> if the politician has 50%+1 votes in his pocket and appoints the bureaucrat, the opinion of the rest of 50%-1 voters have absolutely no weight to him (unless he is of a special rare breed of saint which is so rare in real politics).
This sounds plausible, but it isn't correct. Remember, first of all, that no politician has real access to who did and did not vote for him. He has access to polling data, which generally scrubs well enough to reduce people to demographics. Conveniently, we generally engage with our politics through the lens of demographics anyways. But demographics are effectively never 100% accurate: samples are only samples.
Second, votes matter to politicians only if they want to be re-elected. They also matter on ballot measures and propositions and so on, but those are generally not what people mean when they talk about politician-voter relationships. Obama, since 2012, has no real reason to care about who voted for him in 2012 because he's not going to get any votes in 2016. There are other reasons in play, yes, but electoral votes are irrelevant when a politician has no interest in retaining his seat at the next cycle.
Third, politicians care about public opinion. They balance this against other competing interests, to be sure, but public opinion is the reason most of them ran for office in the first place. Those competing interests run the gamut from commercial interests to legal interests to moral interests to realpolitik, and ultimately, their job is to reconcile every interest with every other interest. That's what a politician is. People are afraid of politicians because they do not understand or recognize the interests they have outside of public opinion.
Public opinion is not votes, because public opinion is not tied to the electoral cycle. It suffers from the same problem of votes--that it is polled and often reduced to demographics--but from a far smaller degree because public opinion is also expressed by individuals who are willing to identify themselves.
The problem with public opinion, though, is that it's extremely rare to get anything solid resembling 50%. Nowhere close to 50% of a population is generally willing to identify themselves, meaning such a thing will always come down to polling data.
The advantage that corporations have in influenceability isn't that 50% could walk away (which will basically never happen on solely moral grounds); it's that it can track their interests with far, far more precision. It can know if you stop spending money, and it can calculate exactly what effect that will have on its bottom line. A politician, on the other hand, cannot track your personal opinion, and even if he could, he cannot determine how that would play out against the myriad other priorities he must keep in mind, not least of which is the rest of his constituency's opinions.
A politician makes a marketer look like an engineer in comparison. And yeah. Improving this would basically be a privacy risk. So we're fucked.