With a topic as sensitive as urban density, where city planners have been bombarding us with the "right-answer" of high-density living for decades, I would expect people to over-report preferring high-density living, especially on a survey conducted by someone trying to prove their case that people prefer high-density housing.
... of the voting population, whose demographics unfortunately don’t match up with the population at large.
There’s also a vested self-interest for property owners to vote in such a way that preserves their property values. And what better way to do so than to restrict supply?
Big caveat: My opinion comes from large amounts of anecdata. But at the same time, it has often been noted (especially on HN, given its demographics) that San Francisco, where there is a huge demand for dense housing, is fraught with many barriers to actually build dense housing.
You can see City Observatory’s (an urbanist publication, so YMMV) take: http://cityobservatory.org/homevoters-v-the-growth-machine/
Your linked homevoter article underlines the point by suggesting that low density housing areas are more likely to be downzoned than zoned for higher density, which is odd if a majority of their population has an unexpressed desire to live in a less suburban area, especially since it's most likely to happen where residents are homeowners and wealthy and white enough to be an influential voting bloc.
Restricting supply is itself a perfectly valid reason for actually preferring lower density housing, but it's only part of that equation. It turns out that many people who might answer survey questions saying that they ideally want a walkable neighbourhood with better transit actually end up obstructing plans to put a train line through their leafy suburb and a mixed-use development towers a few blocks away from their house.
For example, MTV/Palo Alto have the same per sq ft price as san francisco. There are sources showing each one as higher than the other, but not to any significant degree.
Second there are a tremendous number of factors that affect housing prices other than personal preference.
I'm really unsure if you are trying to be serious here, because it's so rare a preference like we are talking about here really has a majority at one of the extremes.
I worked in a city where only the very richest people could live in the very expensive high-density areas. A tiny condo being perhaps four times the cost of my very large luxurious suburban house, maybe ten times the cost of a cheap suburban house. They had experimented generations ago with high-density poor people housing; that was not exactly paradise for anyone involved, so high density is only approved if the rent will be over $3000/mo otherwise the police budget cannot handle the crime issues. There is a self imposed demographic separation where only wealthy live in the penthouses therefore being wealthy the prices charged to fit their budgets are high. Of course there are maybe 1000 suburbanites for every CEO in the nicest five million dollar penthouse. And the population of the burbs combined is approximately 20 times the population of the high density areas. Its possible to cheat such that you are "in the city" but in a tiny house near the dangerous part of town that hasn't been gentrified into unaffordable condos... yet. But I'm not counting SFRs as "high density urban" because its basically substandard suburban lifestyle.
Let me ask you this--why don't the very richest people in your city live in very expensive suburbs instead of very expensive high-density areas?
Don't they? The only rich person that I know that lives in a penthouse is the dropbox CEO. Bill gates, Jeff Bezos, Andy Jassy, Mark Zuckerburg, Larry and Sergey all live in suburbs as far as I know.