Here's an RCT that might have already been done before:
Between-subjects design. Both groups are presented with descriptions of two different fictional political candidates. The descriptions presented to Group 1 are "neutrally worded." The descriptions presented to Group 2 are identical in denotative meaning to the descriptions presented to Group 1, but substitute some neutral words with connotatively "negative" words for Candidate 1 and connotatively "positive" words for Candidate 2.
Did the two groups favor different candidates, with a large effect size? This suggests that many people's choice would "switch" from one candidate to another based not on denotative meaning but on connotations, thus (presumably) choosing the "wrong" candidate for what they care about. (Lots of qualifications could be added here, of course.)
That's about sneaking in connotations, and something like that study has probably been done. I wonder if there experiments for other common "word-mistakes" like those listed in 37 Ways Words Can Be Wrong.
I had a chance to talk to my old cog sci teacher about this. He pointed out that your example is extremely similar to the way the the wording of questions can greatly effect survey results, even if the chance doesn't seriously effect the actual meaning of the question or the content of the explicit information provided. In a later email he also suggested that
Tversky, Amos; Kahneman, Daniel (1981). "The Framing of decisions and the psychology of choice". Science 211 (4481): 453–458.doi:10.1126/science.7455683. PMID 7455683.
might be of interest.
There's plenty of experimental work about how humans make poor judgments and decisions, but I haven't yet found much about how humans make poor judgments and decisions because of confusions about words. And yet, I expect such errors are common — I, at least, encounter them frequently.
It would be nice to have some scientific studies which illustrate the ways in which confusions about words affect everyday decision making, but instead all I can do is make philosophical arguments and point people to things like Yudkowsky's 37 Ways That Words Can Be Wrong or Chalmers' Verbal Disputes and Philosophical Progress.
Which keywords do I need to find experimental work on this topic? I tried Google scholar searches like "fuzzy concepts" "decision making" and effect of connotations on choices but I didn't find much in my first hour of looking into this.