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A note on introducing a “zero‐line” of welfare as an escape route from Arrow’s theorem
Author(s) -
List Christian
Publication year - 2001
Publication title -
pacific economic review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.34
H-Index - 33
eISSN - 1468-0106
pISSN - 1361-374X
DOI - 10.1111/1468-0106.00129
Subject(s) - arrow , arrow's impossibility theorem , transitive relation , comparability , mathematical economics , impossibility , social choice theory , zero (linguistics) , welfare , real line , mathematics , economics , point (geometry) , social welfare function , discrete mathematics , computer science , combinatorics , philosophy , law , political science , linguistics , geometry , market economy , programming language
Since Sen’s insightful analysis of Arrow’s Impossibility Theorem, Arrow’s theorem is often interpreted as a consequence of the exclusion of interpersonal information from Arrow’s framework. Interpersonal comparability of either welfare levels or welfare units is known to be sufficient for circumventing Arrow’s impossibility result. But it is less well known whether one of these types of comparability is also necessary or whether Arrow’s conditions can already be satisfied in much narrower informational frameworks. This note explores such a framework: the assumption of (ONC + 0), ordinal measurability of welfare with the additional measurability of a “zero‐line”, is shown to point towards new, albeit limited, escape routes from Arrow’s theorem. Some existence and classification results are established, using the condition that social orderings be transitive as well as the condition that social orderings be quasi‐transitive.