A Simple Characterization of Borda Rule for Fixed Electorate

We consider axiomatic characterization of social choice functions when there exist a fixed number of voters. Our particular interest is in social choice functions that reflect, to some extent, positional information in voters' preference rankings as well as orders between two alternatives. More specifically, we look for social choice functions that satisfy Neutrality, Positive Responsiveness, and Invariance for Average-Position Preserving Reversals. It turns out that there exists one and only one social choice function satisfying the three axioms, namely, Borda rule