I realize that there are various types of Swiss pairing systems. What would be a minimum set of parameters that needs to be specified in order to avoid ambiguity in pairings? I am thinking of parameters like "initial order", "fold/slide/adjacent pairing", ...
Does such deterministic system actually exist or will there always be some pairings that have to be decided by an arbiter or by flipping a coin?
Trying to clarify with an example: As far as I understand for any major tournament there should be rules (either set by FIDE or the organizers) regarding the way the pairings are done. These rules should specify all kinds of things like for instance, how do you pair players with the same number of points? Do you pair the strongest with the second strongest or you split the group in two and pair the first from the first group (i.e. the strongest) with the first from the second group (i.e. the one of medium strength).
Now if all of these rules/parameters have been set, is there still any ambiguity left? Or conversely, is it possible to satisfy all rules or would some get precedence in case they contradict each other?
For instance FIDE specifies that no player should play three games in a row with the same color. But if there are only two players (who both have played the last two rounds with the black pieces) with 7 points left who are therefore going to be paired. What is going to happen then? Is the FIDE rule of three same-color games going to be violated or are they going to be paired with other players first?
Basically what I am asking is, whether in practice the rules are stated and followed completely (meaning that all kinds of exceptions need to be stated) or whether pairing rules are only laid out roughly and if necessary the organizer is entitled to change some pairings?