Does averaging and averaging percentages make sense in this case? I have a table with ten movies that have been ranked from 1 to 10 by a certain number of people.

(The table doesn't show movie titles, but a numeric ID on the left.) In general, a different set of people has ranked each movie, and these sets aren't necessarily the same size.
I'm having a bit of a brain freeze and I'm not sure if it makes sense to average each column and say that the average movie was ranked as follows:

I'm even less sure if it makes sense to average the percentage of the scores. The table below is the same as the first one, except that it shows the percentage of voters that gave each movie score 10, 9, 8, etc.(So, if you sum along the rows, you always get 100.)

So, for example, 11.19% of the people who ranked movie 4104 gave it score 10, while 28.13% of those who ranked movie 3266 gave it score 10. Still, it may well be that 11.19% of those who ranked movie 4104 is larger than 28.13% of those who ranked movie 3266, because of different voter pool size.
Now, I now that averaging percentages is a tricky matter precisely because of different pool/sample size, but in this case I'm not sure it matters and I'd like a sanity check.
What I'd like to do is average the percentages in each of the SCORE columns, so that I could say that, on average, any of these movies was ranked 10 by x percent of voters, 9 by y percent of voters, etc. I'm strongly inclined to think this is wrong because of the different voter pool sizes, but I'm honestly unsure.
 A: It is generally a bad idea to average ratios that are formed with different numbers of units
Consider the case where you have a set of ratios $R_i = X_i/U_i$ (which can be expressed in percentage terms if you like) formed from counting $R_i$ "successes" out of $U_i$ units.  Suppose we have $n$ data points like this and we define the following quantities:
$$\dot{X}_n = \sum_{i=1}^n X_i
\quad \quad \quad \quad \quad 
\dot{U}_n = \sum_{i=1}^n U_i
\quad \quad \quad \quad \quad 
w_i = \frac{\dot{U}_n}{n U_i}.$$
If we want to know how prevalent successes are in the units we will generally want to form the average $\dot{R}_n = \dot{X}_n/\dot{U}_n$, which is the ratio of the total number of successes over the total number of units.  However, if we were to take the average of the ratios $R_1,...,R_n$ we would get:
$$\begin{align}
\text{Average of } R_1,...,R_n
\equiv \frac{1}{n} \sum_{i=1}^n R_i 
&= \frac{1}{n} \sum_{i=1}^n \frac{X_i}{U_i} \\[6pt]
&= \sum_{i=1}^n \frac{\dot{U}_n}{n U_i} \cdot \frac{X_i}{\dot{U}_n} \\[6pt]
&= \sum_{i=1}^n w_i \cdot \frac{X_i}{\dot{U}_n} \\[6pt]
&\neq \sum_{i=1}^n \frac{X_i}{\dot{U}_n} \\[6pt]
&= \frac{\dot{X}_n}{\dot{U}_n}
= \dot{R}_n. \\[6pt]
\end{align}$$
As you can see, the average of $R_1,...,R_n$ is (generally) not equal to the ratio $\dot{R}_n$ of the total number of successes over the total number of units.  Instead, the numerator of this quantity is a weighted average of the number of successes, where each observation is inversely proportional to the number of units in that observation.  That is, the observations with fewer units are weighted upward and the observations with more units are weighted downwards.
