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AN00150430-00000109-0273  
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Title
Title ダッチ・ブック論証による信念の度合いとしての確率解釈  
Kana ダッチ・ブック ロンショウ ニ ヨル シンネン ノ ドアイ トシテ ノ カクリツ カイシャク  
Romanization Datchi bukku ronsho ni yoru shinnen no doai toshite no kakuritsu kaishaku  
Other Title
Title The interpretation of probability as degree of belief by the Dutch book argument  
Kana  
Romanization  
Creator
Name 高須, 大  
Kana タカス, ダイ  
Romanization Takasu, Dai  
Affiliation 慶應義塾大学大学院文学研究科博士課程  
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Name 横尾, 剛  
Kana ヨコオ, ツヨシ  
Romanization Yokoo, Tsuyoshi  
Affiliation 慶應義塾大学大学院文学研究科博士課程  
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Place
東京  
Publisher
Name 三田哲學會  
Kana ミタ テツガクカイ  
Romanization Mita tetsugakukai  
Date
Issued (from:yyyy) 2003  
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Created (yyyy-mm-dd)  
Updated (yyyy-mm-dd)  
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Name 哲學  
Name (Translated)  
Volume  
Issue 109  
Year 2003  
Month 3  
Start page 273  
End page 289  
ISSN
05632099  
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Abstract
Lots of efforts have been paid for interpreting the concept of probability by another familiar concept such as ignorance, degree of a partial logical entailment, degree of belief, frequency, and propensity. In this paper the subjective theory is addressed. According to this theory, probability is interpreted as coherent degree of belief of a particular individual. This interpretation is achieved through following the two-step replacements: (1) Degree of belief is interpreted as fair betting quotient; (2) Fair betting quotient is interpreted as probability. The first replacement is based on the claim that in a bet (decision-making in an uncertain situation) a bettor's degree of belief whether an event will occur can be measured by a real number which she gives through her judgement on the fairness of the bet. The second replacement is based on the fact that when a bettor makes bets on events, in order to be guaranteed not to lose whatever happens (in order to be coherent) she should assign her betting quotients in accordance with the probability axioms, and vice versa. It is the so-called Dutch Book Theorem that guarantees this fact mathematically. The purpose of this paper is to clarify and confirm the contents of the subjective theory in terms of betting systems along the following approach (Ramsey (1931), de Finetti (1937), Howson  Urbach (1993), Gillies (2000), etc.).
 
Table of contents
1. 導入
2. 主観説とダッチ・ブックの論証
 2.1. 主観説の方策 : 信念の度合いから確率への2段階の置き換え
 2.2. 賭けの一般形式と賭け指数
 2.3. 第1段階 : 信念の度合いと公平な賭け指数
 2.4. 第2段階 : 公平な賭け指数と確率
  ダッチ・ブック定理
3. 結論 : 第1段階と第2段階の統合
付録 ダッチ・ブック定理の証明
 
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研究ノート
 
Language
日本語  
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Journal Article  
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Oct 05, 2010 09:00:00  
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Oct 05, 2010 09:00:00  
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/ Public / Faculty of Letters / Philosophy / 109 (200303)
 
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