When they gather for their conclave on Monday, the 124 eminent electors will be asked to surrender their cellphones. Then they will deliberate and, through means opaque to the outside world, select a leader to guide their venerable, revered institution farther into the 21st century.

No, there will be no white smoke, and these are not cardinals in the Sistine Chapel. These voters are the tenured musicians of the Berlin Philharmonic, and they are set to meet at 10 a.m. on Monday at an undisclosed location in Berlin to make one of the most prestigious appointments in classical music: a new chief conductor and artistic director, who will succeed Simon Rattle when he leaves the orchestra in 2018.

Since the Berlin Philharmonic regularly sits at or near the top of lists of the world’s great orchestras and has legions of fans through its huge catalog of recordings, regular tours and Digital Concert Hall streaming service, the election is being watched closely around the world. The choice rests with the players of the orchestra, a self-governing body, which serves only to make it more intriguing.

But it is a difficult election to handicap: There is no application process, so the major candidates are not even officially declared, except perhaps through strategically aimed winks and nods. That has in no way dampened the frenzy of speculation, as classical music writers have started to pen the kind of relentless who’s-up-and-who’s-down horse-race coverage more often seen in the political pages than the arts section.