Assume the objective function for a democracy includes preventing the majority from tyrannizing the minority. Barriers to voting (voter suppression) help accomplish this: a minority highly motivated not to be tyrannized will overcome the barriers while a majority only slightly in favor of tyrannizing will tend to be stopped by the barriers. This magnifies the political power of the highly motivated, which probably helps things like preventing famine (Amartya Sen).
What is the optimal amount of barriers to political participation to maximize the (still unspecified) objective function of a democracy? Barriers to participation are enacted and dismantled by the democratic political process: does a democracy naturally converge to the optimal amount of barriers?
Barriers to voting probably also decrease the power of demagogues, something democracies probably need to do some -- but not too much: another optimization problem.
The barriers need to be unbiased (e.g., should not discriminate by race), though that seems oxymoronic: whatever the barrier, some people will have an easier time crossing it.
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