You could just remove the reward, any one can mine new block out of the mem pool, if two blocks or tx are in common, a determinstic algorithm could be used to select between the two.
I agree with you. The error in most crypto is the reward, which gives rise to strategies that do not necessarily induce the desired properties. I also think that the only viable kind of crypto currency is where the validation/consensus decision is taken on a voluntary basis, the "reward" being that the system in which you are invested, keeps running correctly.
However, you still need a kind of deterministic decision *that is hard to game* (because you can do "proof of work" like calculations to get the deterministic solution in your advantage). This is why a kind of PoS signature scheme is necessary in my opinion.
@dinofelis, how many times do I have to repeat to you
that voting is not free.
This is not about voting. PoS is not about voting, it is about acknowledging your set of received transactions, according to an agreed-upon (protocol) deterministic rule. The problem with PoS, namely "nothing at stake" only comes because of the reward. If there is no reward in PoS, there's no incentive to stake on multiple chains: you don't care. You stick to a rule, an arbitrary but deterministic rule, to stake on one chain, and not on another, because by not staking on the other chain, you don't lose a reward. As such, there is a normal solution to the "nothing at stake" problem: you apply the rules, because if you're not part of the cheaters that gain something by re-organizing the chain, you can only WIN by wanting the system to come to a consensus, no matter which one ; there's total indifference to what consensus and to whether you stake or not, if there's no reward. Your only stake is that there's a consensus that is reached, or the system in which you are a stake holder, crashes down.
In PoS, it is not difficult to define a rule that you only stake on one of the possible chains (deterministic rule). If you follow that rule, no "nothing at stake" problem occurs ; the only thing is that there's no incentive for you to follow that rule if there's a block reward ! This is why Casper tries to punish those that do not follow the rule ; but then this can be gamed too and you get a hopelessly complicated game-theoretical bungle. If there's nothing at stake (in both senses) with staking, your only stake is that the system works well. If the random deterministic choice of who can stake, is random enough, then it is also essentially impossible to BRIBE you into staking, because in order to find out WHOM to bribe, you'd need to spend a lot of "proof of work" and chances are you'll find one necessary staker who doesn't accept the bribe.
Of course, with sufficiently corrupt players, you can game the system ; and that's OK. The system shouldn't be too secure, and the real risk that the system will one day break down, protects it from too much hot air speculation. Only its real usage as a currency would determine most of the market cap, as it should, and no-one would dream to use it for a very long term hodling idiocy.