Geometry of voting

摘要: Abstract It is shown how simple geometry can be used to analyze and discover new properties about pairwise positional voting rules as well for those (e.g., runoffs Approval Voting) that rely on these methods. The description starts by providing a geometric way depict profiles, which simplifies the computation of election outcomes. This then motivate development “profile coordinate system,” evolves into tool rules. tool, instance, completely explains various longstanding “paradoxes,” such why Condorcet winner need not elected with certain A different developed indicate whether “oddities” dismissed or must taken seriously, explain other mysteries, strategic no-show paradox (where voter rewarded voting), arise. Still another use extends McGarvey's Theorem possible rankings identify actual tallies arise (a result needed supermajority voting). Geometry also all Voting outcomes are admitted given profile; converse becomes relationships. Finally, it lessons learned in social choice, seminal Arrow's Sen's Theorems expanding literature rules, provide insights difficulties experienced disciplines.