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We provide in this paper two properties that are links of london rings necessary and sufficient to characterize the domain of single-peaked preference profiles. This characterization allows for a definition of single-peaked preference profiles without using an ad hoc underlying order of the alternatives and also sheds light on the structure of single-peaked profiles. Considering the larger domain of value-restricted preference profiles (Sen, Econometrica 34:491-499, 1966) we also provide necessary and sufficient conditions for a preference profile to be links of london earrings-caved or group-separable. Our results show that for single-peaked, single-caved and group-separable profiles it is sufficient to restrict to profiles containing of either three individuals and three alternatives or two individuals and four alternatives.In recent years, the Pirate Party of Sweden, the Wikimedia Foundation, the Debian project, the "Software in the Public Interest" project, the Gentoo project, and many other private organizations adopted a new single-links of london bangles election method for internal elections and referendums. In this article, we will introduce this method, demonstrate that it satisfies, e.g., resolvability, Condorcet, Pareto, reversal symmetry, monotonicity, and independence of clones and present an O(C^3) algorithm to calculate the winner, where C is the number of alternatives.We propose a formal concept of the power of voice in the context of a simple model where individuals form groups and trade in competitive markets. links of london bracelets use outside options in two different ways.