I just questioned myself this:

Given that I have on a reddit post:

• $$5$$ net upvotes
• $$65\%$$ upvote ratio.

I think its solvable, but after some math I couldn't formulate the right equations to solve it.

• If you have $u$ upvotes, how many downvotes do you have? How many votes do you have in total? – N. F. Taussig May 17 '19 at 21:26
• @N.F.Taussig I'm not 100% sure but I think reddit shows the net amount of upvotes you have, that means, the number "5" that shows in your upvotes/downvotes section shows the difference between them. In other words, you can have 0 net upvotes, and 1000 votes in total. – Artemix May 17 '19 at 21:40

Let $$U$$ be the number of up-votes . Let $$D$$ be the number of down-votes.

The general idea is that when we have two statements $$S(U,D)$$ and $$T(U,D),$$ and if $$S(U,D)$$ is equivalent to a formula $$U=f(D),$$ then $$S(U,D)\land T(U,D)$$ implies $$T(f(D),D),$$ which is a statement only about $$D$$ and might be enough to determine a unique $$D,$$ and then $$U$$ is determined by $$U=f(D).$$

In this case $$S(U,D)$$ is $$U-D=5,$$ so $$U=f(D)=D+5.$$ And $$T(U,D)$$ is $$U=0.65 (U+D).$$

So $$S(U,D)\land T(U,D)$$ implies $$(D+5)=0.65((D+5)+D).$$

BTW this implies $$D=\frac {35}{6}$$ and $$U=\frac {65}{6}.$$ If fractional votes are not allowed then there is no solution.

• Right, but whats most likely the answer in this case is that the real % value is 0.625 and the answer I would be looking for is 8 total votes, 5 upvotes and 3 downvotes. Which the formula described above doesn't come close to the real result. Is any way to purely mathematically solve this problem? or should I write a programming algorithm to find it? – Artemix May 17 '19 at 23:03
• I understood "5 NET upvotes" to mean 5 more ups than downs, and "65% upvote ratio" to mean U/(U+D)=0.65, not 5/8 – DanielWainfleet May 18 '19 at 4:27

$$x$$ up, $$y$$ down, $$\frac x {x+y} =.65$$, and $$x-y=5$$ solve two equations in two unknowns.

• But if I replace them it gives me 10.8 votes, which is not an integer number, I actually came up with the same result before. – Artemix May 17 '19 at 21:46
• @Artemix I suspect what this means is that $65\%$ is the percentage rounded to the nearest integer. – N. F. Taussig May 17 '19 at 21:50
• Yes you are right, it must be 11 votes in total then. Thanks. Btw, is there a mathematical function that represents an integer?, as in to put in a equation?. @N.F.Taussig – Artemix May 17 '19 at 22:17
• Wait, by doing some quick tests I found out that the closest % would be 62.5 (8 total votes, 3 downvotes and 5 upvotes), which 10.8 doesn't even help me to find. – Artemix May 17 '19 at 22:24