Effects of Social Influence on the Wisdom of Crowds

Wisdom of crowds refers to the phenomenon that the aggregate prediction or forecast of a group of individuals can be surprisingly more accurate than most individuals in the group, and sometimes – than any of the individuals comprising it. This article models the impact of social influence on the wisdom of crowds. We build a minimalistic representation of individuals as Brownian particles coupled by means of social influence. We demonstrate that the model can reproduce results of a previous empirical study. This allows us to draw more fundamental conclusions about the role of social influence: In particular, we show that the question of whether social influence has a positive or negative net effect on the wisdom of crowds is ill-defined. Instead, it is the starting configuration of the population, in terms of its diversity and accuracy, that directly determines how beneficial social influence actually is. The article further examines the scenarios under which social influence promotes or impairs the wisdom of crowds. INTRODUCTION Contrary to popular belief, the wisdom of crowds is a statistical and not a psychological phenomenon. Wisdom, in this context, refers to the aggregate opinion of a population being closer to a true value than most individual opinions. The idea of aggregating over a space of opinions can, in an ergodic fashion, also be applied to aggregating over an individual’s own perspectives over time, with the same benefits – i.e. it may yield a more accurate decision making (Rauhut & Lorenz 2011). However, the wisdom of crowds is not a pure statistical regularity, in the sense that more does not imply better. It necessitates certain conditions, which can be summarised, following (Surowiecki 2005), as diversity and independence of opinions, specialisation in expert knowledge and a mechanism for aggregating individual opinions. From this perspective, the best collective decisions do not rely on consensus building and compromises, but instead on aggregating many heterogeneous views – given enough diversity in opinions, the errors in each of them cancel out until only useful information is left (Surowiecki 2005, p.10). The terms crowd and group are used interchangeably, as are opinions ↔ estimates ↔ judgements ↔ beliefs and configuration ↔ state. Diversity has been identified as instrumental in providing creative perspectives to problem-solving, thus avoiding getting stuck in locally suboptimal solutions (Hong & Page 2004). In fact, the “diversity prediction theorem” (Page 2007) shows that diversity weighs as much as individual ability in determining collective accuracy. From a mathematical point of view, diversity is required in order to balance out uncorrelated imperfections in opinions through aggregation. Intuitively, as no single individual is aware of all traits of a given problem at hand, diversity helps people combine their idiosyncratic perceptions so that together they gain a wider perspective. Diversity, however, is not the pinnacle of optimal decision-making. No amount of diversity can help if the population is completely ignorant on a given issue, or if opinions are diverse, but heavily skewed. Thus, the composition of diversity is as important as diversity itself (Bonabeau 2009). Independence of opinions is another important distinguishing feature of the wisdom of crowds for it either excludes communication, information spreading, learning and social influence processes, such as herding and imitation or limits the effect of such processes should they be present. In this context, it is useful to draw a conceptual difference between wisdom of crowds, as commonly understood, and “collective intelligence”. Wisdom of crowds is a quantification of the state currently occupied by a given group, such as an aggregate opinion. Intelligence, pertains to the ability of individuals to learn, to understand, and to adapt to arbitrary external conditions using own knowledge (Leimeister 2010). Collective, describes a group of individuals pooling their intelligence together for a common purpose. As such, collective intelligence can be seen as the mechanism by which groups converge to a certain collective decision, whereas wisdom of crowds is the numerical representation of the said decision. In this paper, we are interested in how the collective intelligence mechanism affects the wisdom of crowds. Recent empirical evidence has shown that enabling collective intelligence by introducing social influence, can be detrimental to the aggregate performance of a population (Lorenz et al. 2011). By social influence, we underThe theorem states that collective accuracy equals average individual error minus the variance in opinions, i.e. group diversity. Performance is the pair {E(t),W(t)}. See next section. ar X iv :1 20 4. 34 63 v1 [ cs .S I] 1 6 A pr 2 01 2 PROCEEDINGS, CI 2012 stand the pervasive tendency of individuals to conform to the behaviour and expectations of others (Kahan 1997). In separate experiments, Lorenz et al. asked participants to re-evaluate their opinions on quantitative subjects over several rounds and under three information spreading scenarios – no information about others’ estimations (control group), the average of all opinions in each round and full information on other subjects’ judgements. They found evidence that under the latter two regimes, the diversity in the population decreased, while the collective deviation from the truth increased. This result justified the disheartening conclusion that allowing people to learn about others’ behaviours and adapt their own as a response does not always lead to the group acting “wiser”. Rather, as the authors posited, not only is the population jointly convinced of a wrong result, but even the simple aggregation technique of the wisdom of crowds is deteriorated. From a policy-maker’s perspective, such groups are, thus, not wise. Current research has not yet investigated thoroughly the theoretical link between social influence and its effect on the wisdom of crowds. In this paper, we build upon the empirical study in (Lorenz et al. 2011) by developing a formal model of social influence. Our goal is to unveil whether the effects of social influence are unconditionally positive or negative, or whether its ultimate role is mediated through some mechanism, so that the effect on the group wisdom is only indirect. We adopt a minimalistic agent-based model, which successfully reproduces the findings of the said study and gives enough insight to draw more general conclusions. In particular, we confirm that small amounts of social influence lead to faster convergence, however, it is the starting configuration of the population (in terms of its initial diversity and deviation from the truth) that ultimately attribute the net effect of social influence on the wisdom of crowds. The rest of the paper is organised as follows. The next section reviews the empirical study on which our model is based, together with its main results and the measures used to quantify the collective performance of the groups. The model itself is presented after that. Results and conclusions follow as the last two sections respectively.