Logically, you'd want an intelligent person who understands the best approach and methods for running a country in the best possible way. But no, people seem drawn to demonstrations of questionable intellectual abilities. There are a wide variety of ideological, cultural, social, historical, financial and other factors involved, because politics incorporates all of these things, but there are also some known psychological processes that may contribute to this phenomenon.
Confident people are more convincing. This is has been demonstrated in many studies. Most studies focus on a courtroom setting, and suggest a confident witness is more convincing to a jury than a nervous, hesitant one (which obviously has worrying implications for justice), but it can be seen elsewhere. It's a phenomenon used-car salesmen and estate agents have exploited for decades. And politicians are clearly aware of it, hence all the media training and PR management; any politician that doesn't come across as assured and confident gets (metaphorically) destroyed. So confidence is important in politics.
However, the Dunning-Kruger effect reveals that less-intelligent people are usually incredibly confident. More intelligent people, by contrast, aren't at all. Self-appraisal is a useful metacognitive skill, but one that requires intelligence; if you don't have much of it, you don't consider yourself flawed or ignorant, because technically you don't have the ability to do so.
So if you want an intrinsically confident person to publically represent your political party, an intelligent person would be a bad choice in many ways. This can backfire though; studies have shown that when a confident person is shown to be wrong/lying, they are then considered far less reliable or trustworthy than an unconfident person. This may explain the negative image of politics, which is mostly a series of confident individuals making big promises and failing miserably to keep them. That sort of thing really puts people off.
Effectively running a country of tens of millions, all of which have different requirements and demands, is an incredibly complicated job. There are just so many variables that need to be considered. Unfortunately, it's impossible to condense all this into a convenient soundbite for use with the modern media, so personalities tend to come to the fore more often. And the less intelligent personalities are more confident, so are more persuasive, and so on.
People are often put off by intellectual and complex subjects and discussions in any case. They may have no experience with the issue, or may find it too daunting to want to engage with, because doing so successfully would require a lot of time and effort. But politics, particularly democracy, requires people to be involved.
Personality studies suggest that many people demonstrate goal orientation, a disposition toward developing or demonstrating ability in achievement situations. Feeling that you are actively influencing something (e.g. an Election) is a powerful motivator, but if some knowledgeable type starts spouting big words about interest rates or health trust deficit management, this is going to alienate those who don't follow or grasp such things. So if a confident person says there's a simple solution or promises to make the big complicated thing go away, they're going to seem far more appealing.
This is also demonstrated by Parkinson's law of triviality, where people will spend far more time and effort focussing on something trivial that they do understand than something complicated that they don't. The former offers far more scope for contribution and influence. And people do love trivial things, ergo less-intelligent people condensing down the big issues into brief (but inaccurate) snippets is a potential vote-winner.
One of the often-cited qualities of George W Bush was that people felt they could have a beer with him. Ergo, they felt they could relate to him. By contrast, elitism is a negative quality. The idea that those running the country are outside the norms of society is alarming to many, hence constant efforts by politicians to fit in.
The majority of people are prone to numerous subconscious biases, prejudices, stereotyping and prefer their own groups. None of these things are particularly logical and invariably are not supported by actual evidence and reality, and people really don't like being told things they don't want to hear. People are also keenly aware of social status; we need to feel we are superior to others in some way to maintain our sense of self-worth. As a result, someone more intelligent saying complicated things that contain uncomfortable (but accurate) facts isn't going to appeal to anyone, but someone demonstrably less-intelligent is not challenging to someone's perceived social status, and if they're going to say simple things that support inherent prejudices and deny uncomfortable facts, then so much the better.
It's an unfortunate situation, but it just seems to be the way people's minds work. There's a lot more to it than what's mentioned here of course, but including that would make the whole thing more complicated, and that's no way to get people to like something, as should be obvious by now.
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