"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 $α$), but to some degree also stick to their initial opinion (individual conviction $β$). 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 $(α,β)$ 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.
Beyond the Wisdom of the Crowd: How Network Topology Distorts Collective Perception
Sapienza University of Rome（罗马第一大学）；Enrico Fermi Research Center（恩里科·费米研究中心）；Sony Computer Science Laboratories - Rome（索尼计算机科学实验室-罗马）；University Tor Vergata（托尔维加塔大学）；INFN（意大利国家核物理研究所）；Complexity Science Hub（复杂性科学中心）
Wisdom of the Confident: Using Social Interactions to Eliminate the Bias in Wisdom of the Crowds
与个体相比，人类群体可以通过简单地使用个体估计的平均值、中位数或几何平均值来进行非常准确的估计[Galton 1907，Surowiecki 2005，第2008页]。然而，这只对某些任务是正确的，一般来说，这些集体估计显示出强烈的偏见。当考虑到社会互动时，该方法也失败了，这使得集体估计变得更糟，因为个体倾向于收敛到有偏差的结果[Lorenz等人，2011]。在这里，我们展示了社会互动对集体智慧的明显负面影响的光明面。我们发现，有些人抵制社会的影响，当使用这个小组的中位数，我们可以消除偏见的智慧的整个人群。为了找到这个对私人估计比对社会影响更有信心的个体亚组，我们将个体建模为将私人和社会信息与不同的相对权重相结合的估计量[Perez-Escudero & de Polavieja 2011，Arganda et al. 2012]。然后，我们通过排除那些在估计中使用较高社会影响力权重值的群体，计算了越来越小的群体的几何平均值。在这个过程中得到的趋势给出了无偏的结果，与计算整个组的中位数的简单方法相反。我们的研究结果表明，虽然一个简单的操作，如平均值，中位数或几何平均值的一组可能不允许群体作出良好的估计，一个更复杂的操作，考虑到个性的社会动态可以导致更好的集体智慧。
