Published online by Cambridge University Press: 05 January 2013
This chapter is devoted to a detailed investigation of the relationship between committees (formally, simple games) and social choice correspondences and functions. We begin our investigation in Section 3.1 by associating three simple games, which are derived from three different notions of effectiveness, with every social choice correspondence. These games serve to describe the power distribution induced by a social choice correspondence among the various coalitions of voters. We proceed with a study of the properties of, and the interrelations between, the three simple games. Then we consider several examples, including the Borda rule. A social choice correspondence is tight if our three notions of effectiveness coincide for it. We conclude Section 3.1 by demonstrating that certain conditions are sufficient for tightness. In Section 3.2 we consider the converse problem, namely, that of finding representations (i.e., choice procedures or, more formally, social choice correspondences) for committees. We find sufficient conditions for tightness of representations, and we prove, by constructing suitable examples, the existence of tight and “nice” representations. We also find that the solution to the representation problem is closely related to the investigation of cores of simple games.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.