No clue if there are similar laws in Germany or other countries.
The valuation is decided during the arbitration process. From what I understand if there has been previous offer to buy it's quite likely that will be used at least as initial basis for the price.
There seems to be at least one English article about the process: https://insights.fondia.com/fi/en/articles/corporate-law/sha...
There's also requirement (with some exceptions) to make offer to buy publicly listed company's shares when the shareholder's control over the votes increases above 30% and 50%. Normally the price in that case would be the highest price that shareholder paid for the shares during previous 6 months.
This is supposed to protect small investors from finding themselves owning shares they can't sell on the market anymore.
The price is set by the equivalent of the SEC.
If that fails to buy all the shares, the company must sell enough stock so that the market is again liquid enough.
I _think_ many countries have similar rules, as cursory googling shows the London stock Exchange changed their minimum free float requirement some years ago.
If they are private person they can attempt to judgement via court and let enforcement authority liquidate their assets or garnish their wages.
I would guess that it’s part decorum part attempt to minimise the administrative burden. Many European PE’s operate on a “there is enough money to be made by being fair” sort of motto. This can be because they mean it, but it’s also because not being “evil” it a marketable product to many EU investors (this is likely true outside the EU as well, but I only know about EU markets). Then there is the part where private companies are still responsible for keeping track of ownership, as well as informing them. Even if they plan on letting investors trade on some internal platform it’s still a rather large administrative burden that becomes easier the fewer shareholders they have.
This is still just me guessing, but the way I read this it’s a simple message. Investors get a nice out and they’re going to be disappointed if they don’t take it.
if you plan long term strategic shifts, most shareholders will bail out earlier when the quarterly publications once doesn't look too good. which hurts the whole plan.
so if you need to invest long term, it's better to get rid of those short term investors, which can bring everything down. private you don't need to publish your results, that's why most German companies prefer to stay private. they think in 6 year plans, not 1/4th year plans
So they instead offer a large premium and hope/assume those parties will accept.