  Elections for public offices in democratic nations are large-scale examples
of collective human behavior. As a statistical physics problem with complex
interactions among agents, we can anticipate that universal macroscopic
patterns can emerge independent of microscopic details. Despite the
availability of empirical election data, such universality, valid at all
scales, countries, and elections, has not yet been observed. In contrast to all
previous attempts in this direction, in this work, it is shown that the
distribution of vote margins is driven by that of voter turnout. We use
empirical data from $34$ countries to demonstrate that a scaled measure
depending on margin and turnout leads to robust universality. Further, a voting
model is introduced, which reproduces all the observed universal features. The
deviations from universality indicate possible electoral malpractices. We argue
that the universality is a stylized fact indicating the competitive nature of
electoral outcomes.
