The default for wallets right now is 4 but is there a large benefit say using 15 or 20 over 4? Can this be measured? Bigger ring size will help obviously but after a while is it not kind of a waste of transaction size?

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A mixin of 4 means there are 4 decoys in addition to the real input, which means the ring size is 5.

No ring would be needed at all if your output could never be associated with you. However, the exchange or person that gave you the output does know you control it if you told them who you are.

Therefore a ring size of 5 means that when the person that gave you your output sees that the output has been used in a transaction, then when you spend it they can see there is a 1 in 5 chance it was actually you that spent the output. That's until someone else uses the output you were given as a decoy in their own transaction. Then the chances it was you is 1 in (total number of outputs that exist in ring signatures that include your output as a possibility).

Of course, due to stealth addressing, the person that gave you the output in the first place gains nothing from knowing there is a possibility you spent it, because they can't tell whom you spent it with.

So increasing the ring size beyond the default only really matters if someone knows which outputs you were given, and the vendor you spend your outputs with is hacked or otherwise leaks information about what outputs they've received.

If someone that gave you an output can see that you could have spent that output with a compromised vendor because the vendor has been hacked, then they know that the probability that it really was you that transacted with that vendor is 1 / 5, or more generally, 1 / ring size.

Bottom line: I don't see any reason to not use the default ring size.

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