Anyone believing that their Union vote was improperly conducted may contact the Department of Labor after first challenging the conduct of the vote to their respective Union.
http://www.dol.gov/esa/regs/statutes/olms/...s/lmrda-act.htm
Bill of Rights--(29 U.S.C. 411)
SEC. 101. (a)(1) EQUAL RIGHTS.-- Every member of a labor organization shall have equal rights and privileges within such organization to nominate candidates, to vote in elections or referendums of the labor organization, to attend membership meetings and to parti****te in the deliberations and voting upon the business of such meetings, subject to reasonable rules and regulations in such organization's constitution and bylaws.
(2) FREEDOM OF SPEECH AND ASSEMBLY.-- Every member of any labor organization shall have the right to meet and assemble freely with other members; and to express any views, arguments, or opinions; and to express at meetings of the labor organization his views, upon candidates in an election of the labor organization or upon any business properly before the meeting, subject to the organization's established and reasonable rules pertaining to the conduct of meetings: Provided, That nothing herein shall be construed to impair the right of a labor organization to adopt and enforce reasonable rules as to the responsibility of every member toward the organization as an institution and to his refraining
http://www.dol.gov/asp/programs/handbook/unions.htm
Employee Rights--Title I of the LMRDA guarantees certain rights to all union members. These include the right to nominate candidates, to vote in elections or referendums, to attend membership meetings and to parti****te in the deliberations and vote upon the business of such meetings, subject to reasonable rules and regulations in the organization's constitution and bylaws.
Compliance Assistance Available--Additional compliance assistance materials appear on the Internet. OLMS field office staff members are available to answer questions about the LMRDA and to help individuals and organizations affected by the law.
Penalties/Sanctions--The LMRDA authorizes the Secretary of Labor to investigate "in order to determine whether any person has violated or is about to violate" any provisions of the Act (except the Bill of Rights of Union Members and amendments made by the LMRDA to other laws), and to "enter such places and inspect such records and accounts and question such persons" as may be necessary to determine whether a violation has occurred. The Secretary may issue subpoenas to compel testimony or to obtain records and other materials needed to complete an investigation.