  Scoring rules are widely used to rank athletes in sports and candidates in
elections. Each position in each individual ranking is worth a certain number
of points; the total sum of points determines the aggregate ranking. The
question is how to choose a scoring rule for a specific application. First, we
derive a one-parameter family with geometric scores which satisfies two
principles of independence: once an extremely strong or weak candidate is
removed, the aggregate ranking ought to remain intact. This family includes
Borda count, generalised plurality (medal count), and generalised antiplurality
(threshold rule) as edge cases, and we find which additional axioms
characterise these rules. Second, we introduce a one-parameter family with
optimal scores: the athletes should be ranked according to their expected
overall quality. Finally, using historical data from biathlon, golf, and
athletics we demonstrate how the geometric and optimal scores can simplify the
selection of suitable scoring rules, show that these scores closely resemble
the actual scores used by the organisers, and provide an explanation for
empirical phenomena observed in biathlon and golf tournaments. We see that
geometric scores approximate the optimal scores well in events where the
distribution of athletes' performances is roughly uniform.
