Having stakeholders "endorse" blocks has, according to you, the benefits 
of increasing the number of full nodes and making a 51% attack more 
expensive. It seems to me it would have the opposite effects and other 
negative side effects. Any stakeholder that has "won" could just be 
running an SPV client and be informed by a full node that they have won, 
then cooperate to collect the reward. You are mistaking proof of stake 
as a proof you are running a full node. At the same time, the network 
becomes cheaper to attack in proportion to the amount of the block 
reward that is paid to "endorsers". Another side effect is that miners 
would have a bigger economy of scale. The more stake a miner has, the 
more they can "endorse" their own blocks and not others blocks. I 
recommend reading this: https://download.wpsoftware.net/bitcoin/pos.pdf

-Andrew Lapp

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