The study of general election outcomes can be helped by finding better approaches for visualizing large quantities of information and asking questions about its patterning. We review the Nagayama or ‘all possibilities' triangle display, and show that it can only legitimately be used to show an overall ‘field’ of results that is logically feasible, called the effective space of competition, which varies with the number of observable parties. We apply this reductionist view to analysing outcomes in three leading plurality rule systems (the USA, India and Great Britain), focusing on evidence of the Duvergerian psychological effect acting on voters during campaign periods. The Effective Competition Space view illuminates some key differences across countries, and variations with rising numbers of parties competing. We next consider a more holistic approach, the ‘crown’ diagram, which links electoral district outcomes more closely to the most important politico-ideological dimension in each country. Both views suggest some tentative evolutionary hypotheses for the variegated development of plurality rule systems over time. Britain is a highly nationalized party system, but one that has moved substantially away from Duvergerian predictions of two-party focusing, and towards multiparty politics. The USA seems to be a case of ‘stunted development’. India shows a partial Duvergerian conformity, yet combined with a substantial vertical scatter of non-Duvergerian results. Applications to over-time and regional analysis within countries are also sketched.