LONDON — The Liberal Democrats hoped it would happen. The Conservatives warned that it could lead to disaster. And the Labour Party could potentially use it to cling to power for a little while longer.

On Friday, Britain faced a hung Parliament for the first time since the 1970s, a situation in which no party has an overall majority and so cannot pass legislation without support from another party. It is unclear how this relatively unusual situation will play out here, but there are a number of possibilities.

First, the Conservatives, who won the most seats, could try to form a coalition with one or more smaller parties. The leading contender for that role would be the Liberal Democrats, lagging a distant third, who would relish the chance to play kingmaker but have been coy about how they would go about it.