporting and not supporting it. We present a stochastic model in which the probability to announce an attachment depends on an initial propensity to support the party and the number of times support has been announced before. The model reproduces the empirical distributions of the total number of utterances of party preferences in German panel data holding the longest and most dense measurement of Partisanship worldwide.}, Owner = {janlo}, Timestamp = {2013.03.05}, Url = {http://ssrn.com/abstract=2224740} }`

OPD-partyID-1

Opinion pattern diagram for the self-reinforcment model for the strength of party attachments (= number of yearly announced party attachments over 10 years) with respect to the parameter “Interest in politics”.

- J. Lorenz, “Universality of movie rating distributions,” European Physical Journal B, vol. 71, pp. 251-258, 2009. [Abstract]

In this paper histograms of user ratings for movies (1,…,10) are analysed. The evolving stabilised shapes of histograms follow the rule that all are either double- or triple-peaked. Moreover, at most one peak can be on the central bins 2,…,9 and the distribution in these bins looks smooth `Gaussian-like’ while changes at the extremes (1 and 10) often look abrupt. It is shown that this is well approximated under the assumption that histograms are confined and discretised probability density functions of Lévy skew alpha-stable distributions. These distributions are the only stable distributions which could emerge due to a generalized central limit theorem from averaging of various independent random avriables as which one can see the initial opinions of users. Averaging is also an appropriate assumption about the social process which underlies the process of continuous opinion formation. Surprisingly, not the normal distribution achieves the best fit over histograms obseved on the web, but distributions with fat tails which decay as power-laws with exponent -(1+alpha) (alpha=4/3). The scale and skewness parameters of the Levy skew alpha-stable distributions seem to depend on the deviation from an average movie (with mean about 7.6). The histogram of such an average movie has no skewness and is the most narrow one. If a movie deviates from average the distribution gets broader and skew. The skewness pronounces the deviation. This is used to construct a one parameter fit which gives some evidence of universality in processes of continuous opinion dynamics about taste.

`@Article{Lorenz2009Universalityofmovie, Title = {{Universality of movie rating distributions}}, Author = {Lorenz, Jan}, Journal = {European Physical Journal B}, Year = {2009}, Pages = {251-258}, Volume = {71}, Abstract = {In this paper histograms of user ratings for movies (1,...,10) are analysed. The evolving stabilised shapes of histograms follow the rule that all are either double- or triple-peaked. Moreover, at most one peak can be on the central bins 2,...,9 and the distribution in these bins looks smooth `Gaussian-like' while changes at the extremes (1 and 10) often look abrupt. It is shown that this is well approximated under the assumption that histograms are confined and discretised probability density functions of L\'evy skew alpha-stable distributions. These distributions are the only stable distributions which could emerge due to a generalized central limit theorem from averaging of various independent random avriables as which one can see the initial opinions of users. Averaging is also an appropriate assumption about the social process which underlies the process of continuous opinion formation. Surprisingly, not the normal distribution achieves the best fit over histograms obseved on the web, but distributions with fat tails which decay as power-laws with exponent -(1+alpha) (alpha=4/3). The scale and skewness parameters of the Levy skew alpha-stable distributions seem to depend on the deviation from an average movie (with mean about 7.6). The histogram of such an average movie has no skewness and is the most narrow one. If a movie deviates from average the distribution gets broader and skew. The skewness pronounces the deviation. This is used to construct a one parameter fit which gives some evidence of universality in processes of continuous opinion dynamics about taste.}, Collaborationtags = {JL publicationlist}, Doi = {10.1140/epjb/e2009-00283-3}, Eprint = {0806.2305}, Eprinttype = {arxiv}, Groups = {public}, Intrahash = {2661dd0ae2070f60f0f8be177aac0279}, Keywords = {emmyown}, Owner = {janlo}, Timestamp = {2008.08.19} }`

ODP-ratings-1

Opinion pattern diagram for 1-10 star movie rating histograms with respect to movie quality according to a one-parameter fit based on data from IMDb.com.

