The mutual surrender of the right to trial by jury that is necessarily part of an agreement to arbitrate disputes suffices as consideration under contract law.
Regarding any lack-of-consideration argument, it is well-settled in Texas that "[a] mutual agreement to arbitrate claims provides sufficient consideration for an arbitration agreement." Sun Fab Indus. Contracting Inc. v. Lujan, 361 S.W.3d 147, 152 (Tex. App.-El Paso 2011, no pet.) (citing In re U.S. Home Corp., 236 S.W.3d 761, 764 (Tex. 2007) (orig. proceeding) (per curiam)); see In re Tenet Healthcare, Ltd., 84 S.W.3d 760, 767 (Tex. App.-Houston [1st Dist.] 2002, orig. proceeding) (holding arbitration agreement was supported by consideration where "the parties' agreement created mutual promises by both to forego their right to a jury trial"); In re Alamo Lumber Co., 23 S.W.3d 577, 579-80 (Tex. App.-San Antonio 2000, orig. proceeding) ("Since the parties surrendered their rights to trial by jury, these mutual promises supply valid consideration.").
SOURCE: CORPUS CHRISTI COURT OF APPEALS - Nos. 13-12-00564-CV AND 13-12-00620-C - 6/27/2013