It seems that the preferred term in arbitration practice is ‘disclosure’ rather than ‘discovery’.
Worth noting that in P.R.China, a civil law jurisdiction, the term ‘evidence disclosure’ is used in international arbitration.
The following paragraphs are extracted from:
Alan Redfern & Martin Hunter, LAW AND PRACTICE OF INTERNATIONAL COMMERCIAL ARBITRATION Chapter 6, SWEET&MAXWELL 4TH ED. 2004
6–71 In many common law countries it is usual in litigation in the national courts for there to be an automatic “discovery” of documents procedure, which generally means disclosing to each other the existence of all relevant documents, whether favourable or unfavourable, including internal notes and memoranda.
This is not the practice in international commercial arbitration, as will be seen below. Indeed, it is better to avoid the use of the term “discovery” because it is an ambiguous term. To a civil lawyer it means nothing; to a US lawyer it encompasses production of documents and depositions of potential witnesses and experts as well as inspection of the subject-matter of the dispute; to an English lawyer it refers only to production of documents.
There is no practice of automatic discovery in international commercial arbitration. The usual practice is to limit document production as much as possible to those documents that are strictly relevant to the issues in dispute and necessary for the proper resolution of those issues. There is no tradition or practice of the wholesale (or “warehouse”) production of documents. Furthermore, most arbitral tribunals apply the principle of “proportionality”— that is, they will limit the scope (and thus the expense) of document production to an extent that is reasonable in the context of the amount in dispute and the relative significance of the issues in respect of which document production has been requested.
6–72 It is sometimes argued that the position is different in international arbitrations that take place in the US, and that a party is entitled to wide-ranging production of documents. It is true that the Federal Arbitration Act and a number of state arbitration statutes grant broad discretionary powers to arbitral tribunals to require the production of documents, as well as the testimony of potential witnesses given on deposition.It is, however, a misconception that arbitrations taking place in the US are subject to the automatic and extensive discovery procedures available in court litigation in that country. The reality is that in the US there is generally no right to any discovery in international arbitrations and the extent to which discovery is permitted is entirely in the hands of the arbitral tribunal if the parties do not agree.The national courts will not interfere to expand any right of discovery ordered by the arbitral tribunal.