In the [in]famous McCloskey versus McIntyre contest (1984):
Election night totals certified by county officials gave McCloskey, the Democrat, a 72-vote lead. But then, correction of a computation error in Gibson County gave McIntyre a 39-vote lead. That figure was later adjusted for other computation errors, dropping McIntyre's lead to 34 votes. A partial recount ordered by state officials increased McIntyre's margin of victory to 418 votes. A recount conducted by members of the U.S. House of Representatives, however, resulted in a four-vote margin of victory for McCloskey. McCloskey was seated on 1 May 1985 under a cloud of controversy formed by partisan conflict over every decision related to the election outcome, from the state certification process through a series of House task force decisions to invalidate absentee ballots. [...]
Questions regarding the Eighth District race remained even after the exhaustion of state remedies. Were such questions best resolved by the procedures employed by the House? What cost is involved in the use of such procedures? Federal involvement in the decision process of elections is rare. Only about 400 contested election cases have been brought before the House of Representatives since the Civil War. Of these, the vast majority have been dismissed in favor of the contestee. Three major factors set the McCloskey v. McIntyre contest apart from past.
First, House action was initiated by parties other than the candidates by a rarely used motion from the floor. Second, the intervention by the House was not justified on the basis of fraud or irregularities in the count itself, but on the basis of concern over state procedures. Third, since the concern was on state procedures, House investigators set aside virtually all election outcomes. House members elected to undertake a full independent recount.
The article then discusses how initiation from the floor, while rare was not entirely unique, having been done before in Rousch v. Chambers in 1961. And likewise:
In investigating 1960 vote totals, House members were forced to adopt a number of counting rules distinct from those used by the state.
Rousch was declared victor by the House investigation (with a 99-vote lead) and seated, even though Chambers had been certified twice by the state.