直觉和指数增长:参数化和复杂性的偏差和作用。

Q4 Mathematics
Mathematische Semesterberichte Pub Date : 2021-01-01 Epub Date: 2021-08-25 DOI:10.1007/s00591-021-00306-7
Martin Schonger, Daniela Sele
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引用次数: 4

摘要

指数增长偏差是人类直觉上低估指数增长的现象。本文报告了一个实验,在这个实验中,对生长参数化的处理是不同的:对一组用增长率表示指数增长,对另一组用翻倍表示指数增长。当采用倍增时,指数增长偏差要小得多。考虑到在许多应用中,个人面临着不同增长率之间的选择,而不是指数增长和零增长之间的选择,我们提出了一个问题,即增长从高降至低。受试者极大地低估了这种减少的效果,尽管在使用加倍时间的参数化中没有那么低估。这个问题的答案比指数增长问题的答案更有偏见。尽管样本受过高等教育,并表现出指数增长偏见的意识,但这些偏见还是会出现。对教学的影响,启发式的有用性和政策进行了讨论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Intuition and exponential growth: bias and the roles of parameterization and complexity.

Intuition and exponential growth: bias and the roles of parameterization and complexity.

Intuition and exponential growth: bias and the roles of parameterization and complexity.

Intuition and exponential growth: bias and the roles of parameterization and complexity.

Exponential growth bias is the phenomenon that humans intuitively underestimate exponential growth. This article reports on an experiment where treatments differ in the parameterization of growth: Exponential growth is communicated to one group in terms of growth rates, and in terms of doubling times to the other. Exponential growth bias is much smaller when doubling times are employed. Considering that in many applications, individuals face a choice between different growth rates, rather than between exponential growth and zero growth, we ask a question where growth is reduced from high to low. Subjects vastly underestimate the effect of this reduction, though less so in the parameterization using doubling times. The answers to this question are more severely biased than one would expect from the answers to the exponential growth questions. These biases emerge despite the sample being highly educated and exhibiting awareness of exponential growth bias. Implications for teaching, the usefulness of heuristics, and policy are discussed.

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来源期刊
Mathematische Semesterberichte
Mathematische Semesterberichte Mathematics-Mathematics (all)
CiteScore
0.40
自引率
0.00%
发文量
18
期刊介绍: Die „Mathematischen Semesterberichte“ wurden im Jahre 1932 durch Heinrich Behnke und Otto Toeplitz gegründet. Sie enthalten einerseits Berichte aus der Forschung über interessante neue Entwicklungen in der Mathematik und ihren Anwendungen; andererseits behandeln sie grundlegende fachdidaktische Fragen des Lehrens und Lernens von Mathematik an Schule und Hochschule. Diese beiden Ziele verbinden sich in der Auseinandersetzung mit Problemen und Querverbindungen in der Mathematik sowie in Beiträgen zur historischen Entwicklung und zu den Grundlagen der Mathematik. Auf einen klaren, motivierenden Stil der Beiträge wird besonderer Wert gelegt. Die Zeitschrift umfasst die Rubriken "Mathematische Bildergalerie", "Mathematik in Forschung und Anwendung", "Mathematik in der Lehre", "Dokumente", sowie "Philosophische und Historische Sicht". Die zusätzliche Rubrik "Buchbesprechungen" präsentiert und kritisiert neuerschienene Bücher von allgemeinem Interesse. ______ The "Mathematische Semesterberichte" were founded in 1932 by Heinrich Behnke and Otto Toeplitz. On the one hand, they contain reports from research about interesting new developments in mathematics and its applications; on the other hand, they deal with fundamental questions of teaching and learning mathematics at school and at institutions of higher education. These two goals are combined in the examination of problems and cross-connections in mathematics as well as in contributions on the historical development and foundations of mathematics. Special emphasis is placed on a clear, motivating style of the contributions. The journal includes the sections "Mathematical Imagery," "Mathematical Research and Applications," "Teaching Mathematics," "Documents", and "Philosophical and Historical Perspectives." The additional section "Book Review" presents and critiques recently published books of general interest.
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