Go First Dice

A set of four dice that will fairly determine who goes first in a game... or just a very simple game to itself. The four specially numbered twelve-sided dice have the following properties when rolled one against one another:

1. There will never be ties.
2. Each die always has an equal chance of rolling high. This is regardless of whether all four are rolled against one another, or ANY subset of 2 or 3 dice are rolled against one another.
3. The fairness extends to all permutations of lower positions too; meaning that the 2nd highest roll can fairly determine who should go second in a game, the 3rd highest roll determines third player, and so on.