Note in my proposal unwinding only affects double-spent coins, so if you never send a double-spend then your transaction will never be unwound. Note a double-spend is not the same as resending the same transaction.
As mentioned in my prior response— if you did this then your proposal is completely ineffective. First you double spend, and then you spend your double-spent coins to yourself. If you do not also unwind the child transaction then the doublespender walks free for nothing but the cost of an extra transaction. If you do unwind the children then everyone is at constant risk.
I couldn't grok what you wrote before so I ignored it. Now I understand your point.
Definitely derivative transactions will be unwound too (thus my quoted statement is incorrect if you haven't waited the say 100 or so confirmations mentioned below), and this does not violate my assertion that insurance increases as n confirmations does.
As you admitted (in the part I didn't grok before), the risk you speak of applies whether my proposal is implemented or not. For example, in the current implementation of longest chain rule, if you got paid in the public orphaned chain and these are double-spent into the secret chain which becomes the longer chain when publicized (thus orphaning the other chain), then your payments are effectively unwound.
My proposal is that you don't trust the longest chain until considerable n confirmations have transpired, because the majority will be trying to unwind those bogus double-spends. So in my proposal, not only do you not deliver goods until a payment has n (usually 1 - 6) confirmations, but also you don't accept payment from a transaction (history) unless the prior transaction has much more than n (say 100 or so) confirmations. Abstractly the smoothing filter applies from both directions.
Note that CryptoNote ring signatures (and probably Zerocash and Zerocoin also) breaks the type of unwinding in my proposal because derivative transactions are unlinkable.
Edit: similar functionality can be obtained in the current implementation of the longest chain rule, by waiting for 100 or so confirmations before accepting a payment as final (to extend out the duration cost for the extended time attacker has to keep his chain secret so your payment isn't orphaned by the attacker's chain). Thus unlinkable coins could still defeat ephemeral 50+% double-spending attacks, but with very slow payments.
Not to mention the obvious: Double spent coins are the only ones we care about here.
The whole meaning of n confirmations is measuring security against double spends.
Otherwise, 1-2 confirmation would be enough to know the tx was formatted correctly
and was included in the blockchain.
So if you are talking about the possibility of winding them back, then
confirmations lose their meaning, and your "solution" does more harm
than good.
You are confused by aliasing error, which can be ephemeral in my proposal.
The confirmations that matter are those in the chain that has the sustainable majority of the hashrate. The only way to differentiate aliasing error from signal, is for the width of the smoothing filter (i.e. the number of confirmations) to be greater than the period of the aliasing error (another way of stating the Nyquist-Shannon sampling theorem). That period is how long the attacker can sustain the hashrate to maintain the longest chain.