Sorry about the confusion. I hope the new notation makes it easier. (I've removed the graphs.)

Yep, those perverse incentives that you identified are all good criticisms. If there's a theoretical model that says why a system will work, the real-world failure points of that system will be the assumptions of its model. The assumptions can be made to be true with the right regulations. My model assumes that prisons will act lawfully, which I think they will under the right punishments (since there's always a possibility of being caught).

I knew about the prison's incentive to murder high-risk inmates, but I didn't consider the others you mentioned. Maybe some activities should be illegal, such as providing inmates with lawyers, but I'd wait and see how that plays out in the real world before banning it. There's one big problem that you missed: under-reporting of crime (e.g. drug use, rape) within prison (remember prisons have to pay the government for each crime after the auction). To prevent under-reporting, I'd consider mandating that each prison puts microphones and cameras in every room. The recordings could be accessed by government auditors at any time.

I think you'd agree that the main dangers lie with high-risk inmates. To avoid that issue (at least until you have more data on how the system actually functions), you could prevent negative bids from going over a certain size (i.e. you can't bid less than $-x$ dollars). The remaining inmates, whose contracts aren't bid on, would go to public prisons. The bid restrictions could be loosened as we gain a better understanding of the system and impose better regulations.

Public systems have common problems. It's hard to overthrow poorly performing incumbents: If I think I can run prisons better than the existing government, I have to overthrow the entire government in an election. The people in charge of prisons don't have the right incentives: If they could prevent a murder for 2 million dollars, they don't have access to that capital. And sure, they could run tests to see which rehabilitation measures work best, but can they make good decisions on which rehabilitation theories to test, especially when the payoffs for the prison don't exist?

Another perverse incentive: campaign for making more offenses punishable by prison sentences.

That's really interesting - do you have any recommended reading on the UK system?

Thanks for the kind comment.

My guess is that the US would be the best place to start (a thick "market", poor outcomes), but I'm talking about prison systems in general.

I'm not familiar with the UK system, but I haven't heard of any prison system with a solid theoretical grounding. Theory is required because we want to compare a proposed system to all other possible systems and conclude that our proposal is the best. You want theoretical reasons to believe that your system will perform well, and that good performance will endure.

Most systems can work well in the short run, but that doesn't mean they're good. For example, if I were ruled by a good king, I still wouldn't want to have a monarchy in place. If the UK system currently works well, I suspect that you have good regulators who are manually handling the shortcomings of the underlying system.

But perhaps this is what your remark about zero economic profit is meant to address. I didn't understand that; perhaps you can elaborate.

That's correct. $Profit=Revenue-Costs$. The profit that most people think about is the accounting profit. Accounting profit ignores opportunity costs, which is what you give up by doing what you're doing (bear with me a moment). Economic profit, on the other hand, includes these opportunity costs in the calculation. For example, let's say Tom Cruise quits acting and decides to bake cakes for a living. Even if his cake shop earns him $1M in accounting profit, he's giving up all the money he could earn acting instead. So his economic profit is actually negative.

I think you could actually just fix this in the model and still reach the same conclusion (though you'd need extra assumptions to make it work). I really just wanted to introduce my idea for the prison system, rather than make an airtight argument to justify it.

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Predicting the total present value of someone's future tax revenue minus welfare costs just seems extremely difficult in general. It will have major components that are just general macroeconomic trends or tax policy projections.

It is very difficult, but that's exactly what the financial markets do.

While you are in part rewarding people who manage to produce better outcomes, you are also rewarding people who are simply best able to spot already-existing good (or bad) outcomes, especially if you allow these things to be traded on a secondary market.

Yep. If someone is great at running prisons, you want them to do so, regardless of how good they are at predicting the future. Ideally, you would have a system that allows any good expert to thrive, even if they know little about anything outside of their expertise. But companies deal with this all the time. When they're developing a new product, they have to predict which research ventures will be fruitful and which won't be. They have to predict how well products will sell. They have to predict product breakage rates. They have to predict what advertising will work the best. All these things are hard, which is why companies fail. But they are replaced by ones who better succeed at solving all the issues.

