The Fixed Ratio method of money management is a system developed by Ryan Jones and described in his book The Trading Game.

Fixed Ratio Trading, is designed to allow faster growth with smaller account sizes, while reducing drawdown risk for larger account sizes.  Jones sees Optimal f as too aggressive, and most simple rules like "risk no more than 2% per trade" as too conservative, particularly for small accounts.  The major problem with most money management methods is that they give the same risk exposure for a large account as a small one, whereas in practice most traders want to take more risk when their account is small and losing the money won't do them too much damage, and become more conservative to hold on to their gains when the account gets much larger.

With Fixed Fraction trading, the time and profit required to increase the total position size by one contract or share reduces exponentially as the account grows.  In other words, the increase from 100 shares to 200 shares takes much longer than the increase from 1,000 shares to 1,100 shares.  This means that the amount of risk that the account is exposed to increases at an exponential rate when it grows.

Fixed Ratio trading on the other hand works in such a way that it takes much less time to go from 1,000 shares to 1,100 shares than it took to go from 100 to 200 shares.  Compared to Fixed Fraction, Fixed Ratio starts out a lot more aggressively and adds contracts more slowly as the account grows.  Fixed Fraction starts with tiny trades which baloon out into huge positions as the account grows.

To use the Fixed Ratio method you start by defining a number Delta as the amount required per share or contract to increase the position size by one share or contract.  The lower your Delta, the more aggressively you are trading.

Jones is a futures trader, so he talks in terms of the contract as one unit.  A trader of shares would think in terms of shares, so wherever you see the word "contract" you could substitute a share, or a hundred shares. 

    Increase position by one contract when account balance reaches current balance + (Number of contracts x Delta )

 i.e. if your current balance is $25,000 and your delta is $5,000:

• Start trading 2 contracts when account balance reaches $25K + 1x$5K = $30K

• Start trading 3 contracts when account balance reaches $30K + 2x$5K = $40K 

• Start trading 4 contracts when account balance reaches $40K + 3x$5K = $55K

• Start trading 5 contracts when account balance reaches $55K + 4x$5K = $75K

• Start trading 6 contracts when account balance reaches $75K + 5x$5K = $100K

For more information, here is an interview with Ryan Jones on Fixed Ratio Money Management.