Social choice with infinite populations: construction of a rule and impossibility results

AGGREGATION OF PREFERENCES IN CRISP AND FUZZY SETTINGS: FUNCTIONAL EQUATIONS LEADING TO POSSIBILITY RESULTS

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488511006903 ◽

2011 ◽

Vol 19 (01) ◽

pp. 89-114 ◽

Cited By ~ 12

Author(s):

M. J. CAMPIÓN ◽

J. C. CANDEAL ◽

R. G. CATALÁN ◽

J. R. DE MIGUEL ◽

E. INDURÁIN ◽

...

Keyword(s):

Social Choice ◽

Partial Order ◽

Functional Equations ◽

Choice Model ◽

Existence Of A Solution ◽

System Of Functional Equations ◽

Aggregation Of Preferences ◽

Impossibility Results ◽

Individual Preferences ◽

Bivariate Mean

We analyze various models introduced in social choice to aggregate individual preferences. We show that on the basis of most of these models there is a system of functional equations such that, in many cases, the origin of impossibility results in a social choice model is the non-existence of a solution for the corresponding system. Among the functional equations considered, we pay a particular attention to general means and associativity, proving that the existence of an associative bivariate mean is equivalent to the existence of a semilatticial partial order. This key result allows us to explain how the knowledge of associative bivariate means can be used to solve social choice paradoxes. In our analysis we deal both with crisp and fuzzy settings.

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Social choice with infinite populations: construction of a rule and impossibility results

Social Choice and Welfare ◽

10.1007/s003550050067 ◽

1997 ◽

Vol 14 (2) ◽

pp. 303-318 ◽

Cited By ~ 23

Author(s):

Graciela Chichilnisky ◽

Geoffrey Heal

Keyword(s):

Social Choice ◽

Impossibility Results

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The General Will and Social Choice Theory

The Review of Politics ◽

10.1017/s0034670500017174 ◽

1992 ◽

Vol 54 (1) ◽

pp. 34-49 ◽

Cited By ~ 6

Author(s):

Benjamin Radcliff

Keyword(s):

Social Choice ◽

Choice Theory ◽

Social Choice Theory ◽

Collective Choice ◽

General Will ◽

Arrow’S Theorem ◽

Impossibility Results ◽

Arrow's Theorem ◽

Choice Literature

The concept of the General Will has been criticized as being either tyrannical or empirically unattainable. From a social choice perspective, Riker (1982) and others have merged the substance of both perspectives. The new argument maintains that Arrow's Theorem and similar impossibility results imply that the General Will is both dangerous and “intellectually absurd.” While not denying the relevance of the collective choice literature, it is argued that such apocalyptic conclusions are premature.

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