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You say things like "whenever the family uses a government service, the government passes the cost on to the company" as if the costs of doing so are always transparent or easy (or wise) to track. I guess an easy example would be the family driving down a public road, which is in some sense "using a public service" but in a way that isn't usually priced, and arguably it would be very wasteful to do so.

Well, yeah. That's why I say to not measure those things. Only measure the big things. The reason why I mention that later in my post, rather than including it in the core argument, is because you need to "smooth things out" with simplifying assumptions to make logical arguments work.

Other examples are things like using public education, where it's understood that the cost is worth it because there's a benefit, but the benefit isn't necessarily easy to capture for the company who had to pay for the education.

You could actually use my proposal as a secondary, opt-in public education system as well.

Amount of tax paid on salary doesn't reliably reflect amount of public benefit of someone doing their job, for a variety of reasons: arguably this is some kind of economic / market failure, but it is also undeniably the reality we live in.

Sure. But I don't see why we can't fix those systems as well. (Just to clarify, ideally salaries are paid based on marginal contribution, not the total contribution of the industry--which is why we don't pay farmers an infinite amount. But I agree that not everyone is paid their marginal contribution.)

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Once you've extended your suggestion to prisoners and immigrants, I think it's worth asking why you can't securitize anyone's future "societal contributions". One obvious drawback is that once this happens on a large enough scale, it starts distorting the incentives of the government, which is after all elected by people who are happy when taxes go down, but no longer raises (as much) additional revenue for itself when taxes go up.

Yes, that's right! But it is a solvable problem. A taxation system that financially compensates people for rule changes would mitigate this. In effect, the prisons would be paid as if the taxation system were fixed at the time the inmate contract was made.

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In part, I think the above remark goes to the core of the philosophical legitimacy of taxation: it's worth considering how the slogan "no taxation without representation" applies to people whose taxes go to a corporation that they have no explicit control over.

I'm not sure what you're saying here. People still get to vote. The government has simply exchanged their taxation stream for its present value. Are also you saying private companies shouldn't be allowed to buy government bonds?

Has anyone else (politicians, researchers, etc.) ever argued for a system resembling this one?

Robin Hanson has written about similar ideas:

For every immigrant that we admit, the government could track how much that person pays in taxes each year, and also how much the government spends on that person via benefits whose costs can be measured individually. We could probably assign individual costs for schools, Medicare and Medicaid, prison, etc. For types of costs or benefits that can’t be measured individually, we’d could attribute to each immigrant some average value across citizens of their location and demographic type. When there are doubts, let us err in the direction of estimating higher costs, so that our measures are biased against immigrants adding value.

Okay, so now we have a conservative net financial value number for each immigrant for each year, a number that can be positive or negative. From these numbers we can create financial assets that pay annual dividends proportional to these numbers. If we let many people trade such assets, their market prices should give us decent estimates of the current present financial value of this stream of future revenue. And if we allow trading in such assets regarding people who apply to immigrate, with those trades being conditional on that person being admitted and coming, then such prices would estimate the net financial value of an immigration candidate conditional on their immigrating.

We could then admit the candidates for whom such estimates are highest; using a high threshold could ensure a high confidence that each immigrant is a net financial advantage. Those who are skeptical about particular immigrants, or about immigration in general, could insure themselves against bad immigration choices via trades in these markets, trades from which they expect to profit if their skepticism is accurate.

Does any country in the world create estimates of individual citizens' cost to social services? Does any country in the world have a system where companies can bid for the right to collect individuals' future tax revenue? Has anyone else (politicians, researchers, etc.) ever argued for a system resembling this one?

