Other Voting Issues

In addition to the single profile consequences, there are fascinating voting properties which require several profiles. A natural illustration is the Dean’s Council controversy (in the fable) caused by combining the profiles for two subcommittees. Multiprofile issues are important because they help us understand what can happen if a voter votes strategically, or if he doesn’t vote, or whether there are problems should new voters arrive, or when groups combine to form coalitions, or if voters change preferences, or … In Sect. 5.1, problems such as the Dean’s council are explained. In Sect. 5.2, attention turns to how “more can be less.” In Sect. 5.3, the emphasis is on strategic voting. While all of these conclusions depend upon the geometry of profile sets, whenever possible, the simpler geometry of the representation triangle or cube is exploited. Then, to conclude, Sects. 5.4, 5.5 address the intriguing problems of the “list” methods and apportionment of Congressional seats.