@alvinjoelsantosMoreover, there is an issue of what standard of proof should be met. From a legal prospective, generally, in criminal cases, the standard is "beyond a reasonable doubt" and in civil cases, "more likely than not." With 2 to 4 mixin, there is a probability of between 41% to 23%; if this is the only information an adversary is able to deduce, it is not enough proof to establish guilt or liability for a given transaction. Users would have plausible deniability.
You're raising a good point, it is true what you are saying, I doubt any democratic court on this planet can convict someone on the basis of a statistical correlation, something I think we can be very happy about. However the adversary has narrowed down his set of suspects, and there will most likely be more evidence to prove his guilt. A transaction, in itself, is almost never illegal. The adversary can be anyone, they aren't specifically governments either. The juridical process doesn't apply for a lunatic with a shotgun..Even if a particular output can be guessed by an adversary to be the "real" output used in a transaction, this is not enough information to definitively state that "Alice sent x amount to Bob in this particular transaction" given the other features of Monero that hides the transaction amounts and the recipient's public address from the blockchain.
Also true, but the person that sent you the money knows with 100% certainty that that specific output is linked to a stealth address, and in the case of an exchange, they often know the exact identity of the person.
As ebfull has suggested, there are real case scenarios of potential "adversarially controlled mixins" - exchanges for example control a relatively large portion of outputs to pick from as mixins. Let's assume that exchanges control X% of transaction outputs. The average transaction has two mixins, causing the following probabilities to emerge: 1% of tx outs -&g...