Good morning Adam,

> And I'm reminded that a related point is made by belcher in the gist
> comment thread iirc (after we discussed it on IRC): over time a
> "PayJoin-only" merchant doing the simplest thing - using a single utxo
> over and over again, will concentrate more and more funds into it, and
> inevitably violating UIH2 in an increasingly dramatic fashion
> (contributing a 100BTC utxo to a 0.1BTC payment etc.). Suggesting it's
> better if there's a mix of payjoin/non-payjoin.

To be pedantic: as I understand bustapay, it would still not violate UIH2 
(unless I misunderstand UIH2).

Suppose the original transaction is: (0.05 payer, 0.07 payer) -> (0.1 payee, 
0.02 payer)

Then bustapay with such a PayJoin-only merchant with 100BTC UTXO would give: 
(100 payee, 0.05 payer, 0.07 payer) -> (100.1 payee, 0.02 payer).
As I understand it, this technically does not violate UIH2.

It would still conceivably be interpreted as a payment of 100.1 BTC, from a 
payer who happens to have massively lopsided UTXOs being owned, but still does 
not violate UIH2.

However, if that 100.1 UTXO is subsequently used to pay a 100.3 payment, then 
that is used to pay a 100.7 payment, that strongly suggests such a naive 
PayJoin-only merchant.

Perhaps a simple heuristic against this would be:

1.  For every UTXO you own, flip a coin.
    If all of them come up heads, do not payjoin; just broadcast the original 
2.  Else, randomly select a UTXO (value not care?) and payjoin with that UTXO.

However, I have no proper analysis of the blockchain, so --

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