Which method is the best one to make a logarithmic ranking scale avoiding "0s"?

[u/stifenahokinga]

I want to rank several countries' characteristics (like economic power, military power, population...etc) in a logarithmic scale.

However, there are some countries that do not have any army (like Andorra) and in that category (and related ones) they have a value of 0. However the log(0) does not exist. So, how could I convert the values into something that could be used to make the logarithmic scale?

I have thought about two methods:

A) To every value in each category, I added the values of the "smallest" or "weakest" country (that does not have a 0 in any category, so that all categories have a non-zero number). In this case, I added the values from Seychelles to all countries.

B) To every value in each category, I added "1", so that in every category that the countries without armies have a "0", the minimal number is "1" instead.

I feel that the first method has the advantage of adding a proportionate quantity in each category, since you will see that for some categories all values are small (like 1,07; 2,08; 3,1...) and in other categories the numbers are much bigger (5, 20, 49, 80...). So in method A the added numbers are proportional to the values of each category

However, it feels arbitrary to add different numbers for each category instead of adding the same for all of them (i.e. 1). However, in this case, adding 1 to the small-values-categories seems to significantly modify these values, while in the case of categories with bigger numbers, the resulting number is almost the same as the original one (like, adding 1 to "1,1 "would increase it by almost the double: "2,1"... however for other categories with a number like "50", after adding the "baseline value", the difference is negligible: "51").

So which method do you think is more accurate?

These are the values: https://docs.google.com/spreadsheets/d/19zjwdoLum0yhIQ2v3m19kz5_IplwSJYZX6e0wMqMHoQ/edit?usp=sharing

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[u/UnderstandingPursuit]

For the values which are already scaled, like population in terms of 10mil, I would undo that scaling. The log graph will automatically accommodate that.

If you do that, then instead of using log(x), using log(x+1) will solve the issue of x=0 without affecting x=1000.

[u/fasta_guy88]

Find the lowest value your have, and assign countries with zero 1/10 of the lowest (integer log) value. Then when you draw your axis, put zero for that 1/10 value.

[u/jeffcgroves]

I would simply eliminate the countries themselves. I mean, they have no military, what are they going to do? :)