Waniou has a great post stickied at the top of this forum that explains the logic behind avoidance diminishing returns and how to best allocate your stats such that none are wasted. The fact that avoidance diminishes is not something that can be argued against, however it really seems like a large portion of the population doesn't fully grasp the extent to which it happens, or the extent to which it plays a part in our gearing.
At level 85, 179 mastery rating provides 1 mastery skill, which is a good place to start. For the sake of comparison, 179 dodge rating is almost exactly 1% dodge as well, before any diminishing returns. (The actual number is roughly 1.02%, but it's close enough.)
For this experiment, I'm going to be moving my character's gear around to reach different thresholds of dodge, and then adding a piece of gear that has 185 dodge rating on it. This is the closest you can get to the magical 179 number on a current piece of gear. Rather than post a block of code that will leave most people scratching their heads, this thread is simply to provide real-world examples to dispel the myth that DR reduces our avoidance to "microscopic proportions." The numbers here come directly from my character sheet, no need for complicated formulae.
My base, unbuffed dodge is 3.96%. Completely naked, 185 dodge rating gives me 1.08% dodge. This is obviously not a realistic place to start comparisons, because no one starts tanking with their base dodge chance. Instead, let's look at some major thresholds, starting at 8% dodge:
Normal mode dungeon tanks may have around 8% dodge. At 7.95% dodge, another 185 rating gives me .95% dodge. The ratings have diminished 12%.
Heroic mode dungeon tanks may have around 10% dodge. At 10.05% dodge, another 185 rating gives me .89% dodge. The ratings have diminished 18%.
Normal mode raid tanks may have around 12% dodge. At 11.96% dodge, another 185 rating gives me .83% dodge. The ratings have diminished 24%.
Heroic mode raid tanks may have around 14% dodge. At 13.97% dodge, another 185 rating gives me .78% dodge. The ratings have diminished 28%.
Keep in mind that in all of these examples, the next tier of gear has roughly 13% more stat allocation. (This information can be gleaned by comparing stamina levels. Sockets cloud the issue slightly since the budget is taken from other stats seemingly randomly, and also since not all items are perfectly budgeted, however as a whole the stat gain is reliably measurable. )
This information is important to consider since the increased stat allocation offsets the increased cost of more avoidance. Going up a tier will always provide you with significantly more stat points than diminishing returns will take away. Note that it does not entirely balance out--it's not intended to. Avoidance is supposed to diminish, and it does so on a completely reasonable curve.
This seems like a no-brainer, but the idea seems to be going around that there is a currently reachable point where your avoidance diminishes in such a way that you will only be gaining a small fraction of it. This is false. In the best currently available gear, the greatest reduction you will see on your avoidance ratings is roughly 28%, which is only 16% more than what a tank in 333 blues would see.
TLDR: In this expansion's lifetime, you will always gain more avoidance from the increased rating than you will lose from the increased diminishing returns. Avoidance is not a bad stat because it diminishes. Avoidance will continue to provide significant benefits far into the DR curve, including gearing points at which certain classes stop gaining benefit from mastery.