In a primer on nonviolent protest, “Sharp’s Dictionary of Power and Struggle,” Gene Sharp, an American intellectual, described a “dilemma protest” as a performance of an action so inchoate and unorthodox that police are trapped. If they let it happen, they are encouraging it, but if they arrest people they risk looking either silly or arbitrary and unjust, which is the point.

“This type of activity enables resistance to continue against opponents who are applying extreme repression,” Mr. Sharp wrote. Acts of resistance in small groups, he wrote, are effective when larger “bases for resistance have been neutralized, controlled or destroyed by the opponents.”

The tactic has found wide appeal in Belarus, where activists gather to clap, eat ice cream cones, set their cellphone alarms to ring in chorus or simply stand silently.

Mr. Lugar — who may be best known for his 1990s effort, along with Sam Nunn, a Democratic senator from Georgia, for a disarmament program in the former Soviet Union — was criticized throughout the campaign for what critics described as his tendency to cooperate with Democrats. He shifted to the right in 2011, after the threat to his re-election became clear.

Mr. Mourdock, meanwhile, has said that bipartisanship has led the nation to the brink of bankruptcy, and that the nation’s current circumstances call for a time of confrontation, not collegiality.