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In PoW consensus, if a miner could solve the puzzle, they receive some monetary reward (some coins) to incentive miners, since mining process has a considerable monetary cost for miners including providing hardware and energy/electricity cost.
However, in PoS, participation in transactions validation has not a significant monetary cost for validators (i.e. stakeholders) (I hope I am right), and if so, is there any incentive to motivate stakeholders for participating in transactions validation?
Also, what is the penalty of a validator who ex. confirm a double-spent transaction?
Thanks
1I don't know enough about recent PoS work to write a full answer, but two comments: (1) look up the "nothing at stake" problem. (2) it's confusing to call miners/stakers "validators" - what they do is determine the order of otherwise valid transactions (if they would confirm an actually invalid transaction, their chain would be rejected by full node). – Pieter Wuille – 2018-11-12T17:58:44.897