冪次定律的普遍性與恒常性──以台灣之天然災害規模為例

The Universality and Invariability of Power Law: A Case of Scales of Natural Disasters in Taiwan

本文主要探討台灣天然災害的規模是否符合冪次定律（Power law），並試圖解釋何以天然災害的規模會呈現此現象。所謂冪次定律就是個體的規模和其名次之間存在著冪次方的反比關係，R(x)=ax-b。其中，x為規模（在本文中規模定為傷亡人數），R(x)為其名次（第一名的規模最大），a為係數，b為冪次。實證結果發現以傷亡人數作為不同種類天然災害規模的計算，台灣過去一百年的災害規模確實呈現冪次法則的規律。在天然災害規模符合冪次定律的基礎下，再深入探討其背後所代表的意義，以及討論是否可能利用政策的手段去改變其曲線的位置或是形狀，亦即是否可以減少大規模災害的傷亡人數的差距。本文認為僅僅針對特定災害種類增加防災成本並維持總成本不變，並不能減少災害的損失。政府應該針對所有類型的災害提高其防災成本。本研究主要目的為印證冪次定律的普遍性與恆常性，在天然災害的規模中也可以獲得支持，其結果亦可以做為防災政策的參考。 The research explores whether the scales of natural disasters in Taiwan are distributed in terms of a power law, and if they are, explains why. A power law is defined as an inverse relationship between ranks and scales of objects under consideration. Mathematically, this relationship can be depicted as R(x)=ax-b, where x denotes scales in terms of people killed and wounded resulting from disasters; R(x) denotes ranks with one as the largest scale; a symbolizes a constant; and b is an exponential component. Empirical findings showed that the scales of the natural disasters in Taiwan over the past 100 years indeed follow a power law distribution. Under the observation that the distribution of scales of natural disasters fits a power law, we investigate further its implications and explore possible policies that could change the slope and position of the power law, in order to mitigate disastrous damages. We further suggest that increasing disaster mitigation costs for a certain type of disasters while maintaining the total cost of disaster mitigation will not reduce the disastrous loss and that the government should increase disaster mitigation costs for all types of disasters. The research verifies the universality and invariability of power law in the case of scales of natural disasters. The results could provide insights into disaster mitigation policies.

The research explores whether the scales of natural disasters in Taiwan are distributed in terms of a power law, and if they are, explains why. A power law is defined as an inverse relationship between ranks and scales of objects under consideration. Mathematically, this relationship can be depicted as R(x)=ax-b, where x denotes scales in terms of people killed and wounded resulting from disasters; R(x) denotes ranks with one as the largest scale; a symbolizes a constant; and b is an exponential component. Empirical findings showed that the scales of the natural disasters in Taiwan over the past 100 years indeed follow a power law distribution. Under the observation that the distribution of scales of natural disasters fits a power law, we investigate further its implications and explore possible policies that could change the slope and position of the power law, in order to mitigate disastrous damages. We further suggest that increasing disaster mitigation costs for a certain type of disasters while maintaining the total cost of disaster mitigation will not reduce the disastrous loss and that the government should increase disaster mitigation costs for all types of disasters. The research verifies the universality and invariability of power law in the case of scales of natural disasters. The results could provide insights into disaster mitigation policies.