the “lottery winner” in your case assembles a block with transactions from the transaction pool (ie you don’t just make shit up. you are taking useful transaction that people are making them and capturing them into the chain) So the winner does not decide much, except maybe what transactions to select (spoiler alert: the transactions with the highest fees are normally selected).
The consensus is in the sense that: you wanted to create a transaction and that transaction is captured and everyone in the network sees and agrees that the transact happened. The miner cannot alter your transaction. Other nodes in the network cannot arbitrarily reject it. You cannot simply claim you didn’t do it after the fact.
Why would everyone agree that the transaction happened?
once a block is mined it is propagated through the network and it’s verified by all the nodes that see it. In effect, when you get the block and you append it to your local blockchain after verification you agree that the transaction that happened in that block happened.
For nodes that only have access to my chain, they will also go with my chain. This is why being connected to multiple nodes is important.
For nodes that have access to both my chain and the rest of the world's chain, they will go with the chain that has the most work put into it, because that is the one that is clearly supported by the majority computation power. It's irrational to go with the chain that has less power, because the entities that created the chain with more power can easily overwrite the chain with less power by virtue of having more power.
Unless I happen to have more computation power than the rest of the world, the chain with more work put into it isn't going to be mine, which is why it's important that global computation power isn't consolidated into a single miner.
This basically means the entire bitcoin network depends on the entities that have the most computer power behaving correctly, am I wrong?
First you assume that the majority computation power is already colluding. This is not the case.
Let's assume it's the case. As soon as they stop adding all transactions to a block that they would've been expected to, the entire world will notice. In response, the currency will become valueless. That is, it's a public act to abuse your position as a majority power, and the very act of your abuse destroys the thing that you're trying to abuse to your profit.
It is, but with the probability of winning proportional to the "work" you put in. That is crucial.
for bitcoin there is no central authority. the reward for winning is “fixed” and claiming the said reward is dependent on a network that validates that you indeed have the work that incorporates pending transactions into the blockchain. also, “winning” happens at regular intervals of time (average 10 minutes based on difficulty), and what you’re winning is somewhat fixed (the block reward is fixed + some TX fees var).
so it’s not a lottery.