At first glance it appears that you should indeed use cond_broadcast() since you're cond_wait()ing on the baton from multiple threads, but you only want one, specific thread to pick it up. From the docs (emphasis mine):
The "cond_signal" function takes a locked variable as a parameter and unblocks one thread that’s "cond_wait"ing on that variable. If more than one thread is blocked in a "cond_wait" on that variable, only one (and which one is indeterminate) will be unblocked.

...

The "cond_broadcast" function works similarly to "cond_signal". "cond_broadcast", though, will unblock all the threads that are blocked in a "cond_wait" on the locked variable, rather than only one.

update: I overlooked your caveat
The caveat I mentioned is that whilst you can reduce the sleep value to 0.0, if you comment out the sleeps entirely, even the cond_broadcast version hangs almost at once?

If I replace both cond_signal()s with cond_broadcast()s, it works fine, even with all the sleep()s removed completely.

You do still have a problem in that: 

 $baton = int (rand ($no_of_threads)) until $baton != $id;

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Could theoretically take a very long time. and 

$baton = int (rand ($no_of_sprinters)) until $baton != 0;

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Never assigns the baton to thread number $no_of_sprinters (i.e. it won't work with only 1 sprinter)

Use: 

$baton = int (rand ($no_of_sprinters)) + 1;

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Since rand($number) always returns a number LESS THAN $number

"What should it profit a man, if he should win a flame war, yet lose his cool?"

In reply to Re: baton passing threads and cond_signal by Joost
in thread baton passing threads and cond_signal by Anonymous Monk

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