Definition
Max Ratio or β is a value between 0 and 1 which represents the max % of total funds that can be discharged at any given moment. Max Ratio affects the threshold of a proposal. It can be thought of as an “upper ceiling” in asking funds proportional to the total holdings of the Commons.
Detailed explanation
The max ratio is an important parameter of the threshold calculation. The role of the threshold in the conviction voting algorithm is to determine if a sufficient amount of conviction has accumulated in support of a particular proposal, at which point it becomes funded.
The threshold formula and representation can be seen below, where:

r is the number of funds requested in the proposal

R is the total funds in the funding pool

S is the effective supply which is the total number of tokens used to vote

ρ is the “Min Effective Supply” a number between 0 and 1 used to weight the effective supply S of governance tokens.