[Breakthrough] Occasional Anonymity Loss about walletwasabi HOT 5 OPEN

You rediscovered #10096 and #8938; this is exactly the issue explained and tried to be mitigated by implementing these points: (1) getting whales to select less inputs or (2) select inputs smarter, incorporating the insight here.. You can also see that my comment on #10096 explains that another mitigation is to reduce non standard change at all costs, which is kinda similar to the last thing you mentionned: also we can probably improve amount decomposition by getting whales to create more outputs

And by the way, your example would be much worse the other way around:

Like this, the user is losing much more global % AnonScore, and this has an impact both:

• Direct: Global AnonScore will exceptionally decrease directly
• Long lasting: In the following round, this input will tremendously affect the WeightedAverage, hence the AnonScore gains of the other outputs.

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That's a good catch, sounds about right.

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@turbolay it seems you're conflating what our anonymity calculation says about privacy loss and the actual privacy loss is and thus you're bringing in many issues needlessly like #10096 or your example:

And by the way, your example would be much worse the other way around

It's not actually bad for privacy, only for our anonymity calculation thinks so, and by the way it is the fix: #10699

However what's going on in this very issue is bad for privacy, not only our anonymity calculations say so.

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@turbolay Could you elaborate/copy paste the relevant text on this one here?

You can also see that my comment on #10096 explains that another mitigation is to reduce non standard change at all costs, which is kinda similar to the last thing you mentionned: also we can probably improve amount decomposition by getting whales to create more outputs

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@turbolay Could you elaborate/copy paste the relevant text on this one here?

Sure!
This Anonymity Loss is affecting exclusively (or almost exclusively) the big non standard output. If we reduce it, we will lose anonymity on a smaller amount. Hence, the user will be able to spend privately a bigger percentage of its wallet faster, but also the subsequent AnonymityScore will go up faster during remixes because the WeightedAverage will be less affected.

Creating more outputs for whales as you suggested is a good and effective way to reduce this change
One other approach (not mutually exclusive) is that instead of choosing the denomination that has the less cost (this line), we should prefer denominations with less change, especially if this change is suspected to be one of biggest output in the round. Obviously cost should still be acceptable (maybe proportionate to the amount).

Let me also drop here an observation that I made on Slack and that I think relevant here: https://tumblebit.slack.com/archives/CFBJX6MN0/p1682306405947139

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