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One morning, everyone wakes up and finds that the balance in their bank account has changed. In some cases, it's gone down. In others, it's gone up, a lot. A few people even find that they don't appear to have been affected by this. However, most company accounts have also been affected.

After some effort, someone figures out that all the bank balances have been randomised - it's like someone just pulled balances and accounts out of a hat and stuck them together. There isn't any pattern to this, so it doesn't seem to be targeted - it's entirely luck as to whether you (or your company) end up richer, poorer, or about the same as before.

However, other than your memories and environment (e.g. you're in a mansion, so probably were doing ok...), there is no way to prove which balance was previously yours. Backup data has also been altered to be consistent. Every detail apart from the associated names is accurate. If account 123 sent money to account 456, that's still recorded, but account 123 probably belongs to someone other than expected.

What would the overall change in wealth distribution?

I suspect there will be a bias towards getting poorer, with a few stand out cases of someone getting immensely rich. A lot of people wouldn't be affected - anyone without a bank account- but these will probably be disproportionately poorer, since it's harder to be rich without one.

Note: the technical ability to do this is out of scope (short answer: in our world, you probably can't!)

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    $\begingroup$ I would check the dystopic worldbuiling in Mr Robot tv series where the worlds biggest conglomerate(this includes the finance sector) gets totally blacked out(encrypted entirely with back up data centers sabotaged) and no records of ownership before the hack remain. $\endgroup$ – Leon Aug 8 '17 at 9:56
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    $\begingroup$ Does this affect only bank balances, or property and investments more generally? Very wealthy people are likely to have most of their money in shares, bonds, real estate, etc. rather than as cash in a bank account. In the case of Average Jane Citizen, does she still own her house? Her car? Her pension fund? $\endgroup$ – Royal Canadian Bandit Aug 8 '17 at 10:05
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    $\begingroup$ @RoyalCanadianBandit Just bank (building society/credit union/etc) accounts. If you have shares and so on, they're still yours $\endgroup$ – Matthew Aug 8 '17 at 10:52
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    $\begingroup$ If it is a shuffle 1/2 will be less and 1/2 will be more. $\endgroup$ – paparazzo Aug 9 '17 at 0:37
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    $\begingroup$ Note that if this includes business bank accounts, then quite a lot of businesses will have instant cashflow problems and be driven out of business. Everyone ends up worse off. $\endgroup$ – pjc50 Aug 9 '17 at 11:08

11 Answers 11

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If the change affects bank accounts only, the results might be surprisingly modest. Putting cash in a bank account is a very poor investment, especially with interest rates as low as they currently are. Most wealthy people will have most of their money in stocks, bonds, real estate and the like, perhaps with "only" \$100,000 or so in cash at any given time. While for most of us a sudden windfall of $100,000 would be very welcome, it doesn't make you filthy rich.

Most of the wealth redistribution would take place at the middle and bottom end of the scale. The wealthy are relatively few in number, but there are many people with \$10,000 or so in cash savings, and a great many others with little or none. A lot of the former would suddenly have no savings, and many of the latter would receive a windfall. There would be more losers than winners: In the USA, 69% of the population have less than \$1000 in savings.

A few things worth noting:

  • Savings do not correlate exactly with income; many well-paid middle-class people have large credit card debts and minimal savings.

  • Many bank accounts are held by businesses, charities, government departments, and other organisations. If they were affected, a lot of businesses might find themselves with severe cash flow problems.

  • A very roughly analagous situation occurred with privatisation in Russia in the 1990s, in which shares in state-owned industries were distributed among the population. A few individuals became very wealthy by buying up shares at a fraction of their real value.

This would probably become a serious political issue for the government. Would it:

  • Order banks to honour the account records, even though they conflict with people's memories?

  • Somehow attempt to reinstate the distribution of wealth people remember?

  • Take drastic action like resetting the entire banking system from zero, perhaps giving everyone exactly the same amount of cash as a starting point?

