Quantifying the effects of social influence

How do humans respond to indirect social influence when making decisions? We analysed an experiment where subjects had to repeatedly guess the correct answer to factual questions, while having only aggregated information about the answers of others. While the response of humans to aggregated information is a widely observed phenomenon, it has not been investigated quantitatively, in a controlled setting. We found that the adjustment of individual guesses depends linearly on the distance to the mean of all guesses. This is a remarkable, and yet surprisingly simple, statistical regularity. It holds across all questions analysed, even though the correct answers differ in several orders of magnitude. Our finding supports the assumption that individual diversity does not affect the response to indirect social influence. It also complements previous results on the nonlinear response in information-rich scenarios. We argue that the nature of the response to social influence crucially changes with the level of information aggregation. This insight contributes to the empirical foundation of models for collective decisions under social influence.Comment: 3 figure

Enhanced or distorted wisdom of crowds? An agent-based model of opinion formation under social influence

We propose an agent-based model of collective opinion formation to study the wisdom of crowds under social influence. The opinion of an agent is a continuous positive value, denoting its subjective answer to a factual question. The wisdom of crowds states that the average of all opinions is close to the truth, i.e. the correct answer. But if agents have the chance to adjust their opinion in response to the opinions of others, this effect can be destroyed. Our model investigates this scenario by evaluating two competing effects: (i) agents tend to keep their own opinion (individual conviction $\beta$), (ii) they tend to adjust their opinion if they have information about the opinions of others (social influence $\alpha$). For the latter, two different regimes (full information vs. aggregated information) are compared. Our simulations show that social influence only in rare cases enhances the wisdom of crowds. Most often, we find that agents converge to a collective opinion that is even farther away from the true answer. So, under social influence the wisdom of crowds can be systematically wrong

The ambiguous role of social influence on the wisdom of crowds: An analytic approach

"Wisdom of crowds" refers to the phenomenon that the average opinion of a group of individuals on a given question can be very close to the true answer. It requires a large group diversity of opinions, but the collective error, the difference between the average opinion and the true value, has to be small. We consider a stochastic opinion dynamics where individuals can change their opinion based on the opinions of others (social influence $\alpha$), but to some degree also stick to their initial opinion (individual conviction $\beta$). We then derive analytic expressions for the dynamics of the collective error and the group diversity. We analyze their long-term behavior to determine the impact of the two parameters $(\alpha,\beta)$ and the initial opinion distribution on the wisdom of crowds. This allows us to quantify the ambiguous role of social influence: only if the initial collective error is large, it helps to improve the wisdom of crowds, but in most cases it deteriorates the outcome. In these cases, individual conviction still improves the wisdom of crowds because it mitigates the impact of social influence

Quantifying the Impact of Leveraging and Diversification on Systemic Risk

Excessive leverage, i.e. the abuse of debt financing, is considered one of the primary factors in the default of financial institutions. Systemic risk results from correlations between individual default probabilities that cannot be considered independent. Based on the structural framework by Merton (1974), we discuss a model in which these correlations arise from overlaps in banks' portfolios. Portfolio diversification is used as a strategy to mitigate losses from investments in risky projects. We calculate an optimal level of diversification that has to be reached for a given level of excessive leverage to still mitigate an increase in systemic risk. In our model, this optimal diversification further depends on the market size and the market conditions (e.g. volatility). It allows to distinguish between a safe regime, in which excessive leverage does not result in an increase of systemic risk, and a risky regime, in which excessive leverage cannot be mitigated leading to an increased systemic risk. Our results are of relevance for financial regulators

Quantifying the Impact of Leveraging and Diversification on Systemic Risk

Excessive leverage, i.e. the abuse of debt financing, is considered one of the  primary factors in the default of financial institutions. Systemic risk results from correlations between individual default probabilities that cannot be considered independent. Based on the structural framework by Merton (1974), we discuss a model in which these  correlations arise from overlaps in banks' portfolios. Portfolio  diversification is used as a strategy to mitigate losses from investments in risky projects. We calculate an optimal level of  diversification that has to be reached for a given level of excessive leverage to still mitigate an increase in systemic risk. In our  model, this optimal diversification further depends on the market size and the market conditions (e.g. volatility). It allows to distinguish between a safe regime, in which excessive leverage does not result in an increase of systemic risk, and a risky regime, in which excessive leverage cannot be mitigated leading to an increased systemic risk. Our results are of relevance for financial regulators