As a rule of thumb, the optimal voting time is before 5 minutes

First, let's quickly review the different aspects of voting. (As I understand them. Please correct me if there are any misunderstandings.)

Time-based decays

Time	Rewards
0-5 minutes	Some curation rewards are returned to the reward pool. At time 0, 100% of rewards are returned, at time 5 minutes, 100% of rewards are kept. In between, the percentage that the curator keeps increases in a straight line. Basically, for every three seconds that pass, the curator keeps 1 more percentage point in rewards. This is referred to as a "reverse auction", and it was intended to level the playing field between human and bot voters.
5 minutes to 61/2 days	The curator keeps 100% of rewards. Let's call this "normal voting".
61/2 days - 7 days	The full value of the vote starts to degrade to 0 at a rate of 81/3% per hour. This is intended to give curators time to guard against payouts to abusive content (downvotes retain full power). Let's call it late voting.

rshare damping

Votes are damped by the rewards curve, according to the rule: ( ( rshares + s ) * ( rshares + s ) - s * s ) / ( rshares + 4 * s ), where "s" is 2,000,000,000,000. Near the left side of the curve, the vote is reduced to a fraction of its starting value. Near the right side of the curve, as the stake gets bigger, the value is nearly (but not quite) unchanged:

Here it is before converging:

And here it is after (nearly) converging:

Here is the shape of the marginal change curve:

Thus, the marginal benefits of increasing account size increase quickly near the beginning of the curve, but level off as the account size grows.

The goal here was to discourage large stakeholders from voting with multiple accounts, since vote-splitting for large accounts would be deboosted. This was intended to make it easier to find and counter the worst forms of abuse.

This section was corrected. See the comments for details. Thanks to @danmaruschak. Fortunately, this section wasn't needed for the argument about voting time.

Boosts for content discovery

Rewards are distributed using a square-root rule, so that earlier votes receive a larger share of the final rewards pool than later votes. The idea here is that earlier voters are taking a bigger risk, since the post might not get additional votes, so the higher payout encourages them to discover content. That curve is shaped like this (early votes on the left, late votes on the right):

So here's the argument

This argument comes from @biophil, If you're voting open-loop, it's optimal to vote earlier than 30 minutes. The rules have changed, but the logic is the same.

If you combine the reverse auction with the boost for content discovery, you arrive at the following reasoning:

1. The optimal time is no later than 5 minutes, when I get to keep 100% of my rewards. Voting at 5 minutes assures that no other voters will get in line in front of me.
2. On some posts, there will be an optimal time before 5 minutes, where I give up some rewards to the reverse auction, but I get them back - and more - from the content discovery boost.
3. If we average them all together, the optimal voting time (knowing nothing else about the post) must be earlier than its max value - 5 minutes.

The hard question is to decide how much earlier^😉.

Of course, this assumes that we know nothing else about the post. As soon as we start considering factors like post quality and the strength of someone's follower network, the reasoning becomes more complicated.

FTR, this post was prompted by a post from @philhughes, here and a comment thread with SC02 and steem.botto, here.

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Thank you for your time and attention.

As a general rule, I up-vote comments that demonstrate "proof of reading".

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Steve Palmer is an IT professional with three decades of professional experience in data communications and information systems. He holds a bachelor's degree in mathematics, a master's degree in computer science, and a master's degree in information systems and technology management. He has been awarded 3 US patents.

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^{Pixabay license, source}

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