The icelandic bit is allowed in competitions, according to the rules: http://www.icelandics.org/rules.html#classD.
The icelandic bit is similar to the Tom Thumb (jointed mouth piece with shanks) with longer shanks. This is a combination that is fairly severe.
Mark Rashid has an article on his website, titled The Trouble With Tom Thumb.
The article describes the mechanics and action of the Tom Thumb.
"The shank of the bit is beginning to put downward pressure on the headstall
transfers to pressure over the poll of the horse).
The shank is also beginning to pivot on the hinge in the bit, indenting
the horses face just below the cheek teeth.
The curb strap is already fairly tight, even with this slight pressure on
The mouthpiece is beginning to create a "V" inside the horse's mouth as the
joint in the center of the bit begins to collapse."
"Pulling back on the reins causes the hinged mouthpiece of the bit to
collapse and jut foreward and then downward inside the horse's mouth,
putting pressure on the horse's tongue.
At the same time, the bottoms of the shanks (where the reins are attached)
tip backward, causing the top of the shanks to tip forward. This, in turn,
causes the curb strap to tighten under the horse's chin.
Again, pressure is being applied in several different areas and this results
in total confusion for the horse."
The effects of a broken mouthpiece with shanks are extremely abusive, it's kind of liking putting the
horses face in a nutcracker and a vice at the same time.
How do the mechanics noted above compare with the pictures below, and action of the icelandic bit?
This bit has a lot of moving parts which can confuse and hurt the horse. The horse may raise his head, tip it to the side, toss it around, shake it, and / or become unresponsive to the bit.
In watching competitions, evaluations, Landsmot, the World Championship, clinics, trainers, or videos thereof, many of these behaviors can be seen with the icelandic bit. Some can be seen even with the snaffle bit (probably because of excessive heavy contact).
This bit is not for inexperienced riders, not for heavy hands, and may not be of any value at all.
It is said that it should only be used by professional or very experienced riders.... in which case if they were good riders / trainers, they wouldn't need a strong bit.