For the first time, the Iowa Democratic Party will report, on a rolling basis, three numbers on caucus night — a delegate count and the amount of support on both the first and second rounds, known as alignments — leaving open the possibility that more than one candidate could claim victory.

What if Mr. Sanders receives the most support on the first alignment but another candidate wins on the delegate count? What if the top candidates are clustered together, separated by only a few percentage points? Such inconclusive results would make it difficult for any candidate to ride unrivaled momentum into New Hampshire one week later. And should voters remain as undecided in New Hampshire as in Iowa, Democrats could be staring at an extended primary fight that could leave everyone bruised.

For Democrats hoping for a clearer picture after Monday’s caucuses, it could lead to more hand-wringing and division. Candidates have already begun attacking their rivals in a bid for dominance.

Some campaigns have provided clues as to how they will assess the results on caucus night. Senior advisers to Mr. Sanders have indicated the Sanders campaign will declare victory if Mr. Sanders gets the most support on the first alignment. Aides to Mr. Buttigieg, on the other hand, are focusing on the delegate count. The Iowa Democratic Party and other party officials have encouraged the news media to report the delegate count, as has traditionally been done.

With so many undecided caucusgoers, the results could come down to how well organized campaigns are, particularly at the precinct level, where the final persuading will take place. Some campaigns have put in place precinct teams to persuade and wrangle caucusgoers before and after the first alignment. Precinct captains will be in touch constantly with their campaign headquarters for directives on their strategy inside the room.

Among caucusgoers, the persistent discussion of statewide political angst has only produced more angst. The degree of uncertainty, lingering even at this final stage of the precaucus season, has confounded some Democratic officials.