If I were to exhaust all my voting power in one day, how much of the reward pool would I extract?

This is a question I've thought about for a while but after doing some reading, I think I have some understanding. This is just my interpretation of how it works so please forgive me if it is not 100% accurate.

Under the new hard fork, a single upvote depletes 2% of your voting power. Your second vote depletes 2% of what remains after your first vote is used, and so on.

My understanding is that you will never exhaust all your voting power as the way it deteriorates is such that it never reaches zero. Voting power regenerates over 5 days so I am going to look at the case where you use practically all of your voting power in the first hour of the 5 day window. So after that hour, your vote will have an immaterial effect (until it regenerates to a healthier position).

I'm going to take the case of someone with 120,000SP in their account as this would give them an upvote value of about $100 at full power.

I'm going to answer a few questions in this post which you may have asked yourself one time or another.

1. How does voting power degenerate
2. If I used all my voting power, how much of the reward pool would I take and how many upvotes would it take for my vote to have a negligible effect?

How does voting power degenerate

As I mentioned earlier, each additional vote will reduce your remaining voting power by 2%. To see what this looks like I'm going to show how voting power decreases after each vote. Remember, I'm assuming all the votes are made in the first hour so no regeneration has taken place.

The table below shows how someone with 120,000SP's voting power would degenerate over 20, 100% votes (for illustration purposes, I'm not considering part-votes)

The table shows the first 20 votes, the value of each vote, the remaining Steem Power before the vote is given and the cumulative value of the rewards that this user would extract from the reward pool.

If I used all my voting power, how much of the reward pool would I take and how many upvotes would it take for my vote to have a negligible effect?

After 20 votes, $1,661.96 would have been extracted from the reward pool and the voting power would stand at 68%.

After 458 votes, the voting power would be at .01% and the marginal value of a vote would be $0.01. At this point $5,000 would have been extracted from the reward pool.

** If you want to know how much value you can extract from the total reward pool, multiply the value of one upvote (at 100% voting power) by 50. **

Someone with 10,000 SP will have a full upvote value of $8.33 which means they can extract $416 from the total reward pool every 5 days.

So, our user executes all of these votes and has exhausted all of their Steem Power. In 5 days time they could do the same thing again. Repeating this process over a year (assuming everything else remains unchanged) the total amount extracted over a year would be $5,000 * 365/5 = $365,000.

This assumes the account uses all of the Steem Power in a year and the reward value per SP remains as it's been over the last few days since the Hard Fork.

The graph below illustrates this. If the red line were to continue forever, it would never become zero meaning you will always have some Voting Power.

If every account were to use all of there voting power then the reward value per upvote would drop significantly (by how much I don't know).

The reality is only a portion of the full potential voting power is utilized. At the current level of typical voting power usage, a 120k SP account gives a $100 upvote at 100 voting power. This can easily change if voting behaviour changes.

Thank you for reading.