Upvotes and downvotes problematic.

Question

I just questioned myself this:

Given that I have on a reddit post:

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

How many upvotes and downvotes do I have in total?.

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

Answer 1

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.

Answer 2

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