What every user should know about the upcoming change in voting

There has been a significant amount of misinformation and propaganda being spread about the upcoming change from a 40 vote target to a 5 vote target.

The gist of this propaganda is that the change from 40 votes to 5 votes changes nothing, because all votes will be worth 8 times as much. So for example, if I could cast 40 100% power votes worth 10 cents each before the change, I would now be able to cast 40 12.5% power votes also worth 10cents each... or 5 votes worth 80 cents each. This is entirely false.

To explain why, I first have to explain a little about how voting weight works. There are 3 factors that affect your voting weight
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1.your SP.
2.The percentage you choose on the slider
3.Your voting power. This goes down the more votes you cast. You can look at it on steemstats.com.

If 2 and 3 are expressed as decimals, you can use SP* percent*power to get a number that represents the complete power of your vote. Let's call this "P"

The maximum P you can cast per day is by voting the target number (let's call it T)of times at 100% on the slider. At this equilibrium, your vote power will stay at approximately 80%. Currently, the target is 40. So the max P you can cast per day is SP* .81 * 1 * 40

• If you cast more than T, your lose out because your vote becomes too weak. For example, if you cast 80 100% votes per da the rapidly declining power of your vote would cause you to actually cast less P than 40 100% votes. (the decline in your voting power is not linear

• If you cast 20 100% votes, you will lose out based on the number of votes you cast (even though your votes will be slightly more powerful)

The reward pool, and how your voting distributes it.

Note -- the math here is not exact, for a variety of reasons (for one thing, it's based on vests not SP). It does demonstrate how voting awards a share of the total reward pool.

Lets say I vote on a post at 100% on the slider and 80% power with 1000SP. That would make my P 1.810000=8000. How much is that vote worth?

To find the answer to this question, we need two more pieces of information, the total P cast that day by all users (lets call that P (sub A) and the total reward pool (lets call that R). V is the value of my vote.

P/P(sub a)=v/R
PR=V*P(sub a)
PR/P(sub a)=V

For the sake of example, let's say a total of 10,000,000,000P is cast each day, and the reward pool is $50,000.
(8000P*$50,000)/10,000,000,000P=$.04

So under the current 40 vote system, I could cast about 40 votes a day worth about $.04 each, for a total influence of 320,000P or $1.60 a day. Note that there are many other ways I can vote, but none of them will give me a greater daily influence than $1.60.

Note that each individual P cast is worth about 4 cents in this system. We can determine this by dividing the reward pool by P(sub a).

The reward pool is constant.

The new system is not changing that $50,000. The pie that is being divided up is still the same size.
Or 40,000P total. The $ value of this daily influence will do down from $1.60 to $.20

Well, what if we get 8x more P for our 100% vote.

It doesn't matter, if we're getting 40,000Px8 now, so is everyone else who casts a vote. P(sub A) will increase 8x just like P, and the two increases will cancel out. With a constant R and every P would be worth 1/8 as much as it was before in dollar value.

So how come @biophil thinks 100% votes are going to be worth 8x as much?

The reasoning is that because everyone can only vote 1/8 as much as they could before, then the total amount of P cast should go down to 1/8 of what it was before. SO our equation to figure out the $ value of our 80% power, 100%slider vote would be

(8000P*$50,000)/1,250,000,000P=$.32

why biophil is wrong.

This math only works out if every current user is maxed out and casting the optimal number of votes already. That is to say, if the current P(sub a) is 50,000M it will only be reduced to 12,500M by this change if every user is currently casting their optimal 40 votes a day.

So will our votes increase in value at all?

Maybe. They could increase in value, decrease in value or stay the same. Since whales control most of the SP, they also have the biggest effect on the total daily P cast, and thus the most significant impact on the effect of this change. There are three ways this will effect different whales.

1. The Donkeypong effect -- For active whale curators like donkeypong and a few others, this will drastically decrease the amount of P they cast. Voters like this, for the most part, stay maxed out, so they will decrease by about the 7/8 @biophil imagines.

2. The Ned effect -- For infrequent voters, like Ned, who already don't come close to their 40 vote a day quota, this will have very little effect. As an example, let's say ned currently casts 5 votes a day. The change will lower his voting power slightly by keeping it at an 80% equilibrium (instead of near 100% like ti would be now) but nowhere near the 7/8ths it would lower others.

3. The Dan effect: Not to single dan out. Many whales have sockpuppet accounts, but do not use them to vote currently, because they do not need to. They vote their full 40 (or close) every day. However, if they were limited by a 5 vote max limit, they could just as easily bring in their sock puppets to cast the full 40 they're used to (or at least get closer to it). For example, dan typically uses @dantheman to vote, but he has at least one other account @dan, which is twice as strong and which typically hardly votes at all that I can see. Obviously depending on the extent of the sockpuppet accounts, and whether the whales actually bring them in or simply cut down their voting, this could go from having no effect at all to cutting down their voting by the full 7/8.

At the end of the day, some decrease in P(sub a) is very likely (in fact, some decrease in unavoidable). But it will most likely be quite a bit smaller than the 87.5% required to increase voting power by as much as indicated. Personally, i would anticipate a vote value increase per 100% power vote of around 25% to 50% . But thats just me spitballing.

Voters should watch the effects of their votes very carefully after this change (which, i believe, is on the 13th) because if they are significantly less powerful than 8x, then a lot of people have been selling you a bill of goods.