Estimating a percentile among distributed nodes without revealing values
You seem to ask two related questions:


“which indices in the list correspond to the top”
“Estimating a percentile”, “a number X for which … K% are larger”


These may need very different numbers of pairwise comparisons.

An other aspect that may have significant impact is what information is shared. Everybody knows the number he received, knows the sum, and the yes/no results of comparisons they have taken part in. However, you also say that “parties wish to output of which indices in the list correspond to the top” thus you suggest that some information about the indices will be shared. Depending on what exactly is shared you may get very different solutions again.