MoL-2010-09: Independence Weakening in Judgment Aggregation

MoL-2010-09: Mintz-Woo, Kian (2010) Independence Weakening in Judgment Aggregation. [Report]

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The fields of preference aggregation and judgment aggregation have
strong parallels. In both fields, given certain plausible conditions,
there are no aggregators that can universally output consistent and
complete results. Several methods of avoiding these impossibility
results have been proffered. In preference aggregation, weakening the
condition known as Independence of Irrelevant Alternatives has been
suggested by Campbell & Kelly (2007), among others. In judgment
aggregation, the analogue to Independence of Irrelevant Alternatives
is called Independence. Despite the fact that judgment aggregation has
this analogue to Independence of Irrelevant Alternatives, weakenings
of Campbell & Kelly’s type have not been explored.
We argue that weak independence conditions are more defensible
in judgment aggregation contexts than in preference aggregation
contexts and show that the results of weakening independence allow for
further possibilities. In line with Campbell & Kelly’s approach, we
propose several weakenings of Independence, and characterize these
weakenings in terms of dependent sets. We show that, under a weak
version of Neutrality, the implications which hold between Campbell &
Kelly’s (2007) conditions fail to transfer to the judgment aggregation
framework. We demonstrate possibility with several of these weakenings
and show that the aggregators are applicable. However, a stronger
version of Neutrality leads to an impossibility theorem and recreates
one of Campbell & Kelly’s implications. We also determine that
Self-Dependence leads to impossibility over non-simple agendas.

Item Type: Report
Report Nr: MoL-2010-09
Series Name: Master of Logic Thesis (MoL) Series
Year: 2010
Uncontrolled Keywords: preference aggregation, judgment aggregation, Arrow's Theorem, independence of irrelevant alternatives, neutrality
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38

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