Modest difference in individual decisional skills may warrant substantial inequality in power. This claim has been illustrated in Ben Yashar and Nitzan (Economics Letters 174:93–95, 2019), applying the symmetric uncertain dichotomous choice setting and focusing on the skill-dependent (s-d) power of the decision-makers under the optimal decision rule. The same claim is valid when one focuses on the relationship between skill heterogeneity and the distribution of the second type of power, viz., the group members' marginal contribution (mc). This has been shown in Ben Yashar et al. (Journal of Theoretical Politics 33(2):225–235, 2021), where mc has been formally related to s-d power. A preliminary study of the relationship between inequality of the distributions of the two measures has also been presented. The current paper considerably expands this investigation by applying simulations and sheds light on the reason for the increased inequality of the two types of power. Since reward (in terms of status, payment or both) depends on s-d power and mc, inequality of the distribution of rewards depends on the inequality of the two types of power. Comparison of the two types of power inequality is therefore interesting if one wishes to shed light on the role of the two types of power on reward inequality. In particular, the results of the comparison may clarify the effectiveness of the incentives to invest in skills, dependent on the prevailing norms and the institutional characteristics that determine the relationship between rewards and the two types of power. For this reason, the current study focuses on the comparison between inequality of s-d power and marginal contributions showing that, in small (large) groups, on average, the latter is more (less) unequal than the former and both are more unequal than the optimal weights of the decision-makers and much more unequal than their skills. The robustness of these findings is shown by applying alternative symmetric probability distribution functions. Another novel task undertaken in the current study is the sensitivity analysis of inequality of the power measures with respect to changes in the size of the group and the skills of the group members.

个人决策技能的微小差异可能会导致权力的严重不平等。Ben Yashar 和 Nitzan (Economics Letters 174:93–95, 2019) 应用了对称不确定二分选择设置并关注最优决策规则下决策者的技能依赖 (sd) 权力. 当关注技能异质性与第二种权力分布，即群体成员的边际贡献（mc）之间的关系时，同样的主张是有效的。Ben Yashar 等人已经证明了这一点。（Journal of Theoretical Politics 33(2):225–235, 2021），其中 mc 正式与 sd power 相关。还初步研究了这两种测度分布的不平等之间的关系。当前的论文通过应用模拟极大地扩展了这项调查，并阐明了两种权力不平等加剧的原因。由于奖励（在地位、报酬或两者方面）取决于 sd power 和 mc，因此奖励分配的不平等取决于两种权力的不平等。因此，如果希望阐明两种权力对奖励不平等的作用，那么比较这两种权力不平等是很有趣的。特别是，比较的结果可能会阐明投资技能的激励措施的有效性，这取决于决定奖励与两种权力之间关系的现行规范和制度特征。为此原因，目前的研究侧重于 sd 权力不平等与边际贡献之间的比较表明，在小（大）群体中，平均而言，后者比前者更不平等（更少），并且两者都比最优权重更不平等。决策者和他们的技能更加不平等。通过应用替代对称概率分布函数显示了这些发现的稳健性。当前研究中进行的另一项新任务是对权力度量的不平等相对于群体规模和群体成员技能变化的敏感性分析。后者比前者更多（更少）不平等，两者都比决策者的最佳权重更不平等，比他们的技能更不平等。通过应用替代对称概率分布函数显示了这些发现的稳健性。当前研究中进行的另一项新任务是对权力措施的不平等相对于群体规模和群体成员技能的变化进行敏感性分析。后者比前者更多（更少）不平等，两者都比决策者的最佳权重更不平等，比他们的技能更不平等。通过应用替代对称概率分布函数显示了这些发现的稳健性。当前研究中进行的另一项新任务是对权力措施的不平等相对于群体规模和群体成员技能的变化进行敏感性分析。