It's possible the weapon's technically balanced…
The really big deal here is the weapon's damage. I disagree with the argument, but it can be made nonetheless that just maybe this weapon's damage is, perhaps, acceptable. Such an argument says that, essentially, reducing a weapon's base damage by 1 step means in many cases a corresponding increase by 1 step in the weapon's threat range or critical multiplier. Hence, like a greataxe, this weapon could've been originally 1d12/×3 that became 1d10/×4 then 1d8/×5 then 1d6/19–20 ×5 then 1d4/18–20 ×5.
(It should be noted that no published weapon has a critical multiplier of ×5. Also, for comparison, using the above figures, only a handful deal the equivalent of more than 1d12/×3—for example, the pre-errata Talenta sharrash2 (Eberron Campaign Setting 119, 120) dealt 1d10/19–20 ×4 and the subject-to-minor-adjustment-by-the-DM mercurial greatsword (Arms and Equipment Guide 6,8) deals 2d6/×4; by comparison, the more recent and conservative greatpick deals 1d10/×4. All three are exotic weapons, by the way.)
After considering the damage, it's just a matter of eyeballing the other things about the weapon. Reach is good, for instance, and trip is good (although without any bonuses to make trip attacks it won't get used very often for that), but dealing nonlethal damage is bad because of the number of creature immune to it. Being a double weapon is probably good, but it's also weird: there are no martial double weapons and only two simple double weapons.2
However, because it's otherwise treated like a typical whip—except for its reduced reach and the wielder being unable to apply the feat Weapon Finesse to it—, the weapon's limited in the foes that it will damage, it doesn't threaten an area, and the wielder provokes attacks of opportunity when its used. These? All bad. The upshot? A +2 bonus on disarm attempts. That's good. Perhaps, altogether, maybe tilting a little toward too good, but there's also a lot of bad. So, that can be, by some, called balanced, too.
So, to repeat, I wouldn't but someone else who felt more strongly about it could argue that the weapon is balanced strictly according to the rules. If programming a video game, for instance, this weapon would probably fall within the game's barely acceptable range.
But you aren't programming a video game.
…And no DM should allow it into the campaign
First, "You can use a weapon that deals nonlethal damage… to deal lethal damage instead, but you take a –4 penalty on your attack roll" (PH 146), so that problem's solved. Then, just looking at a foe probably reveals if the foe has an armor bonus of +1 or higher, and the party wizard (after succeeding on an appropriate Knowledge skill check) may be able to determine if the foe's natural armor bonus is at least +3. With those things in mind, if this weapon is admitted to the campaign, it will kill everything that can be damaged by it by anyone who opts to employ it.
That's because the only folks who will use the double-whip won't be using it as it's probably intended to be used. Instead, the warrior using it, by level 6, is a fighter who's taken the feats Leap Attack (Complete Adventurer 110), Power Attack (Player's Handbook 98), and Shock Trooper (Complete Warrior 112) and is wielding the weapon two-handed. A nice party wizard can even cast on the double-whip the spell keen edge, too.
Such a warrior doesn't do the cool stuff with with the double-whip like disarm, sneak attack, or trip, though. No, he charges his foes while wielding it! Charging is already one of the only mundane strategies that matters, and this weapon makes that strategy—needlessly, pointlessly—even better. The math is complicated with all of these factors in play, but, suffice it to say, the damage even a middlin' optimized charger can do is impressive. With this weapon as part of the game, the damage dealt by such a warrior on an even slightly lucky roll is potentially enormous. When used against a really narrow segment of possible foes, those foes will just fall over and die (or collapse into unconsciousness).
So the weapon, in the abstract, may be balanced, but it is anything but balanced in play: the weapon punishes weaker foes who don't need further punishment and rewards an already superior strategy.
"What would make a double-whip balanced?"
First, make the double-whip an exotic weapon but keep in mind that when choices like Touchstone (Sandstorm 53) or Shape Soulmeld (Magic of Incarnum 40) exist in the game, being able to use a weapon is only very rarely worth a feat. So, make proficiency in the double-whip come free with proficiency in the whip. Second, make the equivalent of a double-whip-dagger exist and include that weapon alongside proficiency with the whip.
Doing that then makes it easy to just treat a double-whip like any other double weapon, except it's two regular ol' whips mashed together, one a one-handed whip and and the other a light whip, both of which will be harder to disarm. (This DM'd even allow the who shebang to work with the feat Weapon Finesse. Why not?) Make the double-whip cost 10 gp and weigh 4 lbs. and price and weigh the double-whip-dagger appropriately, and you're done.
So instead of having a weapon intended for fancy fighters but actually used by chargers against unarmored commoners and farm animals, you've a weapon that's usable automatically by fancy fighters and may sometimes be used by folks who think the two-bladed sword is an acceptable lifestyle choice.3
1 If you love the pre-errata Talent sharrash, you're in luck. It was reprinted after the errata's release in the Dragon #331 article "The Point of Polearms" with its pre-errata statistics (24, 26). Good luck convincing the DM!
2 The quarterstaff and—I kid you not—the dizzy-boff stick (Dragon #291 337), a quarterstaff dealing nonlethal damage.
3 It's not.