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    $\begingroup$ Keep in mind, this is not just personal banks accounts, corporations are messed up too. The banks are corporations themselves, so their mutual correspondent accounts and accounts with central banks are also affected. Somebody would end up with 100,000,000 in a bank account, but the bank itself may have just 10,000 in liquid, non-cash assets. $\endgroup$ – Alexander Aug 8 '17 at 16:38
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    $\begingroup$ @SteveJessop The distribution of balances is exactly the same before and after, only the names have changed. Surely there are exactly as many winners as losers? $\endgroup$ – JollyJoker Aug 9 '17 at 7:57
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    $\begingroup$ "There would be more losers than winners" Not true. On average, there will be the same number of winners as losers. A permutation is a set of instructions of the form "Give A's account to B." given any permutation of the people, you can make the "opposite" permutation by changing each instruction to "Give B's account to A." If a permutation had X winners and Y losers, the opposite permutation (which is equally likely to be generated) has Y winners and X losers so the average number of winners is equal to the average number of losers. (cc @JollyJoker) $\endgroup$ – David Richerby Aug 9 '17 at 12:11
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    $\begingroup$ Note, though, that it's possible to have nearly everybody win: line up the people in order of bank balance and give each person the account of the person ahead of them in the line, except that the richest person becomes the poorest. Everybody but them wins. $\endgroup$ – David Richerby Aug 9 '17 at 12:15
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    $\begingroup$ @DavidRicherby One potential issue to create more winners than losers is if the rich minority has more bank accounts per person than the poor majority. $\endgroup$ – JollyJoker Aug 9 '17 at 13:48
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If you read Clancy, you know Ryan's Law: If it wasn't written down, it didn't happen. So if all written records say a thing, then it doesn't matter what everyone thinks.

However if the magic does not go so far as to altering paper records and PDFs sitting on hard drives and the like, then it becomes a matter for whatever deposit insurance your nation/world provides. Once it's accepted that this glitch did an unintended redistribution of wealth: a saver who can document that their bank account had between 61,000 and 66,000 quid for the last several years, can expect a £61,000 payout from deposit insurance. This would not help the rich so much; most deposit insurance is capped, e.g. US FDIC at $250,000. Non-savers who had nothing on average for years and suddenly have a million bucks - it will be difficult to pursue them if they alone possess the only records of their history and they want to hide unearned gains (not leasst from the tax man).

But non-savers will tend to lose it. Savings is not innate; it requires a friendly environment (which we presume if in a ”world" where most citizens have bank accounts), luck, and education to avoid the pitfalls of having money. The effects of this lack are seen by the fate of lottery winners. Left to themselves, they are predated upon aggressively and tend to lose it. Good counseling by government or NGOs can significantly improve things. The question is how this counseling will reach savings-scramble winners if they are hiding.

(and of course a person with good circumstance and skills already does well with windfalls).

The same applies to now-broke savers: Their circumstances will allow, and their habits will motivate, them to resume saving. Their accounts will build back up over time.

So there are your four likelihoods:

  • started non-saver, account empty - no change
  • started saver, account has money - no change
  • started non-saver, now full account - tend to lose it.
  • started saver, now empty account - tend to continue saving.
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    $\begingroup$ Your link says almost the exact opposite of your claim about lottery winners: "American lottery winners did not typically quit their jobs and spend lavishly." It is not the case that all or even most poor people are irresponsible with money. $\endgroup$ – Royal Canadian Bandit Aug 8 '17 at 9:57
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    $\begingroup$ @Wildcard: You seem to be saying modern society is a pure meritocracy, operating by Social Darwinism. This is simply not true. As a counterpoint, I recommend this post by the SF author John Scalzi. $\endgroup$ – Royal Canadian Bandit Aug 8 '17 at 11:25
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    $\begingroup$ @Matthew You may want to read the book The Millionaire Next Door. To summarize for the purposes of this discussion, the person who lives in a modest home, has a worn but still reliable vehicle, etc., is far more likely to have a high net worth than the person who lives in a mansion and trades vehicles for new from the factory every 2-3 years, simply because the expenses of the former person are lower. Unless you need the facade in order to maintain your income (which you practically never do, beyond the utter basics), lower expenses typically means higher net worth. $\endgroup$ – a CVn Aug 8 '17 at 12:25
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    $\begingroup$ @RoyalCanadianBandit Being poor is trusting the DM when he says you rolled a 1 again. I don't think either wildcard or myself is trying to turn it into an ideological discussion nor endorse one system over another. I am sticking to the practical/real world, where idealized systems don't work and effective systems are a well-engineered blend. Rich people often go bust - and are momentarily as broke as poor people. What happens next defines the difference, and that is largely a function of habit and training. $\endgroup$ – Harper - Reinstate Monica Aug 8 '17 at 15:38
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    $\begingroup$ Habit. Training. Thinking. As far as I can tell, the argument boils down to "rich people are smart, poor people are stupid, wider socioeconomic factors are irrelevant." If you really believe that, there's no point in continuing this discussion. $\endgroup$ – Royal Canadian Bandit Aug 8 '17 at 19:17
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In 2013, the average checking account balance was US \$9,132. That's personal accounts, not business or government accounts. But for people with an income above US \$160,000 / year, the average balance was over US \$700,000. Again, personal, not business. For those with incomes below US \$45,000, the bank balance was below \$3,600.

