Your right hedgie on the armor being valuable point by point, but from how i understand it dodge works how you just explained there in your reason for DR. Its not effective HP that is linearly increasing like in armor but the actual mitigation % so your effective HP is exponential vs the base attack. I don't know i could be totally wrong, im sure im not as good at math as you.
Dodge confers exactly the same mitigation values as armor, as long as you have sufficient armor to never drop below 0% (Bite, Ground Spikes). This is because if you drop below 0% armor, you take massive bonus damage due to the formula demigod uses.
In fact, point-for-point, dodge is better than armor because Dodge doesn't have DR. However, due to the mechanics of the game (the major sources of damage, abilities, is not dodgeable, and armor pieces that have dodge typically have very little HP), dodge is not something you can economically get without incurring too heavy of an opportunity cost (in skill points, or money that could have gone towards health items instead).
The reason that e.g. 15% dodge is less desirable than 15% armor is because evasion is very unpredictable. Against another demigod, where you might only take 7-10 hits to die, the chance to block one, or maybe two of those offered by 15% dodge isn't nearly as practical as the absolute assurance that you can take one more offered by 15% armor.
Patently false. Evasion is unpredictable but there is no difference between 10% armor mitigation and 10% dodge in terms of "average" lifespan. It ultimately comes down to playstyle, if and only if armor and dodge were equally difficult to acquire. Dodge is a "feeling lucky punk?" stat, but that doesn't make it inferior, just risky. Additionally, if you have dodge are also screwing up with your opponent's mind.
I know that you said afterwards that against high rate-of-fire targets the difference is minimized but you're still misrepresenting the situation, saying that you might get unlucky and die, whereas getting unlucky and dieing is just as possible as getting lucky and winning assuming a perfectly even fight.
If dodge and armor were equally difficult to get (again, not the case since very few dodge items provide health and are usually more expensive), since dodge doesn't have DR, everyone would stack dodge. If the items were rebalanced, and dodge was given a DR, rather than just a hard cap, then you would want to have exactly half dodge, and half armor.
Let's say you have a 50% mitigation "budget". You could do 50% armor, or 50% dodge, or 25% armor, 25% dodge, or 10% armor, 40% dodge, or 40% armor, 10% dodge.
1) 50% Armor gives you 50% mitigation, 200% effective hp
2) 50% Dodge gives you 50% mitigation, 200% effective hp
3) 25% Dodge, 25% Armor gives you 1.25 * 1.25 == 56.25% mitigation, 228.57% effective hp
4) 10% Armor, 40% Dodge gives you 1.1 * 1.4 == 54% mitigation, 217.39% effective hp
5) 40% Dodge, 10% Armor gives you 1.1 * 1.4 == 54% mitigation, 217.39% effective hp
As dodge is currently implemented and itemized, in order for it to be effective, it probably would have to dodge abilities as well (probably dodge % against abilities would be halved, for balance). If dodged were itemized like armor, and found on easily accessible hp items then dodge would be awesome (see above). So awesome it would have to be nerfed and DR'd.