> If you take that wealth and move it to the average person.

Wealth redistribution doesn't necessarily mean taking money/wealth, literally, from wealthy and giving it away to poor. It includes, among others, subsidized education, free access to basic health care, nutritious food, potable water, eradication of epidemics, decent housing, decent retirement income and so on.

This is the problem I see in societies that are highly unequal (read US :-)) where in a democratically elected government is reduced to make way for capitalists. All or most of the above are controlled by multinational corporations whose sole motive is higher profits. So what ends up happening is that even a middle class family is just one calamity away (e.g., death of bread earner, a high cost health problem) from being pushed below poverty line. Even education for that matter has gotten privatized to an extent where only wealthy can afford good education; as various studies have shown education does make a significant difference when it comes to money earned over longer period.
Or take 2008 recession where pension corpus of millions was reduced to zilch for no mistake of theirs.

Wealth distribution, at least in my mind, means that ensuring that most of the citizens are on level playing when it comes to basic necessities. Over and above that of course one must be rewarded as per their contribution to the society and hard work.

Poor are poor not just because they don't have money but also because they are unable to get out of it. They have to go through unspeakable ordeal just to get one meal a day and this places enormous cognitive load on the entire family. So of course children of poor, more often than not, remain poor as their basic intelligence itself gets suppressed due to lack of nutritious food, cognitive load etc.,

The book, "Poor Economics", was an eye opener for me in this regard. I once used to blame the poor for their situation but this book changed all of that. I would highly recommend it; to the extent that this should be made a mandatory reading in all colleges :-).

> We want to make sure that the incentives of the people in power are aligned with the people who are not in power.

This is really a tough ask. Unless decision makers, i.e., those in power, are accountable, every single day, to those not in power, decision makers will soon align themselves with private, capitalist corporations. You have a multi billion dollar arms manufacturer, oil corporations funding millions to election campaigns of US presidents. And then you have US citizens who get to vote once in five years; we also know that the voting itself can be rigged, public opinion can be swayed and etc., Now, whom do you think would the president side with? Oil corporation or US citizens? The answer is obvious! And so you will end up having Iraq war which is yet another way to funnel massive amount of tax payer money to private corporations; the cruel irony is that most of foot soldiers who are fighting the war and dying come from poor, disadvantaged families.

Democracy as it's played out in US (and India) today is a complete farce. The fact that executive powers and policy making is concentrated in so few a hands in itself is indicative that this isn't democracy. Instead of giving power to the few and somehow hoping that their interests are aligned with rest of the citizens what needs to be done is build strong institutions.

Democracy is fundamentally about strong institutions (court of law; education system; health care system; labor friendly laws) which are run and maintained by common citizens. Elected representatives' main job is do minor tweaks to the policies. This way the executive power remains with the commoner.

What has been happening is a very systemic eradication of these democratic institutions; privatized education, private health care; private police force; private fire fighters and so on. Once you have hallowed the core of democracy by privatizing it you are left with just a handful of elected representatives who wield enormous power over rest of the citizens. They of course end up serving private corporations. US is run and controlled, more or less, by just a handful of private corporations which are in turn owned by a hundred individuals. Election, democracy etc., is just to keep the citizens believing that they have a say in the way the society is run when the reality is completely opposite. India, following the foot steps of US, is getting there really fast.