Set of dice that cannot tie

Go First Dice are

“Go First Dice” are a set of dice that allows some number of players to each roll a different single die (picked arbitrarily from the set) and the following conditions hold:

1. There will never be ties.
2. Each possible ordering of the players (determined by highest result, next highest result, etc) has a mathematically equal chance of occurring.
3. The above conditions hold for every subset of the whole set.

The article linked above goes in depth into the mathematics of these dice.

Go First Dice Wiki has even more information.