When the PoW chain ‘pow’ forks into pow1 and pow2 with both sides claiming to be the original ‘pow’, the general public can compare the cumulative hashrate of pow1 and pow2 to ascertain legitimacy (see: Bitcoin v Bcash, 2016).
In PoW, external input to the system — electricity — powers hashrate. Electricity is altogether foreign to the context of cryptocurrency, and by necessitating the wasting of electricity on one fork over another, PoW consensus systems ensure miners can vote on only one side of a fork without bearing additional costs.
When the PoS chain ‘pos’ forks into pos1 and pos2, however, with both sides claiming to be the original ‘pos’, there is no hashrate to base our decision on. External inputs are never burned in any PoS chain’s forward progress.
If a Bitcoin v Bcash political fork were to unfold in a pure PoS context, the general public would be faced with a situation where both pos1 and pos2 chains were equally secure. If pos1 claimed to be the rightful heir to the ‘pos’ title while defensively slashing pos2 sympathizers, it wouldn’t harm pos2’s ability to make forward progress on the pos2 chain while pos2 also slashes pos1 sympathizers and equally claims to be the rightful heir to the ‘pos’ title.
It’s as if an OSS project forked with both forks claiming to be the real thing. If both sides are steadfast, it is ultimately up to the public to pick winners and losers based on nothing besides social signaling. See: 2015-2017 block size debate in Bitcoin for pitfalls to this.
Notice how no math is involved whatsoever in the decision to pick pos1 over pos2.
Notice how human intervention is inherently required to reach a decision as to which side of the pos1/pos2 split is given title to ‘pos’.
Pure PoS consensus is substantially similar to Git repos. If people are just going to trust a nebulous human hierarchy to resolve disputes like this, then the system is de facto permissioned, and a public blockchain isn’t required.