Using a ledger in this way, as a closed system with accounts extending credit to each other, is sometimes called mutual credit.
This term focuses not so much on the clearing aspect, but on the fact that credit can be made available to anyone at any time, and the risk entailed by that credit is spread out across the whole system.
In the event of an account being abandoned rather than being closed at zero, the whole system deviates from the perfect zero, and all members are affected equally when the total supply and total demand leave equilibrium.
This notion of economic equilibrium is a guiding principle of a mutual credit economy, and not of the global economy which is a competition to accumulate the most.
Another word for economic equilibrium, is exchange, because parties give and receive in equal measure. When giving exactly equals receiving, the account balance is zero and only then may the account be closed.
Since all accounts have agreed to close on zero, after Alice has paid Bob ten units, Alice is looking to earn 10 units and Bob is looking to spend ten units; thus supply equals demand. In a fiat or commodity money system, the governors, if they care, must use voodoo to calculate how much money to put into circulation for optimal trading without inflation, without bubbles, and without unemployment.
In a mutual credit system this is a non-question. The political question then becomes, how much can people be trusted to deviate from zero and still return?
The further away a balance is from zero, the greater the risk that that account will fail to reciprocate. If no deviation were allowed there would be no liquidity and no trade. If infinite deviation was allowed, some players would only ever give and others only take. We observed earlier that supply always equals demand. Every force has an equal and opposite force. When accounts are hovering around their limits, struggling to reciprocate, that means there is equal and opposite pressure elsewhere in the system.
A well-managed system will be able to mitigate these pressures by paying attention to those accounts and making it easier for them to trade back in the right direction.
A poorly managed system may be lucky if negative failures to return to zero cancel out positive failures - defaults can be in either direction.
Once the design problem of how credit should be allocated is decided, perhaps by the people whose credit it is, which is everybody, then as much credit can be created as needed.
Any system can of course have tweaks and redistributive mechanisms, but the fundamental properties are still important. Commodity money must be earned (or borrowed at interest) before it can be spent; the more of it you have, the better it is for you, though that might mean others are deprived. Those who have a scarce commodity (money), get more from renting it out. The day to day governance of such instruments is done through interest rate manipulation and taxing/spending, but the flagrant injustices of this paradigm are never fully mitigated by social security and other forms of redistribution.
Usually some accounts have difficulty earning as much as they would like to spend and vice versa. Because these problems can affect the whole system, the whole system has an incentive to support those accounts, either by trading with them preferentially, redistributing credit or coming to some other arrangement.
This mutual support is visible for what it is, not welfare bleeding out of the pay-packets of the people who actually work, but enabling everyone to both give and receive, which is essential for the health of the whole system.
It is well understood how spending locally can create a multiplier effect, and all local currencies seek to strengthen and make visible that virtuous circle. In that sense, a local currency can build solidarity within the local economy insofar as it actually diverts spending towards the local economy, which is a very difficult thing to measure.
But there is a deeper solidarity within a mutual credit system than within the multitude of Euro proxies which have sprung up in recent years. The value of the system depends on the engagement of the members and the quality of their experiences, which is the subject of the third paper in this series.
The wealth gains that come from good governance, a glut of production and the wellbeing of the precarious members are spread around much more in a mutual credit system than in a commodity money system, where all the wealth gains are sent to the top of the pyramid as rents are adjusted.
All of which is why mutual credit is the money of the solidarity economy.