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arrow's theorem
Social Choice
Social Choice Theory
Social Welfare Function
Topological Methods
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Topological Theories of Social Choice
Topological Theories of Social Choice,10.1016/S01697218(10)000183,Handbook of Social Choice and Welfare,Baigent Nicholas
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Topological Theories of Social Choice
(
Citations: 7
)
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Baigent Nicholas
This chapter presents a simple introduction to the main results in topological
social choice
theory. Given a continuous
social welfare
function, these results show the following: (i) Unanimity and Anonymity are incompatible; (ii) Weak Pareto and No Veto are incompatible; and (iii) Weak Pareto implies the existence of a Strategic Manipulator. Given the role of continuity in all these results, its justification is critically discussed. Finally, a remarkable proof of
Arrow's theorem
using
topological methods
is presented.
Journal:
Handbook of Social Choice and Welfare
, vol. 2, pp. 301334, 2011
DOI:
10.1016/S01697218(10)000183
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www.sciencedirect.com
)
Citation Context
(6)
...As examples, if V is the line segment [0,
2
], then, with two agents, V ◊V is a square as in Fig. 2. The Fig. 2a level sets are for the averaging function F(x,y) = x+y 2 . The diagonal y = x describes points of agreement; each level set passes through this diagonal...
...point of the circle and flatten it into a line segment; i.e., each circle is identified with the segment [0,
2
] where the endpoints agree...
JASON KRONEWETTER
,
et al.
FROM DECISION PROBLEMS TO DETHRONED DICTATORS
...This use is partly justified by the analogy of proximity preservation to the continuity condition used in topological social choice theory (see Baigent [
2
] and Lauwers [11] for surveys)...
Christian Klamler
.
The Copeland rule and Condorcet’s principle
...tions see
Baigent (2005)
and Klamler (2005)...
Daniel Eckert
,
et al.
Belief merging, judgment aggregation and some links with social choice...
...(For surveys on the latter see Lauwers 2000 and
Baigent 2004
.) The other conditions mainly used in the topological framework are unanimity and anonymity, the former being weaker than the corresponding Pareto condition, while the latter is stronger than the corresponding Arrovian condition of nondictatorship...
Daniel Eckert
.
Proximity Preservation in an Anonymous Framework
...Baigent [
1
] surveys topological approaches...
...2 Refer to Baigent [
1
] for a discussion and survey of the use of the Kemeny metric in the literature...
Nick Baigent
,
et al.
Transitive closure, proximity and intransitivities
References
(1)
Video microscopy: the fundamentals
(
Citations: 133
)
S Inoue
,
K Spring
Published in 1997.
Sort by:
Citations
(7)
FROM DECISION PROBLEMS TO DETHRONED DICTATORS
(
Citations: 3
)
JASON KRONEWETTER
,
DONALD G. SAARI
Published in 2006.
The Copeland rule and Condorcet’s principle
(
Citations: 8
)
Christian Klamler
Journal:
Economic Theory  ECON THEORY
, vol. 25, no. 3, pp. 745749, 2005
Belief merging, judgment aggregation and some links with social choice theory
(
Citations: 10
)
Daniel Eckert
,
Gabriella Pigozzi
Conference:
Dagstuhl Seminars
, 2005
Abstract Aggregations and Proximity Preservation: An Impossibility Result
(
Citations: 2
)
Nick Baigent
,
Daniel Eckert
Journal:
Theory and Decision  THEOR DECIS
, vol. 56, no. 4, pp. 359366, 2004
Proximity Preservation in an Anonymous Framework
Daniel Eckert
Published in 2004.