In PoW my GPU can only hash one chain at a time so I have to pick a fork to continue on. This is true for everyone else too, so the incentive is to mine the for

In PoW my GPU can only hash one chain at a time so I have to pick a fork to continue on. This is true for everyone else too, so the incentive is to mine the fork that will most likely live since you can’t earn coin without mining. In PoS, I hold tokens and when a fork happens, I’d hold tokens in both forks now (same parent token in both child forks). I can trivially run 2 validators where I stake my tokens in both forks. This is possible because validation in PoS was meant to not consume much resources, so running 2 is affordable. The incentive is to stake both forks because doing so means I’ll pick the right fork (by picking all) and thus preserve my stake in at least one fork.