Given that many large business accounts will have significantly higher balances than the average citizen, and that the wealth distribution is heavily weighted, I suspect the lowest income people will see a rise in bank balance, while those at the highest income levels will see a drop. Those in the middle of that bell curve will have the most randomness to their balances.

But really, the new balances don't matter, as we'll explore below. What matters is the introduction of chaos...

Immediate term

You are going to have serious problems. Day 1, CNN, Fox News, BBC, and all other news outlets flood the airwaves and papers with news that all the bank accounts got mixed around in a big melting pot.

So everyone lines up at the bank. Or logs into the bank. The bank's websites crash, as they're now effectively suffering a DDoS attack as users flood their sites. The lines will be long. The bank support phone numbers will be jammed. Panic.

This will continue for a time. In the USA, the federal government will probably institute an emergency bank holiday. Not sure how long that would last, but during this holiday, the banks would be doing their best to restore from backups, find audit traces, etc. The bank computer systems have pretty thorough audit logs. Banks would spend days, possibly weeks, trying to reconstruct accounts. The OP says these measures will fail, but they would try. Other nations' banks would go through similar steps.

The FBI, NSA, CIA, and similar groups in other countries would go on extremely high alert. I suspect the military would go on high alert as well, at least until it could be proven that this wasn't an act of cyberwar.

Hopefully, governments and businesses would find some sort of interim solution for commerce, because otherwise, people will die. Pharmaceutical companies, food and agriculture, these are critical international markets that if they stop, people don't survive. Remember, most industrialized nations cannot grow enough food to feed their people reliably, year round. So many import food from around the world. Especially produce. That's how we get out-of-season crops.

Then there are cities. It took 200,000 flights to provide Berlin with food and supplies for a year during the Berlin Blockade. Now imagine every city in the world facing the need to feed and supply their citizens when no one can pay for the shipment of any goods. No one can pay for trucking or trains. No cargo ships full of Argentina apples. No meat from out west delivered to your local butcher. Everyone goes hungry. No insulin for your diabetics; who's paying for that? Everyone gets sick or sicker.

If food and medicine deliveries aren't secured, then the riots tear apart every city in the world. And if that happens, no nation will survive. So that's a crisis that governments and industry must solve immediately or die. The rest of this post assumes they hobble together something. Anything else results in anarchy.

Short term

After the banks close, people will panic. News cycles would probably be fueling the panic. Comparisons to the bank collapses around the Great Depression would be constant.

No one can issue paychecks. No one can pay their bills. No one can do anything if they don't have cash on hand. By day 2 or 3 at the latest, the stock markets would be shut down, since businesses no longer have reliable checking accounts either. The markets would have to be shut down to prevent a complete collapse as everyone tries to sell and cash out.

Without paychecks and other cash transactions, trade halts. Government would need to do something to maintain food availability, since most people don't keep enough cash to buy groceries and few people maintain sufficient food supplies to go more than a week or two.

Emergency measures would be taken to prevent riots. There would be riot-gear equipped police in all major cities and many smaller cities/towns.

Everyone would be asking questions. Who, why, how. Within a week, it would be clear that banks cannot fix this. It is a complete, hard, reset on the entire economy.

Medium term

By this time, it would be clear that while some accounts in some cases could be rebuilt from paper records, the system as a whole couldn't be rebuilt. And once people said, "Well, I've got my bank statements going back 10 years, give me my money!" everyone else would demand their money, too. And at least some percentage of people would think they were clever enough to game the system. "I've got a good printer and enough computer savvy to fake my bank statements..." so now the banks can't really trust the statements to be accurate either. That lack of reliable paper combined with the significant percentage of people without paper records, means banks as a whole cannot trust any of the papers anywhere.

Remember, this isn't just your grandmother's savings account or your checking account. This is also the account your employer writes paychecks from. This is where your rent checks deposit to. This is where your grocery store pays it's bills from.

By now, all of the initial panics are done. Banks will still be closed, at least until government figures out what to do. Barter is more popular than ever in living memory. The riots will have been quashed, one way or another. More cities across the world look like the burned out parts of post-riots Detroit than ever since the end of WW2.

The entire world economy has ground to a halt at this stage. No one has the means to pay for anything. Suddenly the Amish, with cash in hand and plenty of garden space, look far wiser than they have in the last 200 years. Doomsday preppers have been laughing this whole time, while they choke down freeze-dried food that's edible but tastes bad.

