It's still a lottery, except the way you buy tickets is by wasting electricity. The more electricity wasted the more lottery tickets you have. It doesn't need be like this, just buy the tickets with effing bitcoins and you achieve the same result without wasting electricity.
It’s not that easy. You can’t secure Bitcoin with a lottery run on Bitcoin, because then you could forge your own tickets and forge the drawing, too.
The proof of stake proposals don’t seem to work that way. They seem to be more a matter of stakeholders having machines that vote about who is trustworthy.
I don't think you would be able to forge your own ticket. For example, the lottery tickets could be "purchased" by sending some amount of BTC to a special/nonexistent address, and these transactions would be required to be present in the block being validated for the block to be considered valid. Admittedly I haven't thought about all the details but it would surprise me if there wasn't an obvious alternative to the proof-of-waste system currently in place.
