From Arrow to cycles, instability, and chaos by untying alternatives

From remarkably general assumptions, Arrow's Theorem concludes that a socia l intransitivity must afflict some profile of transitive individual prefere nces. It need not be a cycle, but all others have ties. If we add a modest tie-limit, we get a chaotic cycle, one comprising all alternatives, and a t ight one to boot: a short path connects any two alternatives. For this we n eed naught but (Ij linear preference orderings devoid of infinite ascent, ( 2) profiles that unanimously order a set of all but two alternatives, and w ith a slightly fortified tie-limit, (3) profiles that deviate ever so littl e from singlepeakedness. With a weaker tie-limit but not (2) or (3), we sti ll get a chaotic cycle, not necessarily tight. With an even weaker one, we still get a dominant cycle, not necessarily chaotic (every member beats eve ry outside alternative), and with it global instability (every alternative beaten). That tie-limit is necessary for a cycle of any sort, and for globa l instability too (which does not require a cycle unless alternatives are f inite in number). Earlier Arrovian cycle theorems are quite limited by comp arison with these.