Congress will be under extreme pressure to "do something". And maybe they will. They must. Though at least in the USA, partisanship politics will make this a difficult time for them as well. At a global level, the UN will be frantically trying to prevent war and economic collapse, too.

If the UN cannot maintain peace between panicked member states, or if any one (or more) nation decides that the other nations somehow are responsible for this mess, then war will break out. Hopefully, these will be relatively small-scale actions in smaller nations. Hopefully, the warfare won't spread up to the 2nd and 1st world nations. But that's not guaranteed. Wars generally occur for three reasons: "the gods demand it", "we need money/resources/things", and "if THEY are the enemy then you won't get mad at how horrible a leader I am". This event triggers the second quite easily and quite suddenly.

Government would have to write laws, too, that prevented civil lawsuits. Otherwise, the courts would be overrun with lawsuits and class-action lawsuits. If those cases were permitted, lawyers would be lining up. Any bank that wasn't already ruined beyond repair would be destroyed.

Long term

Long term, the major goal is to reduce this great depression and prevent global war. A broken nation with no economy and no hopes will often fall into warfare. It's happened before (see also Nazi Germany, which "solved" their unemployment crisis through military spending). Given the scope of this disaster, it would likely happen here. WW3 isn't impossible. It's likely.

Some governments will have nationalized their banks to take control and restore order. Perhaps they socialize the wealth and redistribute it. Perhaps they start over with some other measure. There's no way to predict how each nation will solve this crisis.

But once they do solve it, we will see some kind of major sea-change to how accounting is done. No one will ever trust banks to maintain account histories and balances ever again. This new system will be the most radical rewrite to bookkeeping / accounting since the invention of double-entry bookkeeping.

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    $\begingroup$ "Well, I've got my bank statements going back 10 years, give me my money!" I'm not sure that it necessarily follows that this would be impossible. Remember, the OP's premise is that the accounts are all there; only the mapping from account to account holder is scrambled. Presumably then, transaction histories are intact. If you have papers going back ten years, and those match the bank's records, why would those not be usable as proof that you at least have some rights to the account? Especially if you've got (possibly multiple) photo IDs matching the names involved. Ingenuity shall prevail? $\endgroup$ – a CVn Aug 8 '17 at 13:46
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    $\begingroup$ @CM_Dayton Sure, but will it match the bank's records for the specified account? $\endgroup$ – a CVn Aug 8 '17 at 13:57
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    $\begingroup$ @PatrickTrentin I've tightened up that beginning. Should be clearer what I was trying to say. $\endgroup$ – CaM Aug 8 '17 at 14:01
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    $\begingroup$ @CM_Dayton that's a looooot harder than it sounds. Also the government may just say "Hup, every citizen who can prove he has an account gets \$5000 and every corporation gets \$FORMULA_HERE based on surviving tax data, that's a loan, and we'll square it when able." It would be better for the economy to lump the additional national debt than the economic catastrophe discussed in this answer. $\endgroup$ – Harper - Reinstate Monica Aug 8 '17 at 16:19
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    $\begingroup$ Wars generally occur for three reasons: "the gods demand it", "we need money/resources/things", and "if THEY are the enemy then you won't get mad at how horrible a leader I am". This event triggers the second quite easily and quite suddenly. $\endgroup$ – CaM Aug 8 '17 at 16:28
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What follows is complete social collapse. If it can happen once, it will quite likely happen again, so there is no longer any point in saving or investing. So no companies can be funded, no one has money for their retirement, and so on and so forth.

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    $\begingroup$ You may want to review this answer in light of the OP's recent edit. $\endgroup$ – a CVn Aug 8 '17 at 8:28
  • $\begingroup$ @PatrickTrentin I don't agree. Poor people often don't have much in the way of savings in a bank account at any one time, so they can only benefit from the change. The people with significant, valuable assets (property) are also those with larger bank accounts. On average, someone poorer will end up with the richer account, but someone rich may still have assets to keep going. $\endgroup$ – Samthere Aug 8 '17 at 13:08
  • $\begingroup$ no longer any point in saving You could still physically store your money or buy things with inherent value (e.g., gold) and hold onto that. or investing I do agree with that though. $\endgroup$ – Captain Man Aug 8 '17 at 13:27
  • $\begingroup$ @PatrickTrentin I see your point, although the money being unavailable is a scenario which isn't established in the question or this answer. It's a reasonable point of discussion for its own answer. $\endgroup$ – Samthere Aug 8 '17 at 14:36
  • $\begingroup$ @PatrickTrentin seriously? They limited bank withdrawals in Greece? That defeats the entire concept of "your money" and basically removes all incentive for people to create and innovate. Can someone send them copies of Atlas Shrugged? All they really do is murder domestic banking and your fiat currency - everyone goes BitCoin or USD. That would never be tolerated in the US, and the last time it was, Great Depression. Going into natonal debt so FDIC could cover provable losses ( up to their standard $250k) is the way to go. $\endgroup$ – Harper - Reinstate Monica Aug 8 '17 at 16:09
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CM_Dayton's amazingly detailed answer is spot-on, IMHO, and covers a lot of the societal aspects. As someone who reads a lot of rationalist sci-fi, though, I have to point out one inevitable subplot:

However, other than your memories and environment (e.g. you're in a mansion, so probably were doing ok...), there is no way to prove which balance was previously yours. Backup data has also been altered to be consistent. Every detail apart from the associated names is accurate. If account 123 sent money to account 456, that's still recorded, but account 123 probably belongs to someone other than expected.

This sounds like a perfect use-case for traffic analysis. All we need is a complete set of banking records and a few smart programmers, and we can start crunching the numbers and restoring the state of the world by building outward from a trusted root. Thus:

Bob is the security engineering lead for Chase Manhattan. On Tuesday morning, he wakes up to the ringtone that means a critical production issue. (This is unusual, because Bob is like the third person in the PagerDuty escalation. Things never escalate to him unless the site is actually down or something.)

Well, crap. Nonsense in the banking records. The automatic disaster-recovery plan was already tried, and somehow the backups are wrong too. (Everyone on the engineering team is confirming: their own balance is definitely incorrect.) Okay, check the tape archives. Somehow they're also bad. Now it's getting surreal.

90 minutes later. The site is "down for maintenance" to prevent further chaos. Jan and Dan (and about three junior engineers that nobody cared to forbid) are in a breakout room whiteboarding new ideas. Bob is finally en route to the office, on a call with about three VPs. Nobody knows where Legal is. Someone go pull a junior engineer out of the brainstorming session and get them to make sure Legal is in PagerDuty by EOD, okay?

120 minutes. Dave (who's always been a bit rogue — regulations shmegulations) has written a script to scan all the accounts and locate the ones with balances in a given range, and is going desk to desk asking if anyone remembers exactly how much money was in their account yesterday. Pretty soon he has a couple of hits; some people have the app and look at their balance like the rest of us check Facebook.

There are still millions of accounts that could be theirs. This is going to be tough. But Maria says she's got direct deposit on her rent — now we're cooking! (Jan and Dan are still holed up in the breakout room, but we can see the left half of the board is full of abstract graphs and the right-hand side is a list something like "paycheck / rent / credit card / big-ticket / ...") Twenty minutes later, Dave has v2 of his script. It finds Maria's $1035.21 rent payment in a flash. One down!

In fact, two down, because we also now know the identity of Maria's landlord. (Well, somewhat. His name is John something? He lives down in Gilroy. Never seen him. But we can get him on the phone if we need to.)

Dave uses his script on Rick's direct-deposit paystub. (Normally Rick would have an aversion to revealing his salary, but today isn't "normal". Normally Dave would love to reveal everyone's salary. He's having a ball right now.) Now we have Rick and Maria. This is going great! And Rick says he paid Dan for lunch the other day, it was like $20, so if they can see that payment they'll know which account is Dan's... oh. Hmm. Rick paid Dan with Venmo. So it happened entirely within the Venmo app, and won't be reflected in anyone's Chase balance. Bother. Venmo — and credit cards in general — are going to make this a lot harder than if everyone paid by check all the time!

Here I'm out of my depth and so I'll stop with the details, but hopefully Jan and Dan will come up with something. Jan has some contacts at Netflix; maybe their billing system is still unscrambled, in which case we can resolve a lot of accounts by looking at the timing of their monthly $7.99 payments. (Or whatever it is now. Jan does not have the Chase app.)

I predict that within an hour, Bob and Dave and Accounting will have the ability to shuffle the corporate accounts back into place. Within 24 hours, Dave's "Rentinator" (sorry, "Whiscash"? Why does everything need a code name around here?) will be crunching through the accounts for every employee. However, it will take several days to actually apply the changes, unless Bob's team has been foresighted enough to allow "duplicating" the production system. After all, we don't want to shuffle things on the real production system; that's going to be on lockdown for days, until we figure out whether there's anything Forensics can do with it, and until Legal tells us we won't get in trouble for changing it. So one of the postmortem action items we can see already is that we ought to have a way to test out Dave's script without modifying the production data. Put a couple of engineers on that.

