Readers should note
I commented on the prior linked video upthread. Now I will comment on the second one you've linked to.
Listening to this video further affirmed how lost the Casper design team is.
Around the 27 minute point, Lucius Greg Meredith interjects the salient point that voting on blocks can't be orthogonal to voting on partitions. And you can see the point I made upthread as quoted below, that there is no possible way to partition the gas for scripts. Thus there can't be a Nash equilibrium on partition voting.
Vlad proposes to separate the voting for hashes of "blocks" (these "blocks" don't reference a prior block hash as in Satoshi's design, so Greg renames them "sequences") which he assumes are pre-partitioned, and then separately vote on how these blocks are ordered into a "state root". But the problem is that scripts need gas to run and since it is impossible to partition gas, then the entire assumption is invalid that validators can assume the transactions in their partition are orthogonal.
Bottom line is they will fail. They apparently haven't realized this yet, and they haven't articulated the core essence yet.
I am superior designer (and note that Gregory Maxwell did not reply again because ostensibly he knows I am correct) because I can cut directly to the core issues.
Even if someone argued against my upthread point that strict partitions can't exist for scriptable block chains wherein I claimed this is due to uncontrolled external chaos due to external I/O, there is another unarguable reason that strict partitions can't exist for a scriptable block chain. That is because the gas (currency) transfers must be atomic with the script block confirmation (i.e. if they are orphaned and chain reorganized then they must be done together) so they must be in the same partition. But if the currency for a partition is a static set of UXTO or account balances (i.e. no cross-partition spending), then the system can not function properly.
Yet we also explained above (and even monsterer agrees on this point fwiw) that cross-partition spending breaks the Nash equilibrium.
Thus I continue to maintain my point that Ethereum can not scale with decentralized validation.
The point of the above quote is that gas can't be spent across partitions. There is no way to merge partitions because it introduces the ability to double-spend in more than one partition. Thus if gas can't be spent across partitions then there is no way that gas can be moved in and out of partitions to where it is demanded.
The only way to spend a token across partitions is to have a LCR (a single partial order) for all partitions, i.e. a single partition for inter-partition state changes. LCR means longest-chain-rule. But this can only be a Nash equilibrium when all validators for the LCR validate all partitions (otherwise because as explained upthread, the Nash equilibrium is lost because the winner of a block can't be sure if he is building off an invalid state). Thus cross-partition spending requires centralization of validation (a.k.a. verification) because
LCRs require centralization of validation. So if the point of sharding (a.k.a. partitioning) was to decrease latency and speed up and decentralize validation, it is a futile goal. This is unarguable.
Note an alternative to LCR is a traditional proof-of-stake for enforcing a single partial order (yet the point about validation in the prior paragraph still applies), but which is
highly flawed and loses Nash equilibrium in numerous ways. Worse is that Casper's consensus-by-betting has a combinatorial explosion of partial orders, so as Vitalk admits in the above linked video, the model doesn't converge on enforcing a single partial order. The failure to converge (or the alternative being over fitness and converging on noise, as Vitalik also admitted) is entirely expected because proof-of-stake is self-referential and thus
does not have a reference point from which to anchor a single partial order for which the Nash equilibrium can't be gamed. The way proof-of-stake overcomes this is by being essentially centralized. But I have also shown (see link in prior paragraph) that proof-of-work is also economically driven to centralization of validation.
There is only one way out of this mess for consensus systems, and that is my design which centralizes validation but decentralization control over the choice of validators (and decentralized statistical validation of validators).