Most logical scoring system

I'm involved in a board game tournament where we play the same game over and over. Based on the order of finish, points are awarded. One point for first place, two points for second, down to five points for fifth. At the end of a predetermined number of games, the person with the lowest overall number of points is the winner.

What we can't agree on is how to deal with ties. Suppose two players tie for third place. How should points be awarded?

A. 1 for first, 2 for second, 3 for both thirds, and 4 for fourth
B. 1 for first, 2 for second, 3 for both thirds, and 5 for fifth
C. 1 for first, 2 for second, 3.5 for both thirds, and 5 for fifth
D. Some other option


Most logical scoring system