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Inequality of decision-makers’ power and marginal contribution

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Abstract

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.

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Notes

  1. The potential limitation of the sincerity assumption in the jury context have been discussed, for example, in Austen-Smith and Banks (1996) and Feddersen and Pesendorfer (1997). But in our setting, the sincerity assumption is justified, because under the optimal decision rule the voters have no incentives to behave strategically, see Ben Yashar and Milchtaich (2007).

  2. Earlier studies of such two-alternative models include Austen-Smith and Banks (1996), Nitzan and Paroush (1982), Ben Yashar and Nitzan (1997) and Dietrich and List (2013). For a recent survey of the model and its extensions, see Nitzan and Paroush (2018).

  3. Because of the symmetry assumption, with no loss of generality we can assume that 1 is the correct decision and -1 is the incorrect one.

  4. The same conclusion is valid when reward is assumed to be a linear function the two types of power.

  5. Note that in monopoly cases (i.e., only one member has a positive s-d power), the value of CV is \(1.\)

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Correspondence to Shmuel Nitzan.

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Nitzan, S., Tajika, T. Inequality of decision-makers’ power and marginal contribution. Theory Decis 92, 275–292 (2022). https://doi.org/10.1007/s11238-021-09816-1

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