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Laplace's Theories of Cognitive Illusions, Heuristics, and Biases 拉普拉斯关于认知幻觉、启发式和偏差的理论
CSN: Mathematics (Topic) Pub Date : 2018-12-01 DOI: 10.2139/ssrn.3149224
J. Miller, A. Gelman
{"title":"Laplace's Theories of Cognitive Illusions, Heuristics, and Biases","authors":"J. Miller, A. Gelman","doi":"10.2139/ssrn.3149224","DOIUrl":"https://doi.org/10.2139/ssrn.3149224","url":null,"abstract":"In his book from the early 1800s, Essai Philosophique sur les Probabilités, the mathematician Pierre-Simon de Laplace anticipated many ideas developed in the 1970s in cognitive psychology and behavioral economics, explaining human tendencies to deviate from norms of rationality in the presence of probability and uncertainty. A look at Laplace's theories and reasoning is striking, both in how modern they seem and in how much progress he made without the benefit of systematic experimentation. We argue that this work points to these theories being more fundamental and less contingent on recent experimental findings than we might have thought.","PeriodicalId":166081,"journal":{"name":"CSN: Mathematics (Topic)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115992065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Weakly Monotonic Preference Relations Representable by Concave Utility Functions - It's Easy 用凹效用函数表示的弱单调偏好关系——很简单
CSN: Mathematics (Topic) Pub Date : 2017-12-26 DOI: 10.2139/ssrn.3088441
S. Lahiri
{"title":"Weakly Monotonic Preference Relations Representable by Concave Utility Functions - It's Easy","authors":"S. Lahiri","doi":"10.2139/ssrn.3088441","DOIUrl":"https://doi.org/10.2139/ssrn.3088441","url":null,"abstract":"In this paper we provide conditions under which a preference relation can be represented by concave utility functions. The condition follows naturally from a proof of a theorem about representability of continuous and weakly monotonic preference relations by continuous and weakly increasing utility functions due to Wold (1943). For continuous and homothetic (hence weakly monotonic) preference relations our sufficient condition for the existence of a numerical representation by a concave utility function is also a necessary condition for such a numerical representation. In fact we are able to obtain a necessary condition for numerical representation of a homothetic preference relation by a concave utility function which we call global concavifiability and which is much stronger than concavifiability. On the way, we pick up the result, that all homothetic and continuous preference relations which are convex are numerically representable by concave utility functions.","PeriodicalId":166081,"journal":{"name":"CSN: Mathematics (Topic)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117115503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Fiction of Full BEKK Full BEKK的虚构
CSN: Mathematics (Topic) Pub Date : 2017-01-15 DOI: 10.2139/ssrn.2995461
Chia‐Lin Chang, M. McAleer
{"title":"The Fiction of Full BEKK","authors":"Chia‐Lin Chang, M. McAleer","doi":"10.2139/ssrn.2995461","DOIUrl":"https://doi.org/10.2139/ssrn.2995461","url":null,"abstract":"The purpose of the paper is to show that univariate GARCH is not a special case of multivariate GARCH, specifically the Full BEKK model, except under parametric restrictions on the off-diagonal elements of the random coefficient autoregressive coefficient matrix, provides the regularity conditions that arise from the underlying random coefficient autoregressive process, and for which the (quasi-) maximum likelihood estimates have valid asymptotic properties under the appropriate parametric restrictions. The paper provides a discussion of the stochastic processes, regularity conditions, and asymptotic properties of univariate and multivariate GARCH models. It is shown that the Full BEKK model, which in practice is estimated almost exclusively, has no underlying stochastic process, regularity conditions, or asymptotic properties.","PeriodicalId":166081,"journal":{"name":"CSN: Mathematics (Topic)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133643620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Cooperative Learning by Student Teams - Achievement Divisions Method (STAD) in Statistic Learning of St. Theresa International College's Students in Nakhorn Nayok Province, Thailand 学生团队合作学习——成绩划分法(STAD)在泰国Nakhorn Nayok省圣德蕾莎国际学院学生统计学习中的应用
CSN: Mathematics (Topic) Pub Date : 2016-10-07 DOI: 10.2139/ssrn.2849350
Bandyopadhyay Dwiptendra, Vichian Puncreobutr
