[useryman]

> there are many ways of running a lottery that don't involve burning tons of electricity in the process

You need something to be the limiting factor on the amount that you can try to win such a lottery. With proof of work, it's electricity. (assuming everyone is about as efficient as each other) Early on, they talked about it being proportional to cpu-time. That has become more abstract since.

[lottin]

The limiting factor can be the price of the lottery ticket. (It seems the most obvious limiting factor, by the way.)

[useryman]

But what's the cost of the lottery ticket? Is it a certain amount work done? That's "proof of work". Is it an amount of the currency? That's "proof of stake", kinda.

I haven't heard of any cryptos that require you to risk your coins to mine. Sounds like a neat gimmick, but hard to implement.