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More information is usually considered "better". Let's say a rational agent chooses optimally given his information on the circumstances of a particular decision problem. Then providing him with more or better information makes him (weakly) better off.

Other agents might be made worse off in the process, and total welfare might even decrease. Danove et al. (2003) e.g. argue that the introduction of mandatory "report cards" in New York and Pennsylvania in the 1990ies to evaluate bypass surgeries reduced welfare because it incentivized doctors to avoid treating very old or sick patients. In this example all patients got more information, and some of them, but not all, ended up worse off.

But there are also circumstances where providing agents with more information makes everybody worse off. When visitors are about to leave a crowded theater, truthfully informing them that a fire just broke out behind the curtain might have disastrous consequences for all of them. Informing the public that a particular bank is in trouble could trigger a bank run that leaves everybody worse off.

What are other such phenomena? I am looking for examples (in theoretical models or in the real world) of the latter kind, where exogenously providing a group of agents with more or better information leads to a new equilibrium which is Pareto inferior compared to the old one.

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    $\begingroup$ See also "Reverse Tinkerbell Effect" $\endgroup$ – CodyBugstein Feb 24 at 22:12
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    $\begingroup$ @Nyos: Yes, in my understanding "information" is by definition true, otherwise I'd rather call it disinformation. $\endgroup$ – VARulle Feb 25 at 13:41
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    $\begingroup$ @VARulle The two cases that you mentioned are not fulfilling your criteria: in a theater fire there are potentially people that are better off, those who didn't fall victims to the stampede and managed to exit because of the alarm. In case of a bank run most people are worse off, but not the first ones who withdraw their full balance. $\endgroup$ – user3819867 Feb 25 at 17:04
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    $\begingroup$ I don't have enough reputation for an answer, so leaving this as a comment. How about an old marriage? Both parties have occasional thoughts that they might be happier with someone else (because they're human and we all have these thoughts), but are happier together than they would be if they divorced. But if they each knew how often their partner had occasional stray thoughts, they might end up agreeing to a divorce, leaving them both worse off. $\endgroup$ – CPomerantz Feb 25 at 21:26
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    $\begingroup$ @VARulle I have 100 rep because I have enough rep on other Stack Exchange sites. But you need 10 rep earned on this Stack Exchange to answer because it's a "Highly Active Question". $\endgroup$ – CPomerantz Feb 26 at 15:44
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Traffic reports are another type of information that potentially makes everyone worse off.

A recent working paper (Wiseman and Wiseman 2019, https://drive.google.com/open?id=10B6VudYJOQB5w2UVBrYEjYc5wwzGZc8Z) shows this in a simple model of traffic.

I quote from the paper, "...public information about road conditions tends to increase average travel time when...3) the scale of the traffic network is large." This corresponds to their Theorem 3, where "...in a scaled-up version of any environment with excess capacity, traffic reports increase expected travel time."

Yet another broad way of thinking about your question is in terms of monitoring structures of repeated games. A recent paper (Sugaya and Wolitzky 2018 JPE, http://economics.mit.edu/files/11455) look at imperfect monitoring in cartels and show that less transparency can facilitate collusion, making all participants better off.

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    $\begingroup$ This is a good one. I recall an article (not sure where, now) making this case about map applications that give near-real-time traffic re-routing in response to conditions. Although, the argument there is that the larger pool of information is segmented - Google Maps doesn't know where iPhones are sending their users, and vice-versa, and of course cities have no idea what either service is doing. $\endgroup$ – heh Feb 24 at 15:44
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    $\begingroup$ Another way of thinking about this is that "how bad" it is to be late might not scale linearly with the lateness. It's easy to imagine that there might be a step change in badness when you're late at all. So it's worse, on the whole, for everyone to be 1 minute late than it is for 1 person in 15 to be 15 minutes late. Real time traffic reports that "level out" traffic might make more people a little bit late, even if average travel time were the same or reduced. $\endgroup$ – StackOverthrow Feb 24 at 22:24
  • $\begingroup$ 1. I think traffic information making everyone worse off is a candidate for @Luaan's concept of being more, but insufficient. The everyone worse off here is typically a result of alternative routes with smaller capacity (otherwise there would be the primary, not the alternative) exceeding their capacity. But the outcome may change to everyone better off if you can give sufficient information to just approach but not exceed that capacity ("cars with license plate ending in 1, 2 or 3 please take detour A") 2) these "everyone worse off" thoughts do not consider that some who are in a traffic jam $\endgroup$ – cbeleites unhappy with SX Mar 1 at 15:46
  • $\begingroup$ ... (and the ones waiting for them) are better off already if the information allows them to call that they will be aproximately xxx min late. $\endgroup$ – cbeleites unhappy with SX Mar 1 at 15:48
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This sounds glib, but The Internet is an ongoing example.

