Q:

Why do investors pay trillions for minority stakes in companies, when their only potential payback is modest uncertain dividends?

I'm struggling to understand the core reason to invest in stocks as a minority shareholder. Majority shareholding makes more sense as you effectively control the company, so you can pay yourself dividends or even sell the entire company at will. You can guarantee your own payback.
However, as a minority shareholder, you don't get to make any of these decisions. You're basically just hoping to eventually, some day get paid, if the majority holders decide so.
Why do so many investors agree to pay now huge sums of money (trillions in total) for something that may eventually pay dividends, and even in the best case, these dividends are only a fraction of the price you paid to acquire these stocks?
The average annual dividend rate for the US stock market is 2%. That means if you bought 100 million worth of shares, you'd have to wait 50 years to recover your investment.
Of course, the most probable way you'd eventually get liquidity for these shares is by selling them to some other starry-eyed investor - which makes the whole thing seem like a giant Ponzi scheme.
Given all that, it's unclear to me why the public is willing to spend so much money to acquire minority shares in companies.

A:

Say you buy 25% of a corn field, and the other 75% is owned by others that decide how to operate the whole field (for this metaphor, assume the shares of the corn field are highly liquid and can be traded at "fair" value at any time). Every year, that field produces corn that is then sold for a profit. The majority owner can do two things with those profits: distribute them to the owners (3 parts to them and 1 part to you) or use them to grow the field. They choose to use it to grow the field. They can invest in the field by either buying more land on which to plant corn, more equipment, or more profitable seed. Next year that field increases its yield (and its profits) by 10%. The owners decide to invest in the field again, growing the yield and profits another 10%.  it now makes 21% more profits than when you bought a quarter of it. 
You tell me - is your 25% of that field worth more than when you bought it? At some point, there will be no more ways to grow the field, and so the best use of the profits is to distribute them so that the owners can invest it in other ways. Or, someone may be willing to buy your part of the field, which should be worth about 20% more than when you bought it.
Paying dividends is not always the best way to get part of your investment back. You're effectively "selling" part of your ownership to yourself by removing cash from the value of the company and putting it into your bank account. If the company can use that money to grow and increase the size of the field, on paper your investment has grown.

A:

Why do so many investors agree to pay now huge sums of money (trillions in total) for something that may eventually pay dividends, and even in the best case, these dividends are typically only a fraction of the price you paid to acquire these stocks?
The average annual dividend rate for the US stock market is 2%. That means if you bought 100 million worth of shares, you'd have to wait 50 years to recover your investment.

I challenge your assertions that:

people buy stocks only for dividends, and
that it takes 50 years to get their investment back.

That it because:

a big portion of wealth growth (even when purchasing "dividend" stocks) is asset appreciation, and
you still own the actual asset (the shares of stock).  Worst case scenario is that it goes bankrupt or you buy at the peak of a bubble.

Bottom line: your concept of why people buy stock is fundamentally in error.

A:

As I wrote in another answer, minority shareholders have

the right to resell their shares to another investor (e.g., one who may be accumulating a controlling stake in the company). This works out so that shares are generally valued as if they were an entitlement to profits, because in the long run this is the basis of their value.

That is, if smaller investors were not willing to bid up a stock to a fair price reflecting the value of the company, then a big investor would buy up the majority of the shares at the low price and then make a big profit by controlling the company. This does sometimes happen (e.g., an undervalued company goes private). But generally all investors understand that the potential of a buyout is a concrete reason that each share is worth something real, regardless of the company's current dividend policy.
EDIT: A controlling shareholder is motivated to maximize the long-term value of the company, and any other shareholders, however small, are along for the ride in the same boat. Whoever has the most strategic, optimized, long-term plan for the business is likely to make the highest bid in the stock market and accumulate more of the company. If remaining minority shareholders don't value the stock as highly, the majority shareholder will be happy to take it off their hands and increase their own stake.
In particular, it might indeed be optimal to pay little or no dividends for a long time so the company can grow faster, and then start bigger payouts sometime in the future. (Importantly, these dividends will flow to all shareholders proportionally, so even a small investor will see the same return.) Small investors who want dividends now might not like this, but the key is that less patient investors can sell to more patient investors and get the rewards of a bright long-term future in the form of a higher stock value today. And since everyone knows this, stocks are valued as if all shareholders are patient.

