Ok, I have best single thread performance on my validator machine. What if I have two of those machines?
When used for leader selection, VDF’s offer a substantial improvement over verifiable random functions. Instead of requiring a non-colluding honest majority, VDF-based leader selection only requires the presence of any honest participant. This added robustness is due to the fact that no amount of parallelism will speed up the VDF, and any non-malicious actor can easily verify anyone else’s claimed VDF output is accurate. [1]
[1] https://blog.trailofbits.com/2018/10/12/introduction-to-veri...
how is that different from one miner finding a valid signature faster than the other?
and how is that not parallelization?
Bitcoin miners can parallelize because it's a search problem, so they can probe multiple different candidates simultaneously.
That said, VDF isn't a drop in replacement for Bitcoin style POW. VDF just gives you the ability to say (provably, so no one can cheat) "everyone has to do a 10 minute serialized computation before launching a (parallelizable) POW hash search" so we don't use all the world's available electricity just for mining.
Except it’s going to be worse because VDF is the centralizing factor, it’s like having bitcoin where constructing a block takes really long time. The actor that finishes first has the advantage to start PoW and will win disproportionate amount of blocks by revealing their data at the last possible moment, preferably when or just before another actor publishes their “worse” PoW.