Chapter Twenty-Seven - Geometry of Voting
In: Handbook of Social Choice and Welfare
It is shown how simple geometry can be used to analyze and discover new properties about pairwise and positional voting rules as well as for those rules (e.g., runoffs and Approval Voting) that rely on these methods. The description starts by providing a geometric way to depict profiles, which simplifies the computation of the election outcomes. This geometry is then used to motivate the development of a “profile coordinate system,” which evolves into a tool to analyze voting rules. This tool, for instance, completely explains various longstanding “paradoxes,” such as why a Condorcet winner need not be elected with certain voting rules. A different geometry is developed to indicate whether certain voting “oddities” can be dismissed or must be taken seriously, and to explain why other mysteries, such as strategic voting and the no-show paradox (where a voter is rewarded by not voting), arise. Still another use of geometry extends McGarvey's Theorem about possible pairwise election rankings to identify the actual tallies that can arise (a result that is needed to analyze supermajority voting). Geometry is also developed to identify all possible positional and Approval Voting election outcomes that are admitted by a given profile; the converse becomes a geometric tool that can be used to discover new election relationships. Finally, it is shown how lessons learned in social choice, such as the seminal Arrow's and Sen's Theorems and the expanding literature about the properties of positional rules, provide insights into difficulties that are experienced by other disciplines.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
|This chapter was published in: ||This item is provided by Elsevier in its series Handbook of Social Choice and Welfare with number
2-27.||Handle:|| RePEc:eee:socchp:2-27||Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/bookseriesdescription.cws_home/BS_HE/description|
When requesting a correction, please mention this item's handle: RePEc:eee:socchp:2-27. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.