- J. Lorenz, “Modeling the Evolution of Ideological Landscapes through Opinion Dynamics,” in Advances in Social Simulation 2015, 2017.
`@InProceedings{Lorenz2015ModelingEvolutionIdeological, Title = {Modeling the Evolution of Ideological Landscapes through Opinion Dynamics}, Author = {Lorenz, Jan}, Booktitle = {Advances in Social Simulation 2015}, Year = {2017}, Note = {available in Spring 2017}, Publisher = {Springer}, Owner = {janlo}, Timestamp = {2016.05.26} }`

OPD-boundedconfidence-1

Opinion pattern diagram for the bounded confidence model with random opinion replacement with respect to the homogeneous bound of confidence . m=0.1 means 1 out of 10 agents draw a new opinion at random, while 9 out of ten rely on social interaction under bounded confidence). Notice that the consensus transition () is sharp, while the transition between two- and three-cluster regimes () is smooth.

**Chapter 3: Societal Growth
**This chapter presents the following three papers and concludes with a short discussion on systemic growth effects.

- M. D. König, J. Lorenz, and F. Zilibotti, “Innovation vs. imitation and the evolution of productivity distributions,” Theoretical Economics, vol. 11, iss. 3, pp. 1053-1102, 2016.
`@Article{Koenig.Lorenz.ea2016Innovationvsimitation, Title = {Innovation vs. imitation and the evolution of productivity distributions}, Author = {K\"onig, Michael D. and Lorenz, Jan and Zilibotti, Fabrizio}, Journal = {Theoretical Economics}, Year = {2016}, Number = {3}, Pages = {1053-1102}, Volume = {11}, Owner = {janlo}, Timestamp = {2017.01.23}, Url = {https://econtheory.org/ojs/index.php/te/article/view/20161053/0} }`

- J. Lorenz, F. Paetzel, and F. Schweitzer, “Redistribution spurs growth by using a portfolio effect on risky human capital,” PLoS One, vol. 8, iss. 2, p. e54904, 2013. [Abstract]

We demonstrate by mathematical analysis and systematic computer simulations that taxation and redistribution of wealth can lead to sustainable growth of wealth in a society. The wealth dynamics of each agent is described by a stochastic multiplicative process which, in the long run, leads to the destruction of individual wealth and the extinction of the individualistic society. When agents are coupled by redistributive taxation the situation might turn to individual growth in the long run. We consider that a government collected a proportion of wealth and reduces it by a fraction as costs for administration. The remaining public good is equally redistributed to all agents. We derive conditions under which the destruction of wealth can be turned into sustainable growth, despite the losses from the random growth process and despite the administrative costs. The findings are verified for three different tax schemes: proportional tax, taking proportional more from the rich, and proportionally more from the poor. We discuss which of these tax schemes is optimal with respect to maximize growth of wealth under a fixed rate of administrative costs, or with respect to maximize the governmental income. This leads us to some general conclusions about governmental decisions, the relation to public good games, and the use of taxation in a risk taking society.

`@Article{Lorenz.Paetzel.ea2013Redistributionspursgrowth, Title = {Redistribution spurs growth by using a portfolio effect on risky human capital}, Author = {Jan Lorenz and Fabian Paetzel and Frank Schweitzer}, Journal = {PLoS One}, Year = {2013}, Number = {2}, Pages = {e54904}, Volume = {8}, Abstract = {We demonstrate by mathematical analysis and systematic computer simulations that taxation and redistribution of wealth can lead to sustainable growth of wealth in a society. The wealth dynamics of each agent is described by a stochastic multiplicative process which, in the long run, leads to the destruction of individual wealth and the extinction of the individualistic society. When agents are coupled by redistributive taxation the situation might turn to individual growth in the long run. We consider that a government collected a proportion of wealth and reduces it by a fraction as costs for administration. The remaining public good is equally redistributed to all agents. We derive conditions under which the destruction of wealth can be turned into sustainable growth, despite the losses from the random growth process and despite the administrative costs. The findings are verified for three different tax schemes: proportional tax, taking proportional more from the rich, and proportionally more from the poor. We discuss which of these tax schemes is optimal with respect to maximize growth of wealth under a fixed rate of administrative costs, or with respect to maximize the governmental income. This leads us to some general conclusions about governmental decisions, the relation to public good games, and the use of taxation in a risk taking society.}, Doi = {10.1371/journal.pone.0054904}, Keywords = {emmyown}, Owner = {janlo}, Timestamp = {2011.05.17} }`