In economic models where access to information is an explicit factor, we often gloss over the fact that mere exposure to information about the state of the world is not enough to improve welfare - one also needs the cognitive skills to use those facts to develop plans in support of preferences, and also the abilities necessary to manipulate the environment in execution of those plans. Homo economicus is implicitly assumed to possess both, but this is manifestly untrue about Homo sapiens. "The Death of Expertise" by Tom Nichols is a good first-look at the scope of the problem, viewing the interplay between limited human capacities and unfettered access to information ("signals", really) through a sociological lens. The Dunning-Kruger effect and the competition between identity/belonging goals and accuracy goals are two key elements to this.

If you want to get deeper into it, a host of other empirically-supported cognitive biases - anchoring, affect heuristic, availability bias, and so-on - suggest that the phenomenon of acting in response to an information set that becomes more complete with time exhibits hysteresis. This is tremendously problematic when recognizing that while Homo economicus is presumed to hold all of the available information in her head in one simultanous pre- $t = 0$ moment, each of the information sets held by every Homo sapiens carries a slightly different history than any other. To the extent that these information sets are compiled by experiencing signals available on the Internet, a proiri one should expect that a bigger pool of signals will yield a wider variation in the histories, and less rather than more concensus about the state of the world and which actions (usually requiring the solution of co-ordination problems) might lead to greater social welfare.

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    $\begingroup$ Is this fair, though? Of course wrong information, or information that is improperly interpreted can be bad for you, but that's not exactly a paradox, is it? If I lie to you to make you send me a million dollars, it's not a problem of having too much information, but rather too little :) Indeed, a common way of manipulating people is to tell the truth, but at the same time withhold critical information that puts the truth in context etc. We're dealing with probabilities here - is there correct, well interpreted information that on average gives you worse outcomes than not knowing? $\endgroup$ – Luaan Feb 27 at 14:04
  • $\begingroup$ Well this is why I prefer to use the term "signal" rather than "information". It is also why I include the importance of having the skill to act. Without that, even true signals can lead to sub-optimal outcomes. And finally, it seems like you're still clinging to the assumption that all pertinent information is available pre-$t = 0$; this simply isn't true. We receive a stream of signals that evolves throughout time, and so by definition it will always be incomplete - and some of that missing data will be "critical" in the sense you mean it. There is no real counterfactual to that. $\endgroup$ – heh Feb 27 at 17:18
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The “to be announced” or TBA market for agency mortgage-backed securities is a great example of this.

The short version is as follows: The TBA market is a market wherein one can purchase or sell for future delivery pools of mortgages that conform to certain characteristics (e.g., and to vastly simplify, 30 year mortgages at a 4.5% coupon) without specifying the particular mortgages to be delivered. Only government- or agency-guaranteed mortgages are eligible for TBA delivery. Of course, the incentive is for the pool seller to deliver the worst mortgages possible, but “worst” is entirely based on the mortgages’ prepayment characteristics, not on their credit quality (as they’re all guaranteed).

Why is this good? It makes for a really liquid market, because everyone just prices everything assuming it is bad. Buyers don’t waste a bunch of time trying to analyze pools trying to uncover some marginal advantage, because that’s simply not an option. So they can buy securities in this market blindly, knowing that they’re only being shortchanged in the selection of mortgages in the pools they buy to a predictable degree that is already priced into the market. This is really useful given that most of the buy side doesn’t have a ton of resources to spend on pool-level evaluations.

The result: a multi-trillion dollar market in annual primary volume (not counting financing that occurs in this market), that is estimated to be responsible for reducing the cost of mortgage financing in the US by 10-25bps on average.

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  • $\begingroup$ So basically, everyone having less information makes everyone better off? $\endgroup$ – user253751 Feb 25 at 11:57
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    $\begingroup$ Yes, which also means that if they had more information, they would be worse off (which is true for non-TBA-eligible securities). $\endgroup$ – dismalscience Feb 25 at 12:59
  • $\begingroup$ Except it only looks like you're better off, because somebody else is paying the bill. The guarantee simply makes the information irrelevant - it overrides the reasons why the information is (normally) useful; instead of you being responsible for the quality of your investment, if you make a mistake, the taxpayers pay for it - essentially, you're handing everyone's money to pay for the past times/investments of a part of the population. $\endgroup$ – Luaan Feb 27 at 14:08
  • $\begingroup$ @Luaan You’ve clearly not read the linked paper or any of the relevant literature on this topic. The estimated liquidity benefit is comparing guaranteed TBA-eligible securities to also guaranteed non-TBA eligible securities. What is being valued is not the guarantee at all. $\endgroup$ – dismalscience Feb 27 at 14:20
  • $\begingroup$ No, it just says that if you can have general buy and sell orders, and somebody else guarantees the commodity being bought and sold, you will have a better performing market than if you can't have general buy orders. The liquidity isn't enhanced by the lack of information, it's enhanced because you get the information - how much people are willing to give you for a given commodity, regardless of how good an investment it is. The information "there's 20 people willing to pay me $20 for X" is more valuable than "there's 1 willing to pay $23 for X1, 3 who pay $26 for X2, ..." $\endgroup$ – Luaan Feb 27 at 14:29
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The post of @Mmmmmm about traffic reminded me of Braess's Paradoxon: There are situations in a traffic network (under the assumption that all drivers are rational) where removing some roads leads to a lower average amount of time spent driving.

