This is a very cool topic; skis aren't built the same way at different lengths. There was a great thread about this in which an engineer/physics type - think it was either 219 or Physicsman - corrected my thinking on this. The real issue, turns out, is not length but mass/unit of SA. Meaning that a longer ski SHOULD be a bit softer all else equal because as a ski gets bigger, there's more surface area to deal with your same weight. If you maintained a constant absolute flex, the ski would actually get stiffer and stiffer relative to a constant load.
Here's an example using PM's calculator: Take a typical midfat, 120/82/110. At 170 cm, it's 1581 sq cm. At 177, it's 1646 sq cm. Now if a 160 lb skier uses the 170, the wt/SA is about .10. If he uses the 177, it'll drop a bit, .96 lbs/sq cm. So for him, the longer ski will be stiffer (less weight per unit SA). Unless you make it flex a bit softer, in which case, it'll still have the same flex. Of course, he can just grin and ski it faster, which is a more interesting way to bend stuff than gaining weight.
But with apologies to the engineers/physics guys here, I don't think longer skis are particularly softer. Why? Cuz companies assume that longer skis will have bigger skiers attached to them. So let's say a 185 lb guy straps on the same 177. He'll be at .11 lbs/sq cm, so the 177 will be a little softer for him than the 170 was for for the 160 lb guy. Maybe he'll need to go even longer, or the company may make the 177 actually a touch stiffer to allow for the probability that bigger folks will ski it. Like Sierra Jim says, each company has proprietary formulas for this. I've tried repeatedly, for instance, to get a clear answer from Volkl about their strategies, nada. But my guess is that any prediction model for skier weight to SA at any length is non-linear, meaning that the longest and shortest skis are disproportionately stiff or soft to allow for very big or small skiers. And at the top ends, very fast skiers.
These are big enough diffs to have an impact on ski feel. OTOH where it really shows, and where I think 219 et al. are right on, is in width, since SA is more affected by that than length. Let's say our skiers lust for a fatter version of the same ski: 130/88/120. OK, now the 177 cm length will be at .10 lbs/sq cm for our 185 lb skier, or about the same as the 170 82 mm was for the light skier. Put another way, wider skis need to be disproportionately softer relative to narrower skis to achieve the same flex. Which is why TGR guys who ski pow at 60 mph are always complaining about noodles. If you left 100+ skis with the same build as 88's, they'd all ski like the Supermojo 103.
You'll be tested on this tomorrow.