Are comparison sort algos appropriate for SUBJECTIVE sorting?
I suggest reading about the theory on rating systems and ranking systems.  There are many standard algorithms and methods for this.  I would recommend reading the following resources, to get you started and to give you an entry-point and overview and let you figure out which might be best-suited for your particular situation:


The Bradley-Terry model
Pairwise comparison
The Elo rating system, and other rating systems (TrueSkill, Glicko, etc.)
Resources on Stats.SE: https://stats.stackexchange.com/q/30976/2921, https://stats.stackexchange.com/q/71297/2921, https://stats.stackexchange.com/q/15776/2921, https://stats.stackexchange.com/q/6379/2921
Finally, there is work on experiment design: how to sequentially select which pair of characters to compare, based on the results of comparisons so far.  (Think of this like matchmaking in chess, where you want to figure out which pairs of players to have play each other, based on their results so far.)  I can't remember pointers right now, but I remember that I've seen some material on Stats.SE about this as well, so do some searching there and you might find additional references and resources.


I suspect it is likely that one of these will be a reasonable choice for you.

There is a major caveat.  It is important to understand is that there may not be any linear ordering of characters that has the property you want.

Think of the game rock-paper-scissors; there is no linear ordering of these three choices that ranks them in order of "power", and polling people about pairs of them won't let you find a linear order.  In particular, none of those three choices are any more powerful than any other; rock beats scissors, paper beats rock, and scissors beats rock.  This can show up in fantasy settings, too.