This video shows a number of examples of stocks (apparently few foils survive) and how they recorded debts. https://www.youtube.com/watch?v=0rxAYSXJ41Y .
It explains that they were used to record money that was deposited, essentially a receipt, by removing wood from the then original stick before it was split into the stock/foil. My guess (again not my area) is that it primarily functioned this way:
1. The removed wood representing the debt. I have no confirmation, but I would expect the stock/foil was created in view of the depositor who understood its markings.
2. The entity seeking repayment would not be able to fake their receipt, presumably to indicate they had deposited more money than they had (i.e., by removing wood from their foil). If they tried, the stock would still have that wood present, but the other grooves and grain of the stock/foil would align. The state would easily be able to tell that someone had subtracted wood from their foil.
3. The state could, of course, destroy the stock and claim its nonexistence, but information of that would, presumably, escape and others would be less likely to lend to the state. It appears there is writing on the stock/foil, so perhaps that served a secondary verification function (e.g., handwriting comparison or reference to a paper ledger)?
[EDIT: The process of making English tallies was laid out in the "The Dialogue Concerning the Exchequer. circa 1180" (https://avalon.law.yale.edu/medieval/excheq.asp. It describes making these tally sticks in the section "As to the Maker of Tallies." Unfortunately, I do not see the details of dispute resolution in that document. But, I only skimmed it.]
Having three people present is a way to protect against he said/she said.
This principle is used all over robust engineering, from Raft to best-of-three sensors.
3 is an enhancement for redundancy. Habit an odd number is a false confidence. Think about it: what happens if you have 4 witnesses? They could tie? How is that worse, as it adds more information that maybe 2 of the first 3 are lying or wrong?
So if they do not match the government simply does not give you your money.
If the government decided to say tomorrow that $100 bills with serial numbers AB1234567000-AB12334567999 were counterfeit and should not be accepted, what do you think would stop them?
If we use a split stick to record how much money you owe me, and I simply add more marks to mine, to pretend you owe me more, it's obvious that I'm cheating. But if I simply split a brand-new stick and add marks on it, then our sticks won't match up at all. How will a court know which is the original?
Presumably they had some way to sign them? After all, that's why both parties sign both contracts today. If you go change yours, I still have your signature on mine.
But if I simply throw away my half and make a new half, a court will have no way of knowing which was the original. (Unless each half was signed by both parties.)
Your new half would not match together in the "split" part of the stick, so one could tell that /someone/ made a new half, but not necessarily which party was the forger.
Signing makes sense.
Both parties in a contract can have an incentive to lie.
I don’t think all contracts have an obvious both losing state though.
Think about two situations:
Firstly, if I lend you money, we split sticks, then I throw away my stick and get a new stick that says I lent you more money.
Secondly, if you lend me money, we split sticks, then I throw away my stick and get a new stick that says you lent me less money.
In both cases you're claiming my stick is clearly counterfeit because it doesn't match yours and I'm (falsely, but nobody knows that except the other party) claiming your stick is clearly counterfeit because it doesn't match mine.
What happens next? We're no better off than if we only had a verbal record and were disagreeing. So what is the point in the sticks?
Understand?
Presumably they would say that your stick is the one that is clearly counterfeit.
So how do you resolve that?