  A social choice correspondence satisfies balancedness if, for every pair of
alternatives, x and y, and every pair of individuals, i and j, whenever a
profile has x adjacent to but just above y for individual i while individual j
has y adjacent to but just above x, then only switching x and y in the
orderings for both of those two individuals leaves the choice set unchanged. We
show how the balancedness condition interacts with other social choice
properties, especially tops-only. We also use balancedness to characterize the
Borda rule (for a fixed number of voters) within the class of scoring rules.
