Hello All,

Sorry for being out for a couple of days. I attempted to write a better summary of the protocol (below). I will rewrite protocol description shortly as well. I haven't yet caught up with the discussion, will reply to them separately.

Regards,
Shunsai

Proof-of-Approval Overview:

Proof-of-Approval protocol uses stakes of the parties for consensus and defense against the attacks. Since the parties' stakes are recorded on the chain itself, such systems are inherently different from Proof-of-Work (PoW) like systems where the defense is provided by some external resource requirement. Proof-of-Approval, like other stake based protocols, may also seem overly complex riddled with seemingly unnecessary rules. These rules are required to defend against conditions that cannot occur in a PoW system.

Trade-offs for the protocol participants also differ dramatically compared to those in PoW. While PoW participants benefit from large computational power, additional computational power (beyond a minimum) offers no advantage to participants of most stake based protocols. In Proof-of-Approval, participants benefit not from computational power but from the high performance network connectivity--low latency and high transmission speeds.

Participants of the PoW systems may benefit from specialized computer systems typically housed at their own premises. In Proof-of-Approval, on the other hand, participants benefit from locating their nodes closest to the Internet backbone. Proof-of-Approval nodes, especially for larger stakeholders, are more likely to reside in cloud than on their own premises.

In a typical operation of a blockchain, participants agree on the honest chain up to some blocks below the top. While this concurrence is present implicitly, it is typically not recorded on the chain. As a result, an attacker using History or Costless Simulation attack, may be able to offer an attack chain that can beat the protocol's rules and win. Proof-of-Approval records this concurrence in "epoch approvals." An attacker's attack chain, in addition to beating the protocol rules, must present a higher amount of concurrence in order to win.

Nodes, housed at owners' premises, may face power or network outages or slow connections resulting in fewer stakeholders being live at any time. On the other hand, nodes hosted on cloud, are mostly free of power or network outages and are more likely to be live at any time. Cost of hosting a node on the cloud, although greater than zero, is very small--as low as $5-10/month. Proof-of-Approval benefits from more stakeholders being live at any time. To incentivize nodes to move to cloud, Proof-of-Approval offers block approval award. To win block approval award, a node must be able to quickly send its approvals to the block producers. Block approval award more than offsets cloud hosting cost and is difficult to win without cloud hosting. As a result, Proof-of-Approval expects more than a quorum stake be hosted on cloud and be live for block approvals.

Participants of Proof-of-Approval are expected to have stake distribution like that of other public blockchains. Such distribution is typically modeled by Pareto distribution where a large portion of wealth is held by a small fraction of the population. Proof-of-Approval's incentive system works best for such real world stake distributions and may not work well for a hypothetical near-equal stake distributed over a large population.

The goal of the protocol is to choose a single block in each slot to be placed in the chain. There are many ways of accomplishing this goal, the simplest one being selecting a single party to produce a block. Unfortunately this method results in low liveness of the chain. This protocol chooses multiple parties to produce candidate blocks. The consensus must pick one out of these candidates to be placed in the chain. For security, the protocol also requires that a quorum of stakeholders approve a block. While it is possible to converge a quorum stake to a single block through multiple rounds of voting in one slot, the protocol uses an alternate system--multivoting. This multivoting system requires only one round of voting per slot but it delays its decision by one block. In other words, the stakeholders choose multiple acceptable blocks belonging to the same parent, effectively voting for a single parent. The parent block is a Focal Point or Schelling Point where the stakeholders are expected to converge to thus avoiding splitting of the honest stake among multiple blocks. These approvals are stored on the chain inside the successor block.

The protocol offers block creation award to the winning block in addition to the transaction fees stored in the block. The protocol also offers two additional awards, block approval and epoch approval, to anyone who participates in them in proportion to their stake.

The protocol makes the following assumptions:

1. Stake distribution among parties is like that of other public blockchains (Pareto like).
2. Epoch approval award is large enough to motivate even the smallest stakeholders to participate and requires little computation or network performance.
3. Block approval award is not likely won by nodes not hosted in cloud.
4. Block approval award for some minimum stake, same as the stake needed for block creation, is more than sufficient to cover cloud hosting cost.
5. The combined stake of parties holding that minimum stake is significantly larger than a quorum.
6. All stake hosted in cloud is live all the time.
7. A slot period is sufficiently large for parties to validate candidate blocks and communicate approvals.
8. Adversarial stake is slightly below quorum and the honest stake is larger than quorum.

And the protocol expects the following behavior from its participants:
1. Almost all nodes try winning epoch approval award.
2. Most parties holding some minimum stake are hosted in cloud.
3. At least a quorum stake is live at all times.

Under these conditions, the protocol achieves high liveness and finality after one block. In addition, History or Costless Simulation attack requires nearly all stake at some time in past to win.