A friendless grunt probably wouldn't be in the running...probably.
Let's take two hypothetical candidates.
Candidate A (Mr. Social) has 10 friends, an AVG social score of 10 (arbitrary number), one legendary skill and no artifacts.
Candidate B (Mr. Military Grunt) has 0 friends, an AVG social score of 1 (he doesn't talk to anyone), an AVG Military score of 5 (remember, this will AVG even skills grunt has no point in) 2 legendary skills (legendary wrestler and swordsman), and no artifacts.
Candidate A has a "25" score while Mr. Military Grunt has "16". Friends and social scores count very highly towards the ratio. While Military scores DO count, it's naturally weighted against itself because it does ALL military skills. Not many dwarves get high ranks in EVERY military skill, usually they get wrestling, 1-2 other weapons, armor and shield (again maybe) which makes it inherently harder to gain a high AVG military score as opposed to social skills that get XP all the time the dwarf chats with his friend.
Military isn't the key to victory, social & friends are the big score earners. However, with the age/legendary skills/artifact/military skill bonus, it should weigh things more heavily towards older, established dwarves then just children who've made a bunch of friends. This way you don't have to set arbitrary limits (must be X years old to be elected) because there are many examples of incredibly young people being elected to positions of power because they just were that exceptional.