Also, in the postmortem we always ask "Are we still vulnerable?" In this case the answer is obviously yes; we have no idea what caused the initial scrambling. But transactions were neither blanked nor scrambled; that's how we managed to unscramble everything. And merchant records — amounts, and names, and shipping addresses — seemed to be okay. So there's something kind of "magic" about lossy representations of transaction history. How fast can we start keeping our own redundant lossy record? No reliance on account-UIDs; those get scrambled. But we can store personal names, and street addresses; that'll be good enough for most people. And you know what? Throw in a column with the salted SHA-256 hash of their account-UID. If those get scrambled "correctly" next time, then at least we'll know someone up there can break SHA-256.

And if it never happens again, hey, problem solved. :)

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  • $\begingroup$ I should point out that the (fictional) SRE team's reaction in this story encodes the implicit assumption that when something goes wrong, the best thing to do is put it back the way it was. Nobody really even considers whether we should redistribute the money another way. This was a failure of our company's record-keeping system, so it's up to us to repair it. (The fact that every other bank is also down today is out of our control and doesn't affect our optimal response, just our degree of schadenfreude.) $\endgroup$ – Quuxplusone Aug 10 '17 at 17:05
  • $\begingroup$ This story also assumes that our bank's records got scrambled among themselves, not with other banks' records (whatever that would even mean, given the different database schemas involved). If doing the traffic analysis requires cooperation among every bank in the world, from Chase Manhattan to Podunk S&L to the Bank of Nigeria, I admit it's hopeless. $\endgroup$ – Quuxplusone Aug 10 '17 at 17:08
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In this answer I consider only the shuffle itself: others are talking about the fallout, and in any case you seem to have edited your question with the intent of removing the longer-term effects on society from consideration.

I suspect there will be a bias towards getting poorer, with a few stand out cases of someone getting immensely rich.

It's correct that there are a few standout cases of someone getting immensely rich, since there are relatively few accounts with immense amounts of money in them (relative to the number of people, I mean). But it's more likely than (say) winning the lottery, since there are more big acounts in the banking system than lottery draws in a lifetime. There will also be some big losers who are randomly assigned an account that's more overdrawn than their entire other assets, and become overnight bankrupts. So it goes.

If by "there will be a bias towards getting poorer" you meant, "there's less money on average than before", then perhaps counter-intuitively I think that's probably true. The reason is there are large numbers of abandoned accounts (which somebody owns, but they've forgotten about them, or died and the estate failed to claim them, or otherwise are uncontactable), and I speculate that those abandoned accounts on average have small amounts of money in them. Of course this speculation might be wrong (in the real world and/or your world), in which case this effect is non-existent or is reversed, but supposing it is correct:

After the shuffle, abandoned accounts will on average (in all probability) have (approximately) average amounts of money in them, which is more than small amounts. Since the population of abandoned accounts increases in value, it follows that the population of active accounts will reduce in value. Of course, eventually the banks (or someone else) will reclaim this money provided that the law grants a mechanism for abandoned accounts eventually to be harvested, but the eventual recipient can't put it on their books immediately because they don't know which accounts it is.

If we ignore forgotten/lost accounts, and futher simplify by assuming that every person has exactly one account, then the total (and hence mean) bank balance of course stays the same. But what about the number of people who get richer vs. the number who get poorer?

To address this, line everyone up in order of bank balance. You will be randomly assigned a new position in line: if you move left then you get poorer, if right then richer (I simplify: in fact a significant number of people have equal balances, and so likely a few will see no change. For what it's worth, the probability that at least one person gets their own original account right back is approximately 63.2%, or 1 - 1/e, where e is Euler's constant). It should be obvious that if you're 75% of the way up the line, then you have a 75% chance of getting poorer and a 25% chance of getting richer. The amount by which you become richer or poorer is irrelevant to which of the two happens. Meanwhile, the next person up has a 75.00000001% chance of getting poorer and a 24.99999999% chance of getting richer, and so on. Add it all up along the line, and on average everyone has a 50% chance of getting richer and a 50% chance of getting poorer. The number of winners and the number of losers will with high probability be approximately the same: 50/50 (well, OK, 50-ε/50-ε of richer/poorer, and 2ε of staying the same, where ε is some small number). Of course it's possible, but incredibly improbable, that the shuffle selected moves everybody left one place except the person on the far left, who moves to the far right. So almost everyone gets poorer. Similarly it's possible for the reverse rotation to occur, so almost everyone gets richer. But these are vanishingly unlikely to occur at random.

