King of the Ladder Tournament Rules

In the world of chess and chess variants, there is a debate over which chess variant is strongest.  An attempt to answer this question is these set of rules.  These rules are a proposal at an attempt to have a balancing mechanism using bidding so that regular Chess could be pitted against Shogi or XiangQi, for example.  Exact details on configuration will need to be resolved elsewhere, but this is the starting point of the discussion.

Setup

One side sets up with one variant pieces that follow its rules, and the other side sets up with another set of variant pieces and rules.

Pieces

Two sets, one for each variant.

Rules

These are three approaches towards this:

King of the Ladder (points bidding):
Players bid for based upon how confident they are of their side winning. After reviewing the field of variants (player's side represents a distinct variant army with its own set of rules), players end up bidding how many points they will award their opponent if they are beaten. Player who bids the least goes at the bottom. Player who bids the most would be at the top of the ladder. This then forms a ladder. Player who bid the least ends up playing first, going against the player who bid the second least. Follow rules above for picking side. In event of a draw, both sides are eliminated, in which case, the next player in the ladder would become the new challenger. If a player wins, then they are awarded the points the competitor offered as a prize, plus the total number of points their competitor won. That competitor then ends up playing the next person on the ladder and play continues until there is a top winner. 
In event two players bid the same amount, these two players would faces off against each other to see who wins. The remaining player would remain on and the tied players are knocked off the ladder (no points awarded). If there is a tie among these players, both are eliminated. If more than two players bid, they would do round robin, only counting wins. Player with most wins at end is the survivor, like with just two players. If the top winners end up tying for most wins, then all players who bid the same amount are eliminated. If the number of players who are tied can be divided into a bracket, then a bracket is used to resolve the tie, which can result in ties. Players score no points for a tie.
In the end, the top player is the last survivor. The remaining players are evaluated based on how many points they scored. This bidding system is to have it so the player who is perceived to be the strongest in his judgement will end up playing the least amount of competitors.
It is suggested there is a range on how many points players are allowed to bid.

King of the Ladder (Time to survive):
Similar to the point bidding method where players bid points, and least bidder is to bottom.  This works a bit different.  In this version, players bid number of turns their side will survive (1 turn = both players playing, with .5 turn is the same as a single player's move).  Player view sides they will be going against, and then all bid simultaneously.  Players who bid the same play off against each other, by these methods, and survivor stays in ladder while rest get bounced.  In event of rare tie, all players that tied are eliminated.  Then, positions in ladder are set.

In this, one player tries to survive the number of turns against their opponent as an attacker.  Then there is a second game, where the previous attacker was a defender.  If player doesn't survive their number of turns, they lose the game (have a negative score for the game, based upon how many turns they fell short).  If a player wins both games, they move on.  If they both lost, then the player with the smallest negative score is the winner (smaller being closer to normal).  If they both won their game, then the player with the highest score wins.  In event of a tie, both players are eliminated.  

In this method, I would HIGHLY suggest using the SETS method, and count all the end game conditions there as a way to end the game, including Barring the king, and also capturing opponent's king.  Game is considered ending also on a draw position.


King of the Ladder (Gifford Method.  Players play both games):
Piece set A vs. Piece set B.  2 games are played. 
Game 1 : Player 1 using "A" plays Player 2 using "B"
Game 2: Player 1 using "B" plays Player 2 using "A"
If player 1 wins both games, it would seem he is the better player
If Piece Set A wins both games, it would seem it has a clear advantage over set B.
As more players went through the 2 game process with such piece sets, the picture would become more clear. We might see, for example, that Set A defeats Set B 99% of the time... with the 1% loss being due to a gross blunder.
It is often the case that a player will win, regardless of whether he is playing White or Black in a thematic opening (indicating he is the stronger player).

Notes

Balancing mechanisms to make sure that pieces fits on both still needs to be resolved.  This is a starting point.