Cernel's Multiplayer Bidding System

Cernel

In a multiplayer with "X" sides ("X" powers, if the game is a FFA), with "X" being a natural number equal or bigger than 3:

All players bid, increasingly, from zero to any positive integers, till all but 1 player have passed.
The player than won the bid picks a side of his/her choosing, at 0 bid.
The winning bid is the "next winner bid".
The remaining players bid again, increasingly, from zero to any positive integers, till all but 1 player have passed.
The player that won the new bid picks a side of his/her choosing, at the "next winner bid" (the bid previously called, by the player that got 0 bid, not the latest called bid).
The latest winning bid becomes the new "next winner bid".
Repeat from step 4, until only one player remains unassigned to any side (if this is a 3 sides game, never repeat, but just go to step 8).
The remaining player takes the remaining side at the latest "next winner bid".

Note: Not accepting negative numbers, this system is assured to work only in case all participants believe that picking first (thus having 0 bid) is always advantageous (for example, instead, if everyone would believe that picking first is worse than anything, then nobody would even call 0, as everyone is willingly to pass at any possible numbers, thus step 1 never actually resolving).

Basic Bidding Rules:

Anyone can call a number (as his/her bid) anytime or pass, but you can pass only after someone else called a number or passed.
The number called is valid only as long as no equal number or higher numbers have been already called.
Whoever called the latest (highest) valid number cannot pass nor call more numbers (until someone else calls a valid new number).
Whoever passed cannot call numbers anymore (passing is definitive and irreversible).
Once nobody can call numbers, the bid is won by whoever called the latest (highest) valid number, that number being the winning bid.

Note: Lacking a time limit for calling a number or passing, bidding will never end, if someone never does either (you might want to add a timer of some sort).

I just wrote it down and never tried it (yet). I believe it should work for picking sides in games like the Napoleonic Empires FFA, especially if you believe that some players are bad picks (cough Austria cough), so should get a fair bonus. Opinions or ideas?