Algorithms are maybe objective. A famous example now known how PageRank gives different results by changing the numerical value of what is cold the ”damping factor”. PageRank is based on an assumption how a web-surfer behaves. For a while the surfer will click to links she is seeing in a certain page, but get bored with the actual page she visits, and then jump to another page randomly (as with directly typing in a new URL rather than following a link on the current page). The original algorithm assumed that the probability of being bored is 0.15, so the numerical value of the damping factor was set as 1-0.15=0.85. So, setting the damping factor for other numbers we may get different ranking. The phenomenon is called rank reversal. Rank reversal is a change in the rank ordering depending on some not important, or many times irrelevant factors. While I find the paper of Seung-Woo Son, Claire Christensen, Peter Grassberger, Maya Paczuski PageRank and rank-reversal dependence on the damping factor excellent, my opinion does not count much, during almost six years its citation number is just six.
On a somewhat different note it is reasonable to expect that the ranking of any two candidates, A and B, should be preserved even if one more candidate C enters the race. In the theory of election systems it is called the ”rank reversal rule”. This rule was infamously violated in the US election in 2000, when Ralph Nader captured a few per cent of the vote in Florida, giving the election to George W. Bush (over Al Gore). As all we know Gore would have won if Nader was not in the race.