While the paradox itself was constructed with another goal in mind it assumes that all drivers know the optimal path to take.

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  • $\begingroup$ That's a nice connection. And you're right, they're quite similar in spirit. $\endgroup$ – Mmmmmm Feb 25 at 19:16
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    $\begingroup$ Note that you can also adapt this example to the question: The road does not have to be removed in reality but only from the knowledge of all drivers. $\endgroup$ – Wrzlprmft Feb 26 at 12:34
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Paul Krugman recently discussed the Bloomberg terminal, a classic example of a resource with the following properties:

  1. Those who get it are at an advantage, so naturally everyone gets it;
  2. It's not free, so everyone getting it cancels out the benefits, making even worse off.

The world must be full of examples of this. Dave Gorman once mentioned another example, where everyone on his flight, him included, had paid for priority boarding. You can guess what happened.

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    $\begingroup$ Looks like a classical public goods game, but I don't think it qualifies as an example where providing all agents with more information makes everybody worse off. The extra information has to be purchased here and is not simply provided to everyone (for free). If it were, then everybody would end up as well off as before (assuming that you profit only from an informational advantage over others). $\endgroup$ – VARulle Feb 26 at 8:46
  • $\begingroup$ Another classic example: health insurance. $\endgroup$ – StackOverthrow Feb 26 at 16:34
  • $\begingroup$ @user560822 There's nothing wrong with health insurance in general - it's a service that allows you to trade risks and large sudden sums of money for regular payments. It's no different from taking a loan, for example. What you're thinking of is the "bonuses" health insurance companies try to give their customers to choose their particular company, and which are the main reason the US health system is such a mess - e.g. having doctors increase base-line prices, just so the insurance company can give "discounts" for their customers even though they're just paying the market price. $\endgroup$ – Luaan Feb 27 at 14:12
  • $\begingroup$ The thing is, if people stop doing that, it will become advantageous again - which balances out the information value. If enough people learn there's no point in having priority boarding, it will become useful again :) This is just an example of sub-optimal Nash equilibrium - everyone would be better off if noone did it, but every individual will be at a loss for being the one not to do it. Heck, it's well known in evolutionary biology - trees only benefit from growing so tall because other trees are tall; all trees would be better off shorter, but can't afford to be. $\endgroup$ – Luaan Feb 27 at 14:15
  • $\begingroup$ Arguably, Bloomberg terminals are an example for withholding information (and then releasing it only for a fee), so it could actually be a counter-example. If everybody had perfect market information the market would be closer to perfect; optimal markets again lead to optimal resource allocation which improves overall welfare. $\endgroup$ – Peter - Reinstate Monica Feb 27 at 16:02
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This is a very old idea in general equilibrium models with imperfect information and incomplete markets. More information could be detrimental if the agents that face uncertainty situations decide to insure and the equilibrium under full insurance is pareto optimal.

If in such a situation the state would be revealed with a perfectly informative signal the state of nature would be known before the opening of the market and so the insurance possibilities for the agents are destroyed.

Take a look at this links:

there was also another example in eeckhoudt, gollier and schlesinger "Economic And Financial Decisions Under Risk" but I cannot find it right away.

EDIT: @Giskard Example: Think about an example where you have two consumers with concave utility functions and endowments $ \omega_1=(1,0) $ and $\omega_2=(0,1)$ and state dependent utilities that assign 0 utils to the consumption of one of the two goods in one of the two states.

With the same utility functions and same endowments the economy is in an edgeworth box and as long as the agents are risk adverse they would like full insurance i.e. they will choose a point on the 45degree line with same consumption in the two states.

However, if a perfect signal reveals the state of nature before the spot market opens the guy that has the "bad" good cannot insure anymore because this economy doesn't satisfy the minimal revenue condition and there would be no trade. Overall, the concavity of the utilities and the decreasing returns of consumption guarantee that the welfare is higher in the case of full