The mechanism of PoW makes the coin tremendously more secure even in the event of a 51% attack. PoW means that trying to do anything in the network is costly.
I don't think the cost is that different.
In PoW, mining in the long run has roughly zero profits. That means that if the 51% of miners are doing anything which lets them still keep the mining rewards (like perhaps censoring transactions they don't like), then their costs are canceled out from mining rewards. If a 51% cartel in PoW did something to shake people's faith in them and cause the coin value to tank, then their costs would not be recouped, but they'd have already cashed out most of their mining rewards until that point, so the main cost is the loss of future revenue.
In PoS, if the major coin holders start double spending or do something to cause the coin's value to tank, they are harming themselves immensely because they had to lock up their coins in order to sign blocks, so they won't be able to cash out before they destroy the coin's value.
PoS, by contrast, can be attacked with little to no cost by around 1% of the stakeholders or any entity that can get control of that much stake at any point in the past.
I'm unfamiliar with the "1% attack" in PoS. Do you have a link describing how it'd work? (EDIT: if you're talking about "stake grinding", then I understand. I don't have a good argument against this, so it might doom PoS systems, but I'm still curious about the weak subjectivity issue separately).
Proof of Work gives us proof about the current state of the blockchain, Proof of Stake is not really proof of anything.
It's supposed to be proof that the signers of a block have locked up a certain amount of coins, which will be lost if anyone catches them signing other blocks. If there is some attack where these people can create another fork without losing their deposits, it'd be pretty bad for PoS. My impression is that the only way to do that was via a "long range attack", which is what weak subjectivity disallows at the cost of requiring some trust.
This is why I trust the chain that Bitcoin-QT gives me: I know that anyone who wants to do the actual verification that the chain you get from Bitcoin-QT is the real chain can do so. I know that lots of people have read the code and verified everything, and I don't know of any credible people raising an alarm in the media.
This is why I'd trust the chain that I got from the 20 people I listed above, assuming Bitcoin had switched to a weak subjective system: I'd know that anyone who wanted to verify the chain objectively (by being online at least one a year) could do so if they wanted. I'd know that lots of other people had done that, and I'd know whether credible people were sounding any alarms in the media.
The level of trust required doesn't seem to change significantly for the average user. For the hardcore power user who doesn't want to trust anyone, they can simply be online at least once per year and they won't have to trust anyone.
You can rationalize it all you like. The bottom line is that mathematical proofs can't be replaced by socializing. What are the odds? Greater than 0%. What are the odds that the Bitcoin code doesn't do what the Bitcoin code does? 0%.
The point was that perhaps 99% or more of Bitcoin users are relying on trust/socializing when they use Bitcoin already, and it works well for them because the system is set up in a way where anyone who wants to do the work of objective verification can do so. That 1% of people who read the code and verify everything themselves and refuse to trust anyone could also refuse to trust anyone by being online once a year in a weak subjective system. You can call it "rationalization", but I'm trying to evaluate the practical security implications of both systems and I don't see any argument why the practical differences would be significant.
Also, the chance of being wrong when a person tries to objectively verify the longest Bitcoin chain is not 0%. That is the relevant probability to compare to the chance of being wrong when asking trusted parties. If a person tried to objectively verify the longest Bitcoin chain now, they could make some technical error, be tricked into using corrupted software, be isolated from the rest of the network by some hacker, or be tricked by a hacker that has complete control over their machine. Maybe the probability of any of those things happening is less than 0.0001%, but what if the probability of being wrong using my method above is also less than 0.0001%? No one has attempted to address this. It's just "but trust is worse than not having to trust!" without any effort to measure and compare risks.
I also don't really know what you mean when you say "fake chain". If someone builds a chain following all of the rules of the protocol, can you really call it "fake"? Doesn't it bother you that it's even possible for a blockchain to have multiple valid states?
I was using "fake chain" above in the context of Bitcoin, using PoW as it does today. I meant, when I ask Greg Maxwell and the 19 other people I listed above which chain is the longest chain, what's the probability that they would all tell me some other chain is the longest, when this other chain isn't actually the longest?
For PoS, a fake/invalid chain would be a fork from longer than a year ago which is disallowed by the rules of the system but which I couldn't objectively determine if I hadn't been online in a year.
More than just the lack of rigorous security standards, I'm not sure what Proof of Stake accomplishes exactly. What does it offer that is better than both Bitcoin and average run-of-the-mill financial datacenter?
My motivation for bringing it up is that I'm worried about the long term security / required transaction fees of Bitcoin, when mining rewards run out. I'm trying to evaluate PoS + disallowing long range forks + weak subjectivity as a method of ensuring we have adequate security and low transaction fees in the future. The specific claim I'm trying to evaluate is that this type of PoS system I'm referring to might have better long run security economics than Bitcoin as it exists now, and in practice it might be equally decentralized as what we have now. In other words, the "but you have to trust someone!" point may just be academic, and in practice the difference between this and current-Bitcoin may be negligible.
As I mentioned before, I seem to be trying to evaluate PoS very late, such that almost all smart people involved in Bitcoin have already convinced themselves that PoS is worse than PoW are sick of the topic. I'm willing to believe they're right that PoS is unworkable because they have a lot more knowledge than me, but I'd like to understand the reasons why, and weak subjectivity seems plausible to me.
So far, the best critques of PoS I've seen are:
http://www.truthcoin.info/blog/pow-and-mining/https://download.wpsoftware.net/bitcoin/pos.pdf...sadly neither directly address the attempt to use weak subjectivity to get around the nothing at stake problem.
If anyone has other anti-PoS links that you think I'd find useful, please share them.