In short: if you shuffle a deck of cards then by symmetry there's no overall bias in favour of more cards moving upwards than move downwards. This remains true even if instead of the cards being evenly spaced, we space them according to the same distribution as bank balances, because whether a card moves up or down doesn't depend on the spacing between the cards, only on whether the new position is greater or less than the old position.

If you're just wondering about humans getting richer, as opposed to "legal people": I speculate that the median corporate balance is higher than the median human balance, in which case there is a slight bias for humans to get richer and corporations to get poorer (at least, prior to the knock-on effects which mean people who own shares in the corporations that get poorer, ultimately get poorer too). But it depends to an extent what we mean by "balance". Business accounts can have overdraft facilities, but to stretch a point you might also include short-term loans or bridging loans analogous to overdraft facilities. It might turn out that my speculation is incorrect (in the real world and/or your world), and corporations in fact don't have higher than median balances. I'm pretty sure they have higher-magnitude than average balances, but perhaps often the balance is massively negative. So again, if my speculation is incorrect then the bias disappears or reverses.

You could also consider what happens where people have multiple accounts. For example, for stupid reasons I have 4, 2 of them with very low positive balances. Therefore I get 2 extra shots at the jackpot. But I suspect that as it happens, the mean of my 4 balances is still above the global mean, and so my expected gain is negative.

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People will no longer trust banks, money becomes useless as a means of paying for goods and services as it has no value.

People fall back to systems of barter for services and goods. Maybe some will accept valuables in trade for services, which they then trade on for other goods and services.

In time banking will reappear, but only hard records, written on paper, will be acceptable as proof of ownership of anything.

Which brings us to the linked implication, which is that any computerised system will be viewed with extreme suspicion. It is quite likely a large part of the population will demand a complete ban on computers, maybe even a complete ban on any electronic equipment, because they're afraid of them (many people already are, this would give them an excuse).

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  • $\begingroup$ You may want to review this answer in light of the OP's recent edit. $\endgroup$ – a CVn Aug 8 '17 at 8:28
  • $\begingroup$ Sounds like the Butlerian Jihad. (If you haven't read Dune, it's part of the backstory—a war which was fought, the outcome of which is that all "thinking machines" of any sort are totally banned.) $\endgroup$ – Wildcard Aug 8 '17 at 11:03
  • $\begingroup$ @Wildcard now that you mention it... But it's not uncommon in post-apocalyptic fiction to have similar themes of course. $\endgroup$ – jwenting Aug 8 '17 at 12:01
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There are great answers here, way more interesting to read than mine, but they seem to miss the actual question asked:

What would the overall change in wealth distribution [be]?

From a purely mathematical viewpoint, the change would be ... absolutely nothing. It would have to be.

Visualize all the balances of all the bank accounts sorted like a bar graph, with the balances along the Y axis, and the names of all the account holders as data points along the X axis.

That bar graph represents "wealth distribution" literally. All the money, and how it is distributed between people and businesses

The magic happens, and all the names are shuffled under the bar graph, leaving the balances alone. The distribution is identical, by definition.

I think the other answers about the social consequences are much more interesting to consider, but in answer to the question asked, the distribution doesn't change.

[Edit 1 - addressing comments to both my answer, and the original question]

Original question has been clarified that this isn't all your wealth in a global ledger, just strictly bank accounts, with other assets untouched. As such, I'll augment my answer here with an expansion of the comment I added to the main question.

For bank balances, if like our world, the distribution is a "long tail" graph, or tall pyramid. Many more folks/businesses (in number) have a "below average" (where "average" = mathematical mean) balance due to the few, very, very, high balances. The very few high balance accounts will end up worse off, but the many low ones could change relatively little, or even all go up. It won't be a "half less and half more" split unless the original distribution is balanced.

For example, you could have balances of 1,2,3,4,5,1000 - rotate each owner 1 account to the right. 5 of the 6 people get more money, and only 1 loses (a lot) of money.

Or you could have originally, balances of 1,2,3,1000, and 100 more accounts all at 100 each. In this case, the majority of accounts end up with exactly the same balance (and different payment histories) and only a few people get more and less.

I think my answer still holds. the overall distribution doesn't change (by definition) and under most reasonable assumptions of the shape of that distribution before the incident, most folks don't substantially change, with a few dramatic outliers.

