Abstract cost function

[yuval-block]

This document describes the overall approach to the cost function without going into specific/concrete terms

[bc1cindy]

it was a great to read this

some typos:

• l.3 - "describes how score the outcomes" → "how to score"
• l.21 - "one might considering all actions" → "one might consider"
• l.23 - "not account for everything, that may eventually happen," → "everything that may eventually happen"
• l.27 - "the input that will eventually spend it already known" → "is already known"
• l.37 - "at a higher feerate than of the unconfirmed" → "than the unconfirmed"
• l.47 - "the goal of create some output" → "of creating"
• l.49 - "resulting a transaction" → "resulting from a transaction"
• l.57 - "diminishes from the importance" → "diminishes the importance"
• l.59 - "a transaction which underpay fees" → "underpays"
• l.67 - "the total amount involve" → "involved"
• l.85 - "a cost function for a privacy has" → "for privacy"
• l.89 - "Metrics makes it possible" → "Metrics make"
• l.91 - "Although are other aspects" → "Although there are"
• l.95 - "the coins that an honest does not control" → "an honest user"
• l.97 - "If all actions than those of the victim" → "all actions other than"
• l.97 - "then adversary is able" → "then the adversary"
• l.103 - "targetted" → "targeted"
• l.125 - "incurs a cost can be shared" → "incurs a cost that can be shared"
• l.129 - "should at the very least indifferent" → "should at the very least be indifferent"
• l.129 - "the the actions" → "the actions"
• l.131 - "Alice… they need to add" → "she needs"
• l.133 - "we required that" → "we require that"
• l.135 - "to define honest parties' as being" → "honest parties as"
• l.135 - "the cost function … are indeed monotonically decreasing" → "is indeed"

[bc1cindy]

whose subjective value is at least $x - b_1$ and at most $x - y$

shouldn't this be $x - b_0$? (= nominal minus remaining budget, $(x - y) - b_1$)

as written, $x - b_1$ can exceed the upper bound $x - y$ whenever $y > b_0/2$

e.g. receive 100 sats with a 1 sat budget, coinjoin costs 0.6, so the bounds give [99.6, 99.4], while $x - b_0$ gives [99, 99.4]

[bc1cindy]

The change in the balance of a wallet resulting a transaction is its objective cost.

should this be the decrease in the balance? receiving a payment increases the balance, so under "cost = change" it would come out positive

This can be negative, for example for the case of receiving a payment.

this sentence correctly treats it as negative (a benefit)