So I am trying to put my head around POS. And I have a question about transaction conflict resolution and whether there is an attack risk here.

If I understand correctly how POS works, if there are two transactions who are fighting for legitimacy, then the people voting will be rewarded by the one who is taken into the blockchain and those who have voted for the losing transaction.

So here is the scenario and I would like to know if I missed something or not. Here is the idea: Let's say I send on different machines but at the same time a transaction to send all my ETH from one account to the other. Because it is spread on the globe, some voters will take transaction x, some transaction y and some another transaction. If you have no info on the other transactions yet, you will validate it and bet on it. So what will happen is that a small portion of the voters will be rewarded with the correct transaction and the others will lose their bet. This could be used as an attack to gain ETH from making the other lose. As a voter attacker, I can easily recognize my transaction (by signing them for example) and make sure I don't participate in the voting of the block containing any of my transactions.

What would happen in that case? How can the system resolve these conflicts without penalizing the voters too much?

My observation is that in the case of PoW, conflict resolution does not cost anything, eventually one block will win and that's the end of it. But In the case of PoS, each conflict resolution will result to a cost for people voting for the wrong block without having anyway of knowing they are doing so.