Why do lottery winners usually take an immediate smaller cash payout instead of a larger payout paid periodically over time?

The larger payout amount is an "estimated value" based on the smaller actual payout plus interest.

If you take the larger payout, you are essentially allowing the lottery holders to invest your money. The risk is if the lottery goes bankrupt, you will get nothing. Also, I assume most people would prefer to invest their own money and keep all of it.