what is the difference between arbitray discount rate and risk free rate?

why in this case study, should use risk free rate as discount rate for liabilities?

COMMON MISTAKE States Dig a Multi-Trillion Dollar Hole by Discounting at the Wrong Rate Almost all states in the United States offer their employees Because of their guaranteed nature, the fisk-free rate, a defined benefit pension plan guaranteeing a retirement in which is currently well below 8%, is the correct discount come based on the duration of their employment with the rate for plan liabilities." This error has led states to state and their final salary. These promised payments are the grossly underestimate the value of their liabilities-and plan's liabilities-and because the payouts are guaranteed, underfunded pension plans impose a potential future they are comparable to a risk-free bond. To meet these li obligation on taxpayers. How large is this obligation? abilities, states put aside funds and invest them in risky as Professors Robert Novy-Marx and Joshua Rauh' found sets like stocks and corporate bonds. that total state pension underfunding in 2008 amounted Unfortunately, states make a critical, but common, mis to at least 3 trillion. take when determining their funding requirements: They Rather than correct the error, most states have continued compute the present value of the liabilities using an Irbitrary to let the problem grow. Indeed, by 2016, us.pensiontracker discount rats (typically 8%) that is unrelated to the riskiness .org estimates that the total U.S. public pension liability grew of the plan's liabilities. to $6.7 trillion, or more than $52,000 per household