Why are anime music videos admitted in anime conventions? Anime music videos have public screenings in several conventions, especially in the USA. How do they solve the problem of copyright? 

Some contests forbid the use of dubbed (localized) anime in competitions because of copyright issues. Are there different rules for content in Japanese (usually ripped from airing)? Is there an explicit or implicit agreement between organizers and copyright holders of Japanese works, or it is permitted by the copyright laws?
This is actually a legal gray area. Typically, since nobody's making money of of them, the copyright holders don't usually pursue the claim. But it is ultimately at the whim of the copyright holder. The conventions typically get permission from their sponsors to do AMV screenings, the content show is usually owned by at least one of the sponsors. As they see it, it's free publicity for them at the convention.

Typically AMVs don't qualify as fair use. Though it is highly debated, you will most likely risk getting into legal trouble with copyright infringement if you attempt to use a fair-use defense.

Fair use allows someone to use copyrighted material for certain purposes where its use cannot practically be avoided. For example, if you review a movie, including a few very brief clips of the movie can generally be fair use, because it's difficult to review something without giving the readers a frame of reference. Here the copyrighted material is used to illustrate a concept or idea. This concept can also be applied to content used for educational purposes such as a supplement to lessons being taught in a class. Additionally, protected forms of free speech might unavoidably use or make reference to copyrighted materials, as when a political action group wants to make a point about an undesirable candidate and prepares a parody of his own campaign commercials. Note that most parodies recreate material and don't copy it wholesale.

Ultimately the decision is up to the copyright holders according to the Digital Millennial Copyright Act.

Here's Funimation take on this, from their copyright specialist Evan Flournay:


  "For elements of media that are owned by more than one party, such as the underlying animation, enforcement usually falls upon the party with rights for that territory where such use takes place. Regarding AMV's and fan videos, we don't mind most fan videos, including AMVs. The main reasons for this are that they can often serve a promotional purpose, and legally, they can sometimes constitute Fair Use. The basic thinking going into fan videos is thus: if it whets the audience's appetite, we'll leave it alone. But if it sates the audience's appetite, it needs to come down. Does that make sense?"


Evan Flournay's personal belief is that AMVs should be considered fair use, but that's his legal opinion; and if he decides that a video that includes his intellectual property is not worth taking down, it's within his legal right as the content owner to do so.

Each copyright holder might have their own right view of their legal right, some might turn the other way, others may encourage it (because they are), while some just don't like it at all.