In a comment UserLTK makes a passing reference to an easy and expedient voting strategy:
My grandmother on my mothers side always voted for the better looking candidate.
Suppose a voter is currently too ignorant about the available candidates to make a very rational choice, and therefore rather than not vote, and rather than vote at random, they choose a better looking candidate first strategy.
Is this a better strategy than rolling a die or flipping a coin?
Some objective, (or arbitrary but consistent), algorithm for quickly deciding who's better looking. People seem to be able to do this instantly. The algorithm needn't be universal, cross-cultural, or common -- mutually exclusive idiosyncratic methods would be allowed. Examples: the tallest, tannest candidate. The most intelligent looking candidate. The loudest most confident candidate. Winners of beauty.ai. etc.
Some objective, (or arbitrary but consistent), standard for deciding if an office holder's completed term was satisfactory, which would then be correlated with their looks. Again the standard needn't be universal, so there might be a far right standard and a far left standard, and a standard for all points between on any given political spectrum.
No sour grapes post-facto beauty evaluations or standards revisions. An unsatisfactory office holder cannot be retroactively consigned to the the ugly side.
Arbitrary standards must be plausible or actual. Standards can't be designed to game a desired answer to this question.
Hypothesis: whatever the standards and algorithm, the resulting correlations or lack of them will be consistent in the abstract.
Also note that some people (perhaps many people) actually use this strategy to vote, so this isn't an entirely theoretical problem.