What remedies are available in the first instance?

Procedures for Contested Election Cases in the  House of Representatives

Ordering a Recount of Ballots Under FCEA and Otherwise

The parties to anelection contest case may, by stipulation, agree to the conduct a state recount,or may conduct their own recount, if permitted, which may then become the basisof a stipulation upon which the House may act.77 However, a contestant on hisor her own accord generally may not conduct a recount without the supervisionof the committee after an election contest has been initiated.78 A motion for arecount in an FCEA-initiated election contest may be granted by the committeeif there is sufficient evidence to raise at least a presumption of fraud orirregularity. A recount would not necessarily be ordered by the committee onthe mere assertion of fraud or irregularity. A party to a contested electioncase who would claim that the state recount of the ballots was in error wouldhave the burden of proof to establish such error before the committee wouldorder a recount. […]

http://assets.opencrs.com/rpts/RL33780_20101104.pdf