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Choquet-Integral Aggregation Method to Aggregate Social Indicators to Account for Interactions: An Application to the Human Development Index
Social Indicators Research ( IF 2.935 ) Pub Date : 2021-06-21 , DOI: 10.1007/s11205-021-02726-3
Mehmet Pinar

Composite well-being and sustainability indices are usually obtained as arithmetic and geometric means of sub-dimensions. However, the arithmetic mean does not consider potential interactions across the dimensions of the indices and the geometric mean does not penalize unbalanced achievements across dimensions strongly enough. This paper uses a flexible non-additive aggregation model—the Choquet integral—to account for potential synergies and redundancies of the dimensions that are used to obtain indices, and uses the Human development index (HDI) as an example to illustrate the flexibility of the aggregation procedure. This paper relies on multiple theoretical and empirical studies, which indicate mutually strengthening relationships (positive interactions) among the three HDI dimensions. To illustrate and show-case how positive interactions among the three HDI dimensions could be taken into account, this paper uses five hypothetical weight sets and simulates 500 weight sets that allow varying positive interactions among the three dimensions. The analyses with the HDI data suggest that both geometric and arithmetic mean HDI scores are roughly the same for most countries, even when variations across the three dimensions are relatively large. On the other hand, countries with balanced (unbalanced) achievements across dimensions rank in higher (lower) positions with the Choquet integral aggregation. The illustrations of this paper show-case how Choquet integral is a flexible aggregation method to take into account varying positive interactions across the HDI dimensions and able to detect unbalanced achievements.



中文翻译:

Choquet-Integral 聚合方法聚合社会指标以解释相互作用:对人类发展指数的应用

综合福祉和可持续性指数通常作为子维度的算术和几何平均值获得。然而,算术平均值没有考虑跨指数维度的潜在相互作用,几何平均值也没有足够强烈地惩罚跨维度的不平衡成就。本文使用灵活的非加性聚合模型——Choquet 积分——来解释用于获取指数的维度的潜在协同效应和冗余,并以人类发展指数 (HDI) 为例说明聚合程序。本文依赖于多项理论和实证研究,表明三个 HDI 维度之间的相互加强关系(正相互作用)。为了说明和展示如何考虑三个 HDI 维度之间的积极相互作用,本文使用了五个假设权重集并模拟了 500 个权重集,这些权重集允许三个维度之间发生不同的积极相互作用。对 HDI 数据的分析表明,大多数国家的几何和算术平均 HDI 分数大致相同,即使这三个维度的差异相对较大。另一方面,在各个维度上取得平衡(不平衡)成就的国家在 Choquet 积分汇总中排名较高(较低)。本文的插图展示了 Choquet 积分如何成为一种灵活的聚合方法,以考虑跨 HDI 维度的不同积极相互作用并能够检测不平衡的成就。

更新日期:2021-06-22
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