Social choice theory studies the aggregation of individual preferences into a common or social preference. It overlaps with several social science disciplines, such as political theory (e.g., voting for Parliament, or for a president) and game theory (e.g., voters may vote strategically, or candidates may choose positions strategically). For a general overview see [3] and [4].
In the classical model of social choice, there is a finite number of agents who have preferences over a finite number of alternatives. These preferences are either aggregated into a social preference according to a so-called social welfare function, or result in a common alternative according to a so-called social choice function.
The main purpose of this chapter is to review two classical results, namely Arrow’s [2] Theorem and Gibbard’s [44] and Satterthwaite’s [112] Theorem. The first theorem applies to social welfare functions and says that, if the social preference between any two alternatives should only depend on the individual preferences between these alternatives and, thus, not on individual preferences involving other alternatives, then the social welfare function must be dictatorial. The second theorem applies to social choice functions and says that the only social choice functions that are invulnerable to strategic manipulation are the dictatorial ones. These results are often referred to as ‘impossibility theorems’ since dictatorships are generally regarded undesirable.
Both results are closely related: indeed, the proof of the Theorem of Gibbard and Satterthwaite in [44] uses Arrow’s Theorem. The presentation in this chapter closely follows that in Reny [108], which is both simple and elegant, and which shows the close relation between the two results. The approach in [108] is itself based on a few other sources: see [108] for the references.
Section 11.1 is introductory. Section 11.2 discusses Arrow’s Theorem and Sect. 11.3 the Gibbard–Satterthwaite Theorem.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2008). Social Choice. In: Game Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69291-1_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-69291-1_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69290-4
Online ISBN: 978-3-540-69291-1
eBook Packages: Business and EconomicsEconomics and Finance (R0)