## How mathematical impossibility changed welfare economics: A history of Arrow's impossibility theorem

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**How mathematical impossibility changed welfare economics : A history of Arrow's impossibility theorem.** / Lützen, Jesper.

Research output: Contribution to journal › Journal article › peer-review

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*Historia Mathematica*, vol. 46, pp. 56-87. https://doi.org/10.1016/j.hm.2018.11.001

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*Historia Mathematica*,

*46*, 56-87. https://doi.org/10.1016/j.hm.2018.11.001

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TY - JOUR

T1 - How mathematical impossibility changed welfare economics

T2 - A history of Arrow's impossibility theorem

AU - Lützen, Jesper

PY - 2019

Y1 - 2019

N2 - During the 20th century, impossibility theorems have become an important part of mathematics. Arrow's impossibility theorem (1950) stands out as one of the first impossibility theorems outside of pure mathematics. It states that it is impossible to design a welfare function (or a voting method) that satisfies some rather innocent looking requirements. Arrow's theorem became the starting point of social choice theory that has had a great impact on welfare economics. This paper will analyze the history of Arrow's impossibility theorem in its mathematical and economic contexts. It will be argued that Arrow made a radical change of the mathematical model of welfare economics by connecting it to the theory of voting and that this change was preconditioned by his deep knowledge of the modern axiomatic approach to mathematics and logic.

AB - During the 20th century, impossibility theorems have become an important part of mathematics. Arrow's impossibility theorem (1950) stands out as one of the first impossibility theorems outside of pure mathematics. It states that it is impossible to design a welfare function (or a voting method) that satisfies some rather innocent looking requirements. Arrow's theorem became the starting point of social choice theory that has had a great impact on welfare economics. This paper will analyze the history of Arrow's impossibility theorem in its mathematical and economic contexts. It will be argued that Arrow made a radical change of the mathematical model of welfare economics by connecting it to the theory of voting and that this change was preconditioned by his deep knowledge of the modern axiomatic approach to mathematics and logic.

KW - Arrow's impossibility theorem

KW - Condorcet paradox

KW - Duncan Black

KW - Kenneth Arrow

KW - Order relations

KW - Social choice

KW - Voting theory

KW - Welfare economics

UR - http://www.scopus.com/inward/record.url?scp=85058171941&partnerID=8YFLogxK

U2 - 10.1016/j.hm.2018.11.001

DO - 10.1016/j.hm.2018.11.001

M3 - Journal article

AN - SCOPUS:85058171941

VL - 46

SP - 56

EP - 87

JO - Historia Mathematica

JF - Historia Mathematica

SN - 0315-0860

ER -

ID: 214127239