The structural ageing of the population is one of the key global trends of the 21st Century. In this paper, we outline four axioms that, along with easy interpretability, we believe should underpin a theoretically valid measure of structural ageing: (1) population size invariance; (2) strong dominance; (3) weak dominance; and (4) age sensitivity. We then present a class of structural ageing indices that satisfy the axioms and are easily interpretable, with root-mean-squared-age (RMSA) as our preferred measure within the class. Using historical and cross-national data from the World Population Prospects, state-level data from the US Census Bureau, and local-authority-level data from New Zealand, we demonstrate that our preferred measure is correlated with conventional measures of structural ageing. Nevertheless, in each case there are large disparities in ranking for some countries, states, or local authorities between the different measures. These ranking disparities could be highly consequential for the allocation of resources, particularly between states or local areas within countries. Our proposed class of measures may help to avoid these disparities due to their axiomatically-consistent nature. Finally, we present considerations for future extensions of this important work, including the development of equivalent measures based on prospective age.

人口结构性老龄化是21世纪全球主要趋势之一。在本文中，我们概述了四个公理，连同易于解释的内容，我们认为应该支持结构老化的理论有效度量：（1）人口规模不变性；(2) 支配力强；(3) 弱支配性；(4) 年龄敏感性。然后，我们提出了一类满足公理且易于解释的结构老化指数，其中均方根年龄 (RMSA) 作为我们在该类中的首选衡量标准。使用来自世界人口展望的历史和跨国数据、来自美国人口普查局的州级数据以及来自新西兰的地方当局级数据，我们证明我们的首选衡量标准与结构老化的传统衡量标准相关。尽管如此，在每种情况下，一些国家、州或地方当局在不同措施之间的排名都存在很大差异。这些排名差异可能对资源分配产生重大影响，尤其是在各州之间或国家内的地方地区之间。我们提出的一类措施可能有助于避免这些差异，因为它们具有公理一致的性质。最后，我们提出了对这项重要工作未来扩展的考虑，包括根据预期年龄制定等效措施。我们提出的一类措施可能有助于避免这些差异，因为它们具有公理一致的性质。最后，我们提出了对这项重要工作未来扩展的考虑，包括根据预期年龄制定等效措施。我们提出的一类措施可能有助于避免这些差异，因为它们具有公理一致的性质。最后，我们提出了对这项重要工作未来扩展的考虑，包括根据预期年龄制定等效措施。