Your own !  Or another stakeholder's signature (of which you can, of course, check the validity because it is related to his address).   If a lot of stake holders have signed off successively the validity of all the previous blocks (like miners sign off the validity of previous blocks buy mining on top of it), you can say that all these stake holders have come to consensus that THIS is the list of transactions that are valid, according to the consensus protocol - in exactly the same way that you can say that miners having built blocks on top of one another with PoW, have come to consensus that THAT is the list of transactions that are valid, according to the consensus protocol.

The big difference with mining is that you, as a stake holder, with YOUR full node, are also going to be taking part in the consensus decision if you want to, and you are not at the mercy of miners over which you have nothing to say.  So contrary to the PoW system where full nodes have no consensus decision power (and are hence useless in the decentralization), but can only copy the chain that miners make for them, ALL full nodes with some stake participate in the consensus decision protocol, which makes PoS a much more decentralized system than PoW, because there are no "economies of scale" to be had (apart the few resources to run a full node).  The decentralisation in PoS is exactly equal to the decentralization of ownership of the coins themselves in PoS (and the willingness to participate).


I wouldn't know what that means.  In what way is the block a PoW miner adds, is objective, and the block a PoS decider adds, would be subjective ?


PoS accumulates too: the amount of stake that has "signed off" past blocks is accumulating.  You can of course NOT fake PoS with "old spent keys" if the PoS mechanism is defined correctly: only CURRENT stake holders are eligible to be drawn as the "next staker", with probability equal to their stake (or their stake times the coin age since last staking which is better).  In the same way that in PoW, you're supposed to accept the chain with most PoW in it, you're supposed to accept the PoS chain with most accumulated stake in it, which resolves the consensus problem.  Blocks can orphan in the same way they can with PoW, because of network delays.

You are maybe alluding to the "nothing at stake" problem, but that problem goes away if there is no staking reward.  Multiple staking on different branches has an incentive if you want to win minted coins (if ever the branch you didn't multi-stake on, wins in the end, you would have lost a potential minting gain).  But if there's no reward, your ONLY incentive is to keep the system honest, so that your stake doesn't become worthless in the market.  The bigger your stake, the more probable you will be the next staker, and the more you are willing to keep the system honest.  But even if you are dishonest (that is, you orphan other blocks to "reverse transactions" and you are lucky, and are a randomly selected staker at that moment), or you apply different rules in the block), like with PoW, if the NEXT staker (which you can't be with the same stake in any case) wants to be honest, he won't stake on top of YOUR block (in the same way that another miner won't mine on top of an invalid block) because that other staker doesn't want to lose the value of his stake either in the market.   As a staker, you have no incentive to stake on top of a bad block, because there's nothing to win for you in doing so, you can only make the chain dishonest, and have the market of your coins crash.  Why would you ?