{"title":"Cooperative Learning by Student Teams - Achievement Divisions Method (STAD) in Statistic Learning of St. Theresa International College's Students in Nakhorn Nayok Province, Thailand","authors":"Bandyopadhyay Dwiptendra, Vichian Puncreobutr","doi":"10.2139/ssrn.2849350","DOIUrl":"https://doi.org/10.2139/ssrn.2849350","url":null,"abstract":"The objective of this Research was to compare the average of exercises and the Achievement of Statistic Learning between the Cooperative Learning by Student Teams-Achievement Divisions method (STAD) and the normal study method. The experimental were selected into 2 groups of 40 students of Business Administration Faculty in Academic Year 2015, St. Theresa International College. The assessment was done and stated that:1) The significant of exercise average in Cooperative Learning by Student Teams-Achievement Divisions method (STAD) higher than the normal study method .01;2) The Achievement of Statistic Learning in Cooperative Learning by Student Teams-Achievement Divisions method (STAD) higher than the normal study method .01.","PeriodicalId":166081,"journal":{"name":"CSN: Mathematics (Topic)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126658139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Philosophical Implications of Set Theory in Infinity 无穷中集合论的哲学含义
CSN: Mathematics (Topic) Pub Date : 2016-07-27 DOI: 10.2139/ssrn.2815293
K. Lam
{"title":"The Philosophical Implications of Set Theory in Infinity","authors":"K. Lam","doi":"10.2139/ssrn.2815293","DOIUrl":"https://doi.org/10.2139/ssrn.2815293","url":null,"abstract":"What does the term “Infinity” mean? There are mathematical, physical and metaphysical definitions of the concept of limitlessness. This study will focus on the scription of the three philosophical foundations of mathematics – formalism, intuitionism and logicism – in set theory. Examples will also be provided of the concept of infinity for these three schools of thought. However, none of them cannot prove whether there is an infinite set or the existence of infinity. It forms the foundational crisis of mathematics. Further elaboration on these schools of philosophy leads to the ideas of actual, potential and absolute boundlessness. These correspond to three basic aforementioned definitions of infinity. Indeed for example, by using Basic Metaphor Infinity, cognitive mechanisms such as conceptual metaphors and aspects, one can appreciate the transfinite cardinals’ beauty fully (Nũnez, 2005). This implies the portraiture for endless is anthropomorphic. In other words, because there is a connection between art and mathematics through infinity, one can enjoy the elegance of boundlessness (Maor, 1986). Actually, in essence this is what mathematics is: the science of researching the limitless.","PeriodicalId":166081,"journal":{"name":"CSN: Mathematics (Topic)","volume":"150 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127271461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Hypercubes and the Future 超立方体和未来
CSN: Mathematics (Topic) Pub Date : 2016-05-07 DOI: 10.2139/ssrn.2776969
P. Cottrell
{"title":"Hypercubes and the Future","authors":"P. Cottrell","doi":"10.2139/ssrn.2776969","DOIUrl":"https://doi.org/10.2139/ssrn.2776969","url":null,"abstract":"This paper will provide information on what a hypercube is and how to use them in graphing the financial markets, especially in the Poseidon software that I am developing. What types of hypercubes are there? How to describe the market in higher dimensions? What are the common variables to use in a hypercube? These questions will be explored and expounded upon. Lately, an exploration of future research in quantitative finance is presented, especially in the realm of artificial intelligence and virtual reality.","PeriodicalId":166081,"journal":{"name":"CSN: Mathematics (Topic)","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121656636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Transcendental Analysis of Mathematics: The Transcendental Constructivism (Pragmatism) as the Program of Foundation of Mathematics 数学的先验分析:作为数学基础课程的先验建构主义(实用主义)
CSN: Mathematics (Topic) Pub Date : 2015-10-20 DOI: 10.2139/ssrn.2676626
S. Katrechko
{"title":"Transcendental Analysis of Mathematics: The Transcendental Constructivism (Pragmatism) as the Program of Foundation of Mathematics","authors":"S. Katrechko","doi":"10.2139/ssrn.2676626","DOIUrl":"https://doi.org/10.2139/ssrn.2676626","url":null,"abstract":"Kant's transcendental philosophy (transcendentalism) is associated with the study and substantiation of objective validity both “a human mode of cognition” as whole, and specific kinds of our cognition (resp. knowledge) [KrV, B 25]. This article is devoted to Kant’s theory of the construction of mathematical concepts and his understanding (substantiation) of mathematics as cognition “through construction of concepts in intuition” [KrV, B 752] (see also: “to construct a concept means to exhibit a priori the intuition corresponding to it”; [KrV, Â 741]). Unlike the natural sciences the mathematics is an abstract – formal cognition (knowledge), its thoroughness “is grounded on definitions, axioms, and demonstrations” [KrV, B 754]. The article consequently analyzes each of these components. Mathematical objects, unlike the specific ‘physical’ objects, have an abstract character (a–objects vs. the–objects) and they are determined by Hume’s principle (Hume – Frege principle of abstraction). Transcendentalism considers the question of genesis and ontological status of mathematical concepts. To solve them Kant suggests the doctrine of schematism (Kant’s schemata