Voting Power: The Complete, Definitive, and yes, Ultimate guide. Updated! Again!

I've written a pair of posts explaining how voting power works on Steem. Voting power is one of the many poorly-documented aspects of the Steem reward algorithms, but it doesn't need to be. It's very simple once you sit down and figure it out. Unfortunately, the very very old and outdated Steem Whitepaper tends to give a misleading idea of how it works. I'm here to fix that.

Low voting power is not a penalty!

The only thing everybody knows about voting power is that the more frequently you vote, the lower your power gets and thus the "weaker" each vote will be.

Unfortunately, this makes it sound like low voting power is a bad thing. It isn't really! Here's a simple example:

In this, I'll be talking about something called "slider weight." If you're a minnow, you might not know what this means - but basically once you have enough Steem Power, you're able to set the strength of each of your votes manually. The "slider" votes from 0 to 100.

Suppose you cast 10 votes and they're all at 100% slider weight.

The total influence of those 10 votes is 1000: 10 votes at 100 each, do the math: 10 x 100 = 1000.

So what if you wanted to vote more, but you wanted your total influence to be the same? Then one thing you could do is cast 100 votes at 10% slider weight: 100 x 10 = 1000.

The thing that most people don't know is that voting power works the same way: If your voting power is at 10%, and you cast 100 votes at full slider power, your total influence is, you guessed it, 10 x 100 = 1000. Just because your voting power is low doesn't mean your votes are somehow less "efficient" - it just means they're weaker.

That's the gist of it, now for the real math:

The Basics

You can look up your voting power in a few different places; the prettiest of the places is Steemstats (just enter your account name in the box), the nerdiest is Steemd.com. When you vote, a little voting power is used up, but then it regenerates over time. How exactly does it work? What's the optimal way to vote?

Think of your voting power as a big tank of water. Every time you vote, a valve at the bottom of the tank pops open and squirts out some power. The fuller the tank, the more power squirts out the valve. The amount of power that squirts out the valve is one of the things that determines the impact your vote has on a post's rewards. (The other is your Steem Power, which you can look up in your wallet and is a completely separate thing.)

If you vote and vote and vote without stopping, it's like leaving the valve open, and it won't take long before your tank is empty.

Fortunately for you, there is a steady drip of power coming back into your tank! This drip refills your tank at the same rate, always, no matter what. The rate is hard-coded into the Steem system at a constant 20 percentage points per day. So these two things are both true:

• If your voting power is at 0% right now, it will be at 20% in 24 hours (if you don't vote at all in that time).
• If it's at 75% right now, it will be at 95% in 24 hours (again, if you don't vote in that time).

Got it? You get a fixed number of percentage points per day, not a fixed percentage increase.

What happens to the drip if your tank is full? The drip gets wasted! Think of it like the tank just overflows if it's full; all that voting power just dripping down the sides going to no purpose.

The Summary

How voting power works:

• Your account has a number between 0 and 100 called "voting power."
• When you vote for a post, slightly more than a 200th of that voting power gets "spent" on your vote.
• Your voting power regenerates over time at a fixed rate of 20 points every 24 hours (to be precise, it would grow from 0 to 100 in exactly 5 days).

How to vote optimally:

• In general, you should never vote less than about 10 times per day. If you do vote less, you're letting your voting power go to waste (because your "tank" is full some of that time, and the "drip" is spilling over the brim).
• Surprising news: if you want to maximize your total influence, it doesn't matter how much you vote, as long as you vote more than about 10 times per day. Your total influence is the same whether you vote 1000 times per day or 10.
• However, The more you vote, the less each of your votes is worth. So you could vote 1000 times per day, but each of those votes wouldn't be worth very much. Your total influence would be optimal, but your influence per vote would be very low.
• The one tiny caveat here is that if you cast lots of votes at low voting power, you may lose some curation rewards and influence to rounding errors. Because of this, it's usually slightly better to vote closer to 10x per day than closer to 1000x per day.

The Details

(with formulas, code references, and general jolliness!)

Down to brass tacks. Here is the complete formula for voting power (if you don't want to parse this formula yourself, I'll walk you through it in a minute):

where my variables are (times are given in days, powers are numbers between 0 and 100)

• D is the number of days since your last vote
• D_r is 5, the number of days it takes to regenerate your power from 0 to 100
• V_d is the "equilibrium" number of votes per day, currently set to 10
• p is your voting power right after you last clicked "vote"
• p⁺ is your voting power the moment after you click "vote" this time
• w is the "slider" weight of your vote, between 0 and 1 (where 1 stands for 100% voting-slider power)

Next, I'll just plug the numbers in to make the formula a little less opaque:

Let me walk you through this.

• 20D is the amount of power that has regenerated since your last vote. Note that this is constant, and doesn't depend on p. If it's been one day since you last voted, you've regenerated 20 percentage points of voting power in that time.
• (p+20D) is thus the amount of power you have right before you vote.
• (1-w/50) comes from the fact that if you vote with full slider power (w=1), a 50th of your power gets used each time you vote. If you vote with 50% slider power (w=0.5), you only use up a 100th of your power.
• The last term, 49/5000, doesn't really affect much. Its purpose is to handle an edge case when people vote with very low power. It makes it so that every time you vote, just a little bit more than a 50th of your voting power gets used.

So how much is each vote worth? The formula for how much power gets applied to each vote is this:

If we didn't have that 49/5000, the answer would be "exactly a 50th of your voting power gets applied to each vote." A 50th is 2%, so if your voting power is at 100, then a full-weight vote would drop you down to 98. If your voting power is at 50, a full-weight vote would drop you down to 49.

The Code

Here is a list of code references for each of the components of this:

• steem_evaluator.cpp #1165 regenerated power, (100D/D_r)
• steem_evaluator.cpp #1166 available power, (p+100D/D_r)
• steem_evaluator.cpp #1170 multiplied by slider weight
• steem_evaluator.cpp #1186 used power, the 50th, and the 49/5000
• steem_evaluator.cpp #1232 voting power update