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    $\begingroup$ I'm not sure... If you have assets in terms of property, expensive cars, luxury yachts and so on, that wealth remains yours. Likewise, if you keep everything in cash, still yours. It's just the nebulous banked money which moves, after all. $\endgroup$ – Matthew Aug 8 '17 at 19:52
  • $\begingroup$ Sure, but OP wasn't specific about other sources of wealth in this hypothetical world. From the form of the question, I'm assuming "bank account" was meant to encompass primary stores of wealth, and the focus of the question want meant to be limited to "just banks," but rather a sort of Global ledger of wealth. $\endgroup$ – JesseM Aug 8 '17 at 19:57
  • $\begingroup$ I took the question to be about the distribution of the changes to people's balances (which of course is non-zero with probability almost equal to 1), not the change in the distribution of balances (which of course is zero as you explain). $\endgroup$ – Steve Jessop Aug 9 '17 at 0:28
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    $\begingroup$ @SteveJessop If the question is purely about the effect of permutations on distributions, it's off-topic here, anyway. That's mathematics, not world-building. $\endgroup$ – David Richerby Aug 9 '17 at 12:19
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    $\begingroup$ Nice that at least someone answers the actual question. Note that under the assumption that your bank account is positively correlated with other assets, reshuffeling accounts would actually make the distribution more even. $\endgroup$ – Dennis Jaheruddin Aug 9 '17 at 14:24
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Are things like credit cards affected? If not, then it isn't that bad.

Firstly, the real problem is that people only really keep money in their bank accounts to pay off debt. If that money increases, great. Otherwise, you have people unable to pay mortgages, utility bills, etc. Credit cards offer some relief if they are unaffected. Without them, you have individuals and businesses suddenly declaring bankruptcy, unable to pay employees and service providers.

Nobody is going to risk attempting repossession or debt recovery, but services will be stopped until bills are paid, since the service providers need to pay their own bills, but unless the services are up, people and businesses cannot work to get money to pay those bills, and so the cycle continues.

Secondly, while people who can afford to, keep most of their wealth in non liquid assets, they still have bills to pay. Once their ready cash stock disappears, they'll need to convert some of their wealth to cash--except that everyone who has wealth but needs cash will be doing the same. The 1929 Stock Market crash is an excellent case study of what happens next.

Thirdly, those fortunate few, who woke up, heard the news and rushed to the bank only to find themselves filthy rich, will fall into two groups. Group 1 will try to withdraw as much as they can before the mistake is corrected. The banks fearing a run will limit funds. This will result in more people trying to get their money while they can. The ones who do manage to get a sizeable sum will immediately become targets of everyone else, including law enforcement. If they manage to get home alive, they still won't be safe when people figure out where they live. Group 2 will have figured all this out and will only pay off their immediate debts through the bank then go home with only a small amount in cash.

Once the government figures out what is going on, mainly through their own accounts suddenly emptying, the most likely response will be an excise on any amount over a certain floor. This will outrage the lunatic right and the army will have to be mobilised. The major advantage the government has, is that it can print cash, can pay off most of its immediate debt. The rest will vary from country to country: some might end up in civil war, others in long depressions; one outcome of the 1929 crash was the rise of Nazism.

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It reminds me of what happened in Poland after the fall of Communism. The government wanted to build capitalism, but there were no rich people, no businessmen, no nobles, no aristocracy. Many people had savings for decent elderhood, but not enough to build big business. So they issued the hyperinflation, which meant, all savings were practically confiscated, and the money was pumped to more or less random people.

The most obvious consequence is that old people get terribly poor. They've lost any money they saved and they stick to little payment from government.

Another is, many random people got rich, but many of them got poor very quickly, going on spending spree and ignoring any risks.

The criminality rose upon heaven, criminals feasting on easy money. For many years, the difference between business and mafia was vague.

After many years, the society adapted to new conditions. The people who lost everything just before retirement are slowly dying out. There is no easy money lying on the street anymore, so young people must work hard to achieve anything in life. The people who got rich easily are still balancing on the edge of legality, but they are slowly more and more restricted by better laws. Many people hope than within next generation, the situation will come back to balance.

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What would the overall change in wealth distribution?

This is a statistical question well-suited for Cross Validated. The actual "change" in the nature of wealth distribution would depend on the nature of the utilised univariate distribution that would be used to derive the new random account balance figures. For instance, platykurtic distribution would be likely to reduce average differences between single account balances, assuming that the pre-existing distribution was leptokurtic (more likely).

You could look at a number of existing household income / affluence surveys, and construct casual statical models replacing likely existing account values with random ones and assess how that change impacts the overall "wealth distribution" derived from the utlisied data set.

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