What are the potential fall outs of old DPOS+LIB algorithm?

Question

In EOSIO Dawn 4.0, DPOS Last Irreversible Block Algorithm has been upgraded to DPOS 3.0 + BFT due to potential fallouts of consensus.

DPOS with the last irreversible block (LIB) algorithm (as it exists in Steem & BitShares) has the potential to fall out of consensus in certain extreme network connectivity disruptions

How exactly new tweak introduced to DPOS in EOSIO Dawn 4.0 brings fault-tolerant finality? Can you give some example of potential failure which could happen in the older version?

Related: DPOS Consensus Algorithm - The Missing White Paper.

Answer 1

On GitHub, Dan Larmier discusses the issue with the older DPOS 2.0 algorithm. To summarize, the old algorithm allowed a situation where, in a situation where there is a small network interruption, a producer could end up producing a block that inadvertently confirms a block that he hadn't previously seen. This occurred because producing a block on a chain indirectly confirmed all other blocks on the chain.

To address this, DPOS 3.0 added a header field containing the highest numbers block that the producer had confirmed. The produced block, then only acts as confirmation for blocks between that block and the one it is currently producing.