Just to point out, you're using a common term very differently than others in cryptocurrency who say "Proof of Stake". This will add friction to your conversations.
With "Proof of Stake" to mean a consensus system, are you saying the Ethereum Proof of Stake implementation doesn't do anything to guarantee against a cartel of bad actors?
My understanding is "slashing" may be one such mechanism. This is where staked funds are taken away from bad actors. ie if you propose a block with bad transactions, the 32 ETH you have staked will be reduced by some fraction as punishment. When your stake is slashed down to 16 ETH you are booted from the system. So that us a clear punishment against a bad actor, though I'm not sure what a cartel means i this case. Perhaps you know about this already however.
Proof of Work is not resilient to a sufficiently large 'cartel' either in this case. If your cartel is 51% of bitcoin miners by hashrate, they can agree to let each other spend their bitcoin twice. Of course, this is sufficiently hard to do with proof of work, as with proof of stake, as to make it infeasable, perhaps even moreso with proof of stake.
As an example with bitcoin specifically, it would probably be cheaper to buy enough mining hardware to constitute 51% of the bitcoin network than it would be to buy 51% of all bitcoin.
Of course, both would be very expensive endeavors.
Proof of stake is a decentralized consensus mechanism that is (usually) trustless, and prevents attacks like double spending.
Most notably, Solana, Cardano, Polkadot, Avalanche, Terra, Algorand, Polygon, Elrond, and Fantom are all using permissionless networks where nodes which have some amount of the native token of those blockchains staked produce blocks and validate transactions
Your answer reads like a marketing blurb and only tells about the goal (on which we agree) and not the mechanism (where we disagree). I tried reading a few of the coins you mentioned and all of them were witness ("validator") based...
They still do not prove that they have something in possession, they stake their own coin on being honest... BIG difference.
Do they allow you to prove that you (and you alone) have possession/control of the coin itself, and if so, how? (That is the part that I consider impossible).
The whole problem is that proof-of-stake has been redefined by the new PoS networks and does have the original meaning of "stake" (i.e. sole possessor) anymore.
I can prove to you that I have access to a gold coin by taking it out of my purse and showing it to you.
You can do three simple tests (weight, volume and ringing) that ensures that it cannot be any other material than pure gold (due to any material that is both cheaper and heavier than gold is tungsten and that does not ring). You can also be sure that it is not a clone of another coin so that it "just disappears" or gets double spent.
There is also no witness/validator that can break your trust and betray you.
Every POS network I have ever looked into (and I admit that it has been a while) relies on witnesses. And that removes my way of knowing whether the witnesses lie or not.
Is there any of the socalled PoS networks that actually allow you to prove that you have exclusive possession/control of the digital coin in question without any witnesses ('validators')?
If so, their founders can already book their ticket to the Nobel Gala next year, as that would AFAIK be a feat in the same scale as disproving gravity...
When I say proof of stake, I mean it in the way of "proof of possession"