Subjectivity is essential in everyday life. All around us, the world is created and run based on the opinions of individuals and groups. In addition, real life is analog. We don't all move around on a hex grid. We don't measure all quantities in whole numbers.
For me, however, subjectivity in gaming is unwelcome. In all situations, the rules, the mechanics, and the resolutions should be 100% objective. For example, if the same situation came up in 100 different game groups, the result would be the same.
Let me begin by dismissing one kind of subjectivity: ambiguous rules. While the gaming world is occasionally infected with this disease, I don't think this is a matter of opinion. Right? We all want clear unambiguous rules? If you disagree, you better stop reading now, or your brain may melt.
The first form of intentional subjectivity is analog games. Mostly this pertains to miniatures, but has some carry over into traditional wargames. Units move around using rulers or other measuring devices. Line of sight is determined by looking at a target from a unit's point of view and "guessing". There is no instantaneous point at which a unit goes from seen to unseen. It's a guess. If the players disagree, there has to be a "random" resolution. On two different days, the decisions may be different. Range is a similar problem. You have to measure the distance between two units. Does the line touch his foot or not?
Likewise, with wargames. Line of sight may need to be measured across hexes that contain buildings o or other obstructions. In many cases it's perfectly clear that the "string" crosses something or does not. But often, there are edge cases. Well you gave me that last one, so I'll give you this one. Yuck.
I'm sure that miniatures players actually enjoy the unpredictability of the system. If I move there, will I be able to see him? Will I be in range? I'll admit it is more "realistic". But it also forces the need to "argue" about all the close calls. I've heard of various solutions, like allowing a player to make a call in his favor 3 times, etc. Or perhaps you roll a die on all close calls. How does this solve anything? It's just changes the conditions to say something is close. Close call, I'm going to roll. It's not close enough to roll; It's clearly blocked. No it's not...
I can't imagine playing a game where I have to constantly either argue to get something in my favor, or give in all the time. The end result will always feel unsatisfying. I won only because I'm more assertive, or I lost because I didn't want to argue.
The second type of intentional subjectivity is by rules. This is not the same as ambiguous rules where the designer forgot some case or combinations. It is the kind where the designer is intentionally leaving it up the players to decide how things should go. Again, yuck! Two examples of this are Shadows Over Camelot and Mystery of the Abbey.
In Shadows Over Camelot, the rules on collaboration are as follows (from SoC rules © Days of Wonder):
"Declarations of intent can be made freely; resources and capabilities can all be discussed openly, as long as your comments are general and nonspecific. However, you must never reveal or discuss the explicit values of cards in your hand, or volunteer any other specific game information not readily available to your fellow players."This is ridiculous, and is the sole reason I would never buy a game that otherwise sounds incredibly fun. I've seen all the arguments. Even among those who play and enjoy SoC, there is disagreement as to what is acceptable. Some play it's ok to say exactly what you have as long as you role-play it. Some play that you cannot say anything that gives away your holding even indirectly. Still very subjective. If any given statement by a player cannot be 100% resolved as allowable or unallowable by the rules, then the game is broken.
In Mystery of the Abbey--another game by Days of Wonder--the problem is again to do with player interaction. You are allowed to ask questions of basically any kind, but you are not allowed to lie, even if the question is about the future. This leads to some interesting paradoxes and other unpleasant things. Fortunately, there are other reasons not to buy this game, so the subjectivity wasn't the deal breaker for me.
If I want a role-playing game, I'll play a role-playing game, not a board game. Player interaction in board games is fine. There are lots of board games with huge amounts of player interaction that are completely objective: Diplomacy, Traders of Genoa, Werewolf, Bohnanza. I'll stick to those.