I have a character who can suggest things to people, and what she says, they believe to be true. Is there a way to scientifically explain this, even vaguely? I was wondering if perhaps a form of intricate telekinesis only affecting neurons would be even slightly plausible, or is there a better explanation? The character is also a psychopath, but I'm not sure whether this would affect her ability.
It may actually help her greatly.
I would say you may not even need the magic, super-powers and mind-control tags for this, but always believing her, regardless the implausibility of her statements probably require that.
Humans are social animals. Regarding a given situation, we subconsciously take are cues from each other. We depend on our non-verbal communications (body-language, tone, etc.) to determine what kind of situation we are in. Let's call this Frame!
This Frame are decided by the participants upon contact. If the situation, relation of the participants to each other is not clear cut from the get go, or established previously, this quickly established Frame will dictate how the situation will unfold.
Let's take an example from the military. You could take from anywhere in life as it is omnipresent, but it is easier to demonstrate this way.
A new, inexperienced officer full of doubt will give orders weakly. Their Frame will telegraph it and others will pick up on it, and challenge them.
A trained drill sergeant will issue orders with the absolute certainty that they will be obeyed, and obeyed without thought the moment he issued them. His Frame will telegraph this too, others pick up on it and act accordingly. Won't even think to challenge his authority.
Policemen, fireman, etc. are trained to behave in certain way when dealing with civilians.
Finally, here comes your psychopath. Most people doubt themselves, especially when they are being harmful to others. They empathize with others pain, which make them hesitant. This will leak into their frame, making the more observant people pick up on and doubt the others sincerity.
Psychopaths don't have this problem. In their mind, only themselves and their needs exist above any other consideration.
This give them an edge in Framing. You can add, other natural, but helpful factors. Her appearance can be authoritative and beautiful. The later is helpful, as it puts her higher in social status, which will make others naturally wanting to please her. She could tailor her tonality, body language and other non-verbal cues to induce trust.
Using this trust, she can tell others to act upon her wishes. Humans aren't rational, they are rationalizing. Compelled by the right Frame, they will act upon it and later explain to themselves why they did it.
(My understanding of this issue may be flawed, so unless verified by others take it with a grain of salt.)
"Who are you going to believe, me, or your lying eyes?"
This happens all the time. The first part is to create doubt about what someone would be most likely to believe. Go after the facts, or pose alternate facts, or somehow muddy the waters of logic, fact and first hand experience. That is called "Gaslighting" https://en.wikipedia.org/wiki/Gaslighting. There is a ton out there about this. Gaslighting neutralizes the primacy of fact and logic in people's thinking.
Once that happens the mind tends to fall back on emotion and gut instinct to decide if it will believe something, or decide what to do next. Unlike logical thinking, the mechanics of gut decisions occur outside most people's awareness. All we are aware of is the final feeling, certainty, or instinct about what to do, or what to believe. And that is easily manipulated with emotional messaging, like fear about safety or wellbeing or its opposite - thoughts of great windfalls. Triggering or even referencing fear or anger is another way to force decisions on what to believe. The gut is easy to fool if the person knows what they are doing. It can be done just with the sequence of neutral ideas in a conversation, before asking someone to believe something. It is the art of a con artist. It also can wear off when the victim is out of the perp's immediate presence.
At a smaller level, it's also how every one of us decides to believe or not believe someone who may be lying, when we can't get the facts. All gaslighting does is neutralize the few facts we do have, and force us into emotional decision making. "Who ya going to believe, me or your lying eyes?"
So for your story, the woman could be powerfully aware of this. Sociopaths are often a genius at this stuff and highly aware of how they use it to manipulate others. It is the stock and trade of people with Narcissistic Personality Disorder, who might or might not be aware they are doing it. And it also plays critical roles in the other 'Cluster B' disorders where the manipulator is probably unaware, and is actually desperate to believe their understanding of a situation that matches their own powerful emotions. Desperate as though they were actually terrified deep deep down inside. Part of their intense struggle to explain things, and to believe their understanding is for them to manipulate others to believe it too, thus making their belief more stable. For your story, it's not uncommon for people with "Cluster B" disorders to destabilize and become suicidal or homicidal when their alternative 'reality' becomes overwhelmed with the 'true' reality where they are not powerful or right or "the good guy." For example, when someone escapes a horrible abusive home and takes the kids, and then the abuser goes on a homicidal rampage.
It's not the exact science of how this happens in the neurons and synapses, but it happens all the time, and your villain could just be powerfully good at it. It's maybe even more scary if the ability, to a lesser degree, is in all of us.
If your story depends on a non-social engineering solution based on exploits of the human psyche, then maybe your character is telepathic and tele-empathic enabling her to transmit and perceive other peoples thoughts and emotions.
Once pseudo-science explanation for this is that reality is constructed by a universal consciousness and that our perceptions of reality are mind-first and physicality second. This proposition implies that someone who is consciously aware of this 'fact' can interact with the universal consciousness and use it as a conduit to reach other people as well. Again, this is the pseudo-science explanation for this, not my personal beliefs.
This is how I imagine it working. The psychotic-psychic forms mental images and relays them through the universal consciousness into other peoples brains at the subconscious level. This establishes a bias in her targets to agree with what she actually says out loud, since to them, she is confirming their hunches and expectations. For individuals that rely more on reasoning and less on hunchs and emotion, she can also plant whispers in their head that, in effect, do what other answers are suggesting -- gas lighting, appealing to greed, etc.
Pheromones are secreted or excreted chemical compounds that trigger certain social responses in other members of the same species; similar to how hormones trigger such responses inside an individual.
Pheromones can trigger alarm response or sexual response, they can mark territories or trails, and they can trigger long- or short-tem changes in behaviour or even developmental changes. Aereal pheromones play an important part in human sexual response, though the target is typically not aware of the presence of pheromones and the effects they have.
Hence, it is not far-fetched to imagine a pheromone that makes the recipient more likely to believe what is being said. It might be a mix of sexual pheromones causing strong attraction and releaser or signal pheromones influencing behaviour (i.e., being more receptive to suggestion). This might be related to Beta Androstanol; a human pheromone that supposedly triggers uplifting moods, social comfort and ease, internal peace and increased confidence.