I'm not aware of any "net tax contribution" measurement, but I haven't done an extensive search either. I'm not aware of anyone arguing for anything close to the system I proposed. The closest (but still far away) system that I've heard of is social impact bonds, which have been implemented in Australia to some degree. In the implementations of them that I've seen, they give prisons bonuses for reaching a low level of recidivism.

There's several weaknesses of that model. Maybe one prison happens to get allocated inmates that are not likely to reoffend, in which case, they get paid for no reason (bidding on inmate contracts stops this). A reoffending murderer is given the same weight as a reoffending thief, so the prison is indifferent to who they rehabilitate (valuing "equivalent compensation" of crimes stops this). And the government is not cost minimizing (again, bidding stops this). It also doesn't incentivize prisons to increase the net tax contribution of the convict (whereas mine does).

I'd have loved to hear thoughts in the post on how we might "carefully work towards" a system that works so differently from any that (AFAIK) exist in the world today. What intermediate steps get us closer to this system without creating a full transition?

I have some ideas, but no strong theoretical reasons for believing they're ideal.

You could implement a subset of the system: Just the income tax paid and welfare used. That data already exists. This data could be linked to the inmate's attributes, which would allow the prisons to have good reference classes from which they could estimate their profit-maximizing bids. The primary difference between this half-measure and the full proposal is that the prisons don't pay the government when a crime is committed (secondarily, income tax paid is different from tax incidence).

When you have the right metrics for the full system (valuations of equivalent compensation for all crimes, and tax incidence) if, for some reason, tax incidence data can't be generated for the past, you could keep the half-measure system in place for a few decades. But during that time, you do the measurements and store the data. When it's time to implement the full system, again, prisons have good reference classes from which they can estimate their optimal bids.

If politicians are particularly skittish on the idea, they could say to the prisons "We'll pay you 80% of what we would under the current scheme, and pay you 20% of what we would under the new scheme." I wouldn't recommend this, because some viable rehabilitative measures won't be taken.

I'd have been more convinced by the post if it referred to any existing policy which mirrors any aspect of these proposals.

I think the best argument for conservativism is "Out of all possible sets of institutions, the one we're in is pretty good". But this doesn't mean "never implement radical change" (if you never do so, you'll get stuck on a local optimum). It just means that when you're implementing radical change, you have to have good evidence. I wouldn't implement this system based off the mathematical justification I've given here. But I think the problems with the argument could be solved with minimal changes to the actual system. And if one of the assumptions of the argument fails when the system is implemented, we can always change back to the existing system. But if it is successful, it has implications for other policy areas (such as immigration).

An example of radical, evidence-supported policy is the kidney-exchange reform. Rather than exchange kidneys between pairs of people, they now chain groups of people together. The new system facilitates far more exchanges between willing donors and people in need. Countries that waited for the "evidence" (by which they mean "empirical evidence") let people die because they didn't value the logical argument.

The hospital-intern matching algorithm is another example (it was also applied to student-to-school allocation).

The most prominent system that's supported on a theoretical-level is free markets. It is supported by the general equilibrium model. When the assumptions that model stray too far from reality, the system breaks down. When they're close enough, it works very well.

So the question is "Are the assumptions of the prison-policy argument close enough to reality". I think they mostly are, and where they're not, the error is balanced by a countervailing error.

My instinctive emotional reaction to this post is that it worries me, because it feels a bit like "purchasing a person", or purchasing their membership in civil society. I think that a common reaction to this kind of idea would be that it contributes to, or at least continues, the commodification and dehumanization of prison inmates, the reduction of people to their financial worth / bottom line

No one is going to run a prison for free--there has to be some money exchanged (even in public prisons, you must pay the employees). Whether that exchange is moral or not, depends on whether it is facilitated by a system that has good consequences. I think a worthy goal is maximizing the societal contribution of any given set of inmates without restricting their freedom after release. This goal is achieved by the system I proposed (a claim supported by my argument in the post). Under this system, I think prisons will treat their inmates far better than they currently do: allowing inmates to get raped probably doesn't help maximize societal contribution. "Commodification" and "dehumanization" don't mean anything unless you can point to their concrete effects. If I've missed some avoidable concrete effect, I will concede it as a good criticism.

