Having just looked at the idea of using equivocation to force a result on a player without their knowledge, I want to explore the concept of choices more generally.
Players need structured choices. A player with too few choices is not a player but an audience. A player with too many choices is not a player but a DM. When there is nothing but choices, play becomes unfocused, the story becomes bogged down in debate, and everyone stops having fun. The job of the DM is to narrow down the infinite canvass of possibility into the tight structure of a story.
DMs should give players choices for good reasons. There are a limited number of good reasons, and they are these.
1) A test of skill.
The player is given a small range of options, one of which is "right" and the others of which are varying degrees of "wrong". The player is given enough information in the environment to discern the right choice, if he or she is clever, perceptive, or patient enough. The choice rewards players for their intelligence.
2) A chance for self-expression.
The player is given a broad range of options, where the eventual choice meaningfully defines both the character and the game. This may be, for example, a "morality call", a setting of priorities, or a chance to define the future development of a location or NPC. The choice made says something important about who the character is and how they think, and lets the player express their uniqueness and individuality.
3) A means for player feedback.
The player is given two or three options, with information as to the likely gameplay consequences of choosing each option. There may be a "dangerous" option and a "safe" option, a "quick" option and an "extended" option, or a "roleplaying" option and a "combat" option. The player's choice lets them direct the game towards the the type of situations they enjoy and away from the ones they find dull or unpleasant.
That's it. They're the only meaningful choices. If your choice doesn't fall into one of these categories, then you shouldn't be offering it to the players. Or, alternatively, it should be a false choice such as the one we looked at a moment ago, where despite the illusion of choice the players proceed on to the same consequences regardless.
Needless choices will distress your players, and they'll make it unnecessarily hard for you as DM to deliver a high-quality game experience. Give your players a meaningful choice whenever possible, but don't stuff around with other ones. Your players will thank you.