Three times rent...but with (1, 2, 3!) kids?

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I've read that most landlords require a (gross?) income of three times the monthly rent.  What if the applicant has children?  Fair housing laws prohibits discriminating against parents, but common sense tells you that someone with no dependents making the same amount will have more discretionary income.  How do you account for that while staying on the right side of federal laws?

The metric is gross income, not net.  Although you bring up a good point in that someone with a good deal of revenue may not have a great deal of discretionary income.

It's a very rough guideline. Regardless of dependents, someone who bought a fancy car and is making big payments on it and has huge student loans is a greater risk than someone who paid cash for an affordable car and doesn't have any debts. Typically on your rental application you would ask about all recurring obligations. The income doesn't necessarily have to be three times the rent plus other payments, but you need to take those into account.

You are right in that single people have more discretionary funds than typical families with the same income and everything else similar.  But I would not categorise rent as discretionary.  Housing and security are basics in the hierarchy of needs. Does a bank charge a lower mortgage to a family than they do a single person? Or is the debt to income ratio adjusted when determining if they qualify. If you publicly announce your policy on income is rent multiplied by the variable and stick to it you are not discriminating. If you have multiple properties for rent, explain how they don't qualify for one but they do for another. This enforces the idea they were not qualified based on income and not because they were a family. 

There's really no difference between childless people and parents in this regard.  Single people find ways to spend that extra money.  Parents have no choice but to spend that money on their children.  You won't find many middle class parents taking multiple long vacations each year.  Single people spend more money on cars, clothes, and hobbies.  Parents spend more money on children.  In the end, the money is spent and the responsible adults (with or without children) pay their rent on time.