(indeed, parts of your analysis explicitly ignore non-monetary aspects of people's interactions with society and the state; as far as I can tell, all of it ignores the benefits to the inmate of different treatment by different prisons).

Not every desirable thing needs to be explicitly stated in the goal of the system: Good consequences can be implied. As I mentioned, inmates will probably be treated much better under my system. Another good implicit consequence of satisfying stated goal, is that prisons will only pursue a rehabilitative measure if and if it is in the interests of society (again, you wouldn't want to prevent the theft of a candy bar for a million dollars).

I account for the nonmonetary aspects of the crimes. But yes, the rest is ignored. If this ignored amount correlates with the measured factors, this is not really an issue.

That's a good point to bring up. There are a few ends that other people assign to prisons that come to mind: rehabilitation, deterrence, punishment, and removing the criminal from the population (protecting innocents). However, some of these goals can be achieved by other systems. The death penalty is completely compatible with the system I proposed: Though you may disagree with killing criminals for other reasons, it is (at least on the face of it) a deterrent, and it doesn't need to be carried out by prisons. The law could specify ways in which the prisons must treat their inmates. For example, it could forbid prisons from providing computer access.

If the punishments are not dictated by law, they are the ad hoc decisions of the prison warden (or the decisions of the other inmates).

The graphs show what is encapsulated by what. The area to which a label corresponds is the smallest convex shape that encapsulates the label. For example, $M$ is the whole lower-left quadrant, which also encapsulates the monetary effect of crimes (which is why the monetary effect of crimes is not explicitly included in the formulas). $M$ doesn't stand for all monetary factors. It stands for every monetary factor except $Funding$.

If the convict pays tax, that's a good thing for society (all else being equal). $\Pi$ should increase. And it does, since more tax means a higher $M$. If the convict has to use welfare, that's bad. $\Pi$ should decrease. And it does, since you get a lower $M$. If the convict's incarceration requires more funding, that's bad (all else being equal). $\Pi$ should decrease. And it does, since funding is subtracted. And so on. There is part of the graph that is not included in $\Pi$: The nonmonetary effects that are not crimes. One of my simplifying assumptions was to ignore this section ("Let us ignore Bob’s other nonmonetary contributions for simplicity.")

This system has an advantage over public prisons in that it provides a mechanism to choose which research should be pursed. Should we trial inmates wearing pink uniforms? Is that worth the cost of research or not? I don't know. But there are people who are informed enough to be willing to make a bet on the matter. The people who believe strongly that they can get good outcomes will make those bets. If they're wrong, they lose money and leave the market. If they're right, they make money and gain a greater share of control.

One thing I want to note: I'm not saying "Implement the system as I've described by next month". I think the system is something to carefully work towards.

No, I think they imagined I wanted to imprison all immigrants (which, as you can see, is not what I'm suggesting). To be clear, I'm not talking about preventing anyone from leaving your country; I'm talking about how to select which non-citizens can become permanent residents in your country.

As for non-open borders being equal to imprisonment, that's incorrect. The fact that I can't live in North Korea does not mean that I'm imprisoned in my country. By this definition of imprisonment, everyone is the world is imprisoned.

I believe this system would allow for more immigrants than there are currently. Government is slow at determining which people can enter (at least in my country). This might fix that. And knowing that every immigrant family is a positive contribution to the government's balance sheet (and unlikely to commit crimes) will probably help society see immigration as a good thing, which may help gain political support for more immigration.

As an offtopic aside, I'm never sure how to vote on comments like this. I'm glad the comment was made and want to encourage people to make comments like this in future. But, having served its purpose, it's not useful for future readers, so I don't want to sort it to the top of the conversation.

Oh okay, thanks for the advice. I'll see if I can get it to work.