RIOPLATENSE 1995 Problem 5

Consider $2n$ points in the plane. Two players $A$ and $B$ alternately choose a point on each move. After $2n$ moves, there are no points left to choose from and the game ends. Add up all the distances between the points chosen by $A$ and add up all the distances between the points chosen by $B$ . The one with the highest sum wins. If $A$ starts the game, describe the winner's strategy.

Clarification: Consider that all the partial sums of distances between points give different numbers.