Are you saying the Sapphire 5850 Xtreme model is built on a smaller process (nanometers) than the normal 5850's ? Because the stock voltage you listed for it is the same as my original reference 5850.
It's crazy how it's totally luck of the draw with GPU chips. I have two reference 5850s, one that still has the stock red blower heatsink on it and will do 400+ MH/s, and one with a crazy aftermarket heatsink on it that keeps it at 55c, RAMsinks, and air blowing over the ram and vrm's, and it won't go any over 870 MHz nor will it accept any overvolting whatsoever (instant lockup)
Also as to the extra voltage being linear or exponential, according to ohm's law it seems like it should be linear, but I have also read elsewhere that power increases with the square of the voltage added (maybe due to excess heat being lost through the transistors?), so I don't know which is correct. What I do know however, is once you hit the ceiling clock with stock voltage and begin adding extra voltage to go higher, it quickly gets into diminishing returns and the extra voltage needed goes exponential.
Too bad they stopped making 5850's and 5870's, they really were powerful little cards even by today's standards!
I'm sorry, I've been assuming that the 5xxx cards and 6xxx cards use a different size process. A quick look online suggests they both use a 40nm process but I can't be sure. What I do know is that the Sapphire HD5850 Xtreme cards are quite a bit shorter than the reference 5850s and are built more like the 6xxx family.
I appreciate that I've been extremely lucky with my cards. Perhaps the manufacturer has a lot to do with it. I do know that when running a GUI and with stock cooling the maximum stable clocks of the cards were around 900 MHz but I didn't do any testing after removing the GUI and replacing the coolers so I can't say which of these two had the most impact. A card that only goes to 870 MHz even with good cooling, and doesn't accept even a small overvoltage, sounds like a very bad card to me. I assume that if you undervolt the card you lose stability at 870 MHz.
Ohm's law is "Voltage = Current * Resistance" but there are two caveats to mention here.
1) Current is not Power. Check out Joule's Law to see that both heat and power are proportional to the square of the current.
2) As temperature increases, resistance increases, so current will grow slower than linearly as voltage is increased.
I agree that the maximum stable clock seems to grow logarithmically as voltage is increased (and so voltage must be increased exponentially to increase maximum stable clock linearly). However, just as 1 + x is a good approximation for exp(x) for x close to 0,
small changes in voltage close to stock voltage will affect maximum clock rate approximately linearly.
Also, I'm fairly sure that increasing the clock rate increases the power consumption linearly. Combining this with the above, if you increase both your voltage and core clock by 10% you should expect the power consumption (of the core) to increase by 33.1% (a cubic relationship). I think some people choose to do this is because, for them, 10% more MH/s is actually more valuable than 33.1% more power + shorter card life. I'm sure some people do it because they think it's profitable when it is not for them. Some people do it because they are overclockers and are actually slightly more interested in configuring, pushing, and comparing cards than the bitcoins. These people will invest in after-market coolers or water cooling (not profitable), do copious testing (more profitable to just get reasonable settings and let the card run), and will post what they learn online (not profitable as it increases the network hashrate).
I think you can still get the Sapphire HD5850 Xtremes (I think they were released even after some of the 6xxx family!) They cost about 130 GBP each. I can't vouch for their power in gaming but they certainly fare well with the 6xxx family for mining. Indeed, I believe the 5970 is the fastest mining card (I'm fairly sure it's capable of 1GH/s underwater and I don't think the 6990 can do that) so the 5xxx family is doing something right.