- J. Lorenz, F. Paetzel, and M. S. Tepe, “Just Don’t Call it a Tax! Framing in an Experiment on Voting and Redistribution,” Journal of Experimental Political Science, 2017.
`@Article{Lorenz.Paetzel.ea2017JustDontCall, Title = {Just Don't Call it a Tax! Framing in an Experiment on Voting and Redistribution}, Author = {Lorenz, Jan and Paetzel, Fabian and Tepe, Markus S.}, Journal = {Journal of Experimental Political Science}, Year = {2017}, Note = {to appear March 2017, preprint available at SSRN}, Doi = {10.2139/ssrn.2611534}, Owner = {janlo}, Timestamp = {2015.06.30} }`

**Chapter 4: The Wisdom of the Crowd
**Besides presenting the results of three papers, this chapter presents a thorough discussion and definition of the wisdom of crowd in group guesstimation tasks (Sec. 4.2). It presents and analyzes three datasets (Sec. 4.1), from which one is the data set from Galton’s famous 1907 paper, while the other twoare collected by my. The later ones were only treated in this blog before. Take a look at the histograms and how different measures of aggregation perform:

**Galton-Data-1**

Viertelfest-Hist-1

OL-Plot-1

The chapter also presents a new concept to relate systematic bias to the expected fraction of “ad hoc” experts in a crowd (Sec. 4.5) and how this transforms to a measure for optimal crowd size. Finally, the concept of diversity sampling is presented (also Sec. 4.5) which shows the doubleedge that it improves the correctness of aggregate estimates for small crowds for the arithmetic mean, while it reduces it for the median.

The papers presented are:

- J. Lorenz, H. Rauhut, and B. Kittel, “Majoritarian Democracy Undermines Truth-Finding in Deliberative Committees,” Research & Politics, iss. 2, pp. 1-10, 2015. [Abstract]

The median of independent judgments usually outperforms individual estimates of vaguely known facts. It is well known that communication undermines this wisdom-of-crowd effect because it makes judgments mutually dependent. Instead, according to deliberative democratic theory, the transparent and honest exchange of knowledge and opinions should promote generally acceptable and correct decisions. We study the effect of deliberation, majority rule and unanimity rule on the wisdom-of-crowd effect. We conducted a non-competitive group experiment where subjects in small deliberative committees had to communicate and finally judge vaguely known facts. Subjects’ rewards were inversely related to the distance of the true value to their individual, their majoritarian or their consensual final judgment. Taking the median of initial individual private estimates as a benchmark, the results show that after communication groups perform worse when they were to decide by majority compared to groups deciding unanimously or with individual rewards. The reason for lower collective intelligence after deliberation under majority rule is probably that epistemic motivation of individuals is low because estimates need not be taken into account by others, while at the same time social motivation to change opinion for majority’s sake is high.

