Thanks. Much appreciated.
Overnight, my mind drifted to a popular UK government scheme called National Savings & Investments
http://www.nsandi.com/.
Millions of people buy government bonds through small purchases. In return each bond serial number is entered into a random draw and a prize fund is distributed ranging from £10 - £1m to individual winners.
The more bonds you have the more chances you have of winning the jackpot.
The underlying economics of this model are:
* You don't lose your initial stake, you lend the money to the UK government.
* The UK government doesn't give you a guarantee you will get anything in return for your loan.
* The UK government enters your bonds serial numbers into a weekly draw (not sure of period) and most people get some form of payout over a 12 month period.
* The target winnings are, on average, at equivalent and competitive lending rates for the government - it pays out to winning bond holds a few percentage points per person on average over a year.
A variant of this and a lottery might have a slim chance of working for Bitcoin node holders. Their BTC address could be associated to their serial bond which is picked out at random on a weekly basis. Their bond number could be linked to their Bitnodes address / IP address, but held elsewhere to remove the link between the users IP and their Bitcoin address.
The extra effort to make this step would be desirable to make it easier for novices to host full nodes without having to change BTC addresses if they didn't know why they needed to do that when they first get started.
With an element of chance added, a full node might win the equivalent of a Block reward, or possibly smaller denominations which could be enough for people to consider their costs to own a full node as worth the bet. Some weeks they might get enough to cover costs, some weeks they might make a small profit, some weeks they might hit the jackpot, but some weeks they might not get anything.
The problem is funding the incentives.
* You could tell people to loan money as a bond which will be sent off as loans to traders via exchanges, generating 0.45% interest charges per day (apparently this goes on at these high borrowing levels), and that could generate the rewards for the network.
* You could ask vendors to add a 0.001% full nodes tax to their sales to fund the incentives.
It's messy, but I might ponder on it a little more.