From aj at erisian.com.au  Wed Oct 28 00:15:29 2015
From: aj at erisian.com.au (Anthony Towns)
Date: Wed, 28 Oct 2015 10:15:29 +1000
Subject: [Lightning-dev] Lightning fees vs miner fees
In-Reply-To: <87mvv4w1h6.fsf@rustcorp.com.au>
References: <20151027054029.GA6185@navy>
 <87mvv4w1h6.fsf@rustcorp.com.au>
Message-ID: <20151028001529.GB2409@navy>

On Wed, Oct 28, 2015 at 06:03:25AM +1030, Rusty Russell wrote:
> Anthony Towns <aj at erisian.com.au> writes:
> >  C. Without lightning, as bitcoin adoption increases, either fees rise,
> >     or number of transactions per block increases proportionally. If
> >     1% of people know about bitcoin, and use it whenever it's cheap;
> >     then 2% of people knowing about bitcoin gives twice as many
> >     transactions at any given price level.
> Metcalf's law?  Both sides need to "know about bitcoin".

I think Metcalf's law would be a lower bound -- you're more likely to
adopt bitcoin if the people you transact with use bitcoin, so they're
not independent. ie,

  P(tx via bitcoin | bitcoin is cheaper than alternatives)
    = P(consumer can use bitcoin) *
        P(merchant can use bitcoin | consumer can use bitcoin)

If those are independent and P(consumer)=P(merchant), you get Metcalf's
law. If P(merchant|consumer)=1 you get my assumption above.

I assume reality would be somewhere in between; because I think once
a merchant had a few customers asking for bitcoin they're more likely
(though not certain) to offer it as a payment method. Getting an actual
model would probably depend on what marketing strategy was undertaken
for lightning.

> Say: 1 billion people, each initiating 100 txs per year.  But only 1%
> know about bitcoin, so those 10M can only use it for 1 of their annual
> transactions.  At 2%, 20M can use it for 2 of their annual transactions...

Yeah, so if Metcalf's law applied directly, you'd just have:

 p_tx = p_u^2

or p_u = sqrt(p_tx), where p_u is the proportion of users with access
to bitcoin, and p_tx is the proportion of transactions that could be
done on bitcoin (what I called "adoption").

> Not sure how this alters the rest of your calculations.

I don't think I actually used the proportion of users in any calculations
in the original mail.

It would matter for adoption rates, and I think it matters for comparing
how many bytes are needed for lightning anchor txs on the blockchain
(as per my previous mail) though.

Cheers,
aj