`@Article{Lorenz.Rauhut.ea2015MajoritarianDemocracyUndermines, Title = {Majoritarian Democracy Undermines Truth-Finding in Deliberative Committees}, Author = {Lorenz, Jan and Rauhut, Heiko and Kittel, Bernhard}, Journal = {Research \& Politics}, Year = {2015}, Number = {2}, Pages = {1--10}, Abstract = {The median of independent judgments usually outperforms individual estimates of vaguely known facts. It is well known that communication undermines this wisdom-of-crowd effect because it makes judgments mutually dependent. Instead, according to deliberative democratic theory, the transparent and honest exchange of knowledge and opinions should promote generally acceptable and correct decisions. We study the effect of deliberation, majority rule and unanimity rule on the wisdom-of-crowd effect. We conducted a non-competitive group experiment where subjects in small deliberative committees had to communicate and finally judge vaguely known facts. Subjects' rewards were inversely related to the distance of the true value to their individual, their majoritarian or their consensual final judgment. Taking the median of initial individual private estimates as a benchmark, the results show that after communication groups perform worse when they were to decide by majority compared to groups deciding unanimously or with individual rewards. The reason for lower collective intelligence after deliberation under majority rule is probably that epistemic motivation of individuals is low because estimates need not be taken into account by others, while at the same time social motivation to change opinion for majority's sake is high.}, Doi = {10.1177/2053168015582287}, Owner = {janlo}, Timestamp = {2014.01.10} }`

- J. Lorenz, H. Rauhut, F. Schweitzer, and D. Helbing, “How social influence can undermine the wisdom of crowd effect,” Proceedings of the National Academy of Sciences, vol. 108, iss. 22, pp. 9020-9025, 2011. [Abstract]

Social groups can be remarkably smart and knowledgeable when their averaged judgements are compared with the judgements of individuals. Already Galton [Galton F (1907) Nature 75:7] found evidence that the median estimate of a group can be more accurate than estimates of experts. This wisdom of crowd effect was recently supported by examples from stock markets, political elections, and quiz shows [Surowiecki J (2004) The Wisdom of Crowds]. In contrast, we demonstrate by experimental evidence (N = 144) that even mild social influence can undermine the wisdom of crowd effect in simple estimation tasks. In the experiment, subjects could reconsider their response to factual questions after having received average or full information of the responses of other subjects. We compare subjects’ convergence of estimates and improvements in accuracy over five consecutive estimation periods with a control condition, in which no information about others’ responses was provided. Although groups are initially ”wise,” knowledge about estimates of others narrows the diversity of opinions to such an extent that it undermines the wisdom of crowd effect in three different ways. The ”social influence effect” diminishes the diversity of the crowd without improvements of its collective error. The ”range reduction effect” moves the position of the truth to peripheral regions of the range of estimates so that the crowd becomes less reliable in providing expertise for external observers. The ”confidence effect” boosts individuals’ confidence after convergence of their estimates despite lack of improved accuracy. Examples of the revealed mechanism range from misled elites to the recent global financial crisis.

`@Article{Lorenz.Rauhut.ea2011HowSocialInfluence, Title = {How social influence can undermine the wisdom of crowd effect}, Author = {Lorenz, Jan and Rauhut, Heiko and Schweitzer, Frank and Helbing, Dirk}, Journal = {Proceedings of the National Academy of Sciences}, Year = {2011}, Number = {22}, Pages = {9020--9025}, Volume = {108}, Abstract = {Social groups can be remarkably smart and knowledgeable when their averaged judgements are compared with the judgements of individuals. Already Galton [Galton F (1907) Nature 75:7] found evidence that the median estimate of a group can be more accurate than estimates of experts. This wisdom of crowd effect was recently supported by examples from stock markets, political elections, and quiz shows [Surowiecki J (2004) The Wisdom of Crowds]. In contrast, we demonstrate by experimental evidence (N = 144) that even mild social influence can undermine the wisdom of crowd effect in simple estimation tasks. In the experiment, subjects could reconsider their response to factual questions after having received average or full information of the responses of other subjects. We compare subjects' convergence of estimates and improvements in accuracy over five consecutive estimation periods with a control condition, in which no information about others' responses was provided. Although groups are initially ''wise,'' knowledge about estimates of others narrows the diversity of opinions to such an extent that it undermines the wisdom of crowd effect in three different ways. The ''social influence effect'' diminishes the diversity of the crowd without improvements of its collective error. The ''range reduction effect'' moves the position of the truth to peripheral regions of the range of estimates so that the crowd becomes less reliable in providing expertise for external observers. The ''confidence effect'' boosts individuals' confidence after convergence of their estimates despite lack of improved accuracy. Examples of the revealed mechanism range from misled elites to the recent global financial crisis.}, Doi = {10.1073/pnas.1008636108}, Keywords = {emmyown}, Owner = {janlo}, Timestamp = {2011.04.13} }`