are “acts of pure thought\" [KrV, B 81]), which is compared with the contemporary theories of mathematics. We develop the dating back to Kant original concept of the transcendental constructivism (pragmatism) as the as the program of foundation of mathematics. “Constructive” understanding of mathematical acts is a significant innovation of Kant. Thus mathematical activity is considered as a two-level system, which supposes a “descent” from the level of rational under-standing to the level of sensual contemplation and a return “rise”. In his theory Kant highlights ostensive (geometric) and symbolic (algebraic) constructing. The article analyses each of them and shows that it is applicable to modern mathematics, in activity of which both types of Kant's constructing are intertwined","PeriodicalId":166081,"journal":{"name":"CSN: Mathematics (Topic)","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129066894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Microeconomic Optimization of a Retail Outlet: Combinatorial and Probability Theory Methods 零售网点的微观经济优化:组合与概率论方法
CSN: Mathematics (Topic) Pub Date : 2015-04-12 DOI: 10.2139/ssrn.2593471
Savva Shanaev, Mikhail Vasenin
{"title":"Microeconomic Optimization of a Retail Outlet: Combinatorial and Probability Theory Methods","authors":"Savva Shanaev, Mikhail Vasenin","doi":"10.2139/ssrn.2593471","DOIUrl":"https://doi.org/10.2139/ssrn.2593471","url":null,"abstract":"In this article we develop a completely new method of microeconomic optimization of a retail outlet. It shows how many substitute goods of each kind a firm should purchase within a trading period in order to maximize its profit given the purchase prices, trade margins and the preference structure of the customer base (i.e. a share of potential customers who prefer good A to good B, a share of customers who prefer good B to good A and an indifferent, \"neutral\" share, respectively). The element of uncertainty emerges due to the fact that the order in which the customers come to the outlet is not defined in advance. The method uses combinatorics and probability theory. The practical application of the method can be, particularly, airline meal optimization.","PeriodicalId":166081,"journal":{"name":"CSN: Mathematics (Topic)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125519028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cross-Efficiency Aggregation by OWA Operator Weights with Fuzzy Data 模糊数据下OWA算子权重的交叉效率聚合
CSN: Mathematics (Topic) Pub Date : 2014-02-09 DOI: 10.2139/ssrn.2392955
F. Adjogble, Elham Rostamiyan
{"title":"Cross-Efficiency Aggregation by OWA Operator Weights with Fuzzy Data","authors":"F. Adjogble, Elham Rostamiyan","doi":"10.2139/ssrn.2392955","DOIUrl":"https://doi.org/10.2139/ssrn.2392955","url":null,"abstract":"Cross-efficiency evaluation is an effective way of ranking decision-making units (DMUs) in data envelopment analysis (DEA) and can be performed with different formulations (aggressive or benevolent), secondary goals and models. In this paper we use neutral formulation for cross-efficiency aggregation. The neutral formulation determines one set of input and output weights for each DMU from its own point of view without being aggressive or benevolent to the other DMUs. Existing approaches for cross-efficiency evaluation are mainly focused on the calculation of cross-efficiency matrix, but pay little attention to the aggregation of the efficiencies in the cross-efficiency matrix. This paper focuses on the use of ordered weighted averaging (OWA) operator weights for cross-efficiency aggregation. The use of OWA operator weights allows the decision maker (DM)’s optimism level towards the best relative efficiencies. But in real world, we are often conformed to ambiguous and uncertain data. So, there is an undeniable need for fuzzy logic to evaluate the efficiency unit.","PeriodicalId":166081,"journal":{"name":"CSN: Mathematics (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132773458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Precision Effect: How Numerical Precision Influences Everyday Judgments 精确度效应:数值精确度如何影响日常判断
CSN: Mathematics (Topic) Pub Date : 2013-06-01 DOI: 10.2139/ssrn.2229833
Manoj. T. Thomas, Joowon Park
{"title":"The Precision Effect: How Numerical Precision Influences Everyday Judgments","authors":"Manoj. T. Thomas, Joowon Park","doi":"10.2139/ssrn.2229833","DOIUrl":"https://doi.org/10.2139/ssrn.2229833","url":null,"abstract":"Numerical precision – unusually precise or sharp numbers – can trigger heuristic processing and influence judgments. Numerical precision triggers heuristic processing because it causes computational difficulty or encoding difficulty. The authors propose that the discrepancy attribution model can offer a parsimonious explanation for the effects of numerical precision on everyday judgments.","PeriodicalId":166081,"journal":{"name":"CSN: Mathematics (Topic)","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130693162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
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