- H. Rauhut and J. Lorenz, “The wisdom of crowds in one mind: How individuals can simulate the knowledge of diverse societies to reach better decisions,” Journal of Mathematical Psychology, vol. 55, pp. 191-197, 2010. [Abstract]

The joint knowledge of many diverse individuals can outperform experts in estimation and decision-making problems. This wisdom of the crowd has been demonstrated in different societal areas such as internet search engines, political elections or stock markets. Recently, psychologists argued that humans may even simulate a diverse society in their own mind by drawing different answers from their brain (Vul & Pashler, 2008). The underlying idea is that individuals can access different knowledge areas in their brain, whose joint evaluation yields better estimates than their separate consideration. This article presents a mathematical treatment of the wisdom of crowds and two potential mechanisms to quantify the wisdom of crowds in one mind. The implications of both methods are analyzed and applied to new experimental data (N=144), which contain five consecutive estimates from the same individuals. The theoretical and empirical analysis demonstrates limitations of the wisdom of crowds in one mind: Asking oneself several times is on average less powerful than asking only one other individual. This is due to the smaller diversity of estimates of similar individuals and the larger average bias to which they converge. Further, individuals cannot perform independent draws from an “internal distribution”. Hence, there may be other mechanisms at work such as talking oneself into believing initial guesses or eliciting progressively wilder ones.

`@Article{Rauhut.Lorenz2010wisdomofcrowds, Title = {The wisdom of crowds in one mind: How individuals can simulate the knowledge of diverse societies to reach better decisions}, Author = {Heiko Rauhut and Jan Lorenz}, Journal = {Journal of Mathematical Psychology}, Year = {2010}, Pages = {191--197}, Volume = {55}, Abstract = {The joint knowledge of many diverse individuals can outperform experts in estimation and decision-making problems. This wisdom of the crowd has been demonstrated in different societal areas such as internet search engines, political elections or stock markets. Recently, psychologists argued that humans may even simulate a diverse society in their own mind by drawing different answers from their brain (Vul \& Pashler, 2008). The underlying idea is that individuals can access different knowledge areas in their brain, whose joint evaluation yields better estimates than their separate consideration. This article presents a mathematical treatment of the wisdom of crowds and two potential mechanisms to quantify the wisdom of crowds in one mind. The implications of both methods are analyzed and applied to new experimental data (N=144), which contain five consecutive estimates from the same individuals. The theoretical and empirical analysis demonstrates limitations of the wisdom of crowds in one mind: Asking oneself several times is on average less powerful than asking only one other individual. This is due to the smaller diversity of estimates of similar individuals and the larger average bias to which they converge. Further, individuals cannot perform independent draws from an ``internal distribution''. Hence, there may be other mechanisms at work such as talking oneself into believing initial guesses or eliciting progressively wilder ones.}, Collaborationtags = {JL publicationlist}, Doi = {10.1016/j.jmp.2010.10.002}, Keywords = {emmyown}, Owner = {janlo}, Timestamp = {2009.09.18} }`

Source file for the submitted version including R-code are here

- J. Lorenz, “Source files and scripts of the Habilitation Work submitted to Jacobs University Bremen,” , 2017.
`@Other{Lorenz2017Sourcefilesand, Title = {Source files and scripts of the Habilitation Work submitted to Jacobs University Bremen}, Author = {Jan Lorenz}, Doi = {10.5281/zenodo.238807}, Note = {Provided at github.com/janlorenz/habil archived under doi:10.5281/zenodo.238807}, Owner = {janlo}, Timestamp = {2016.11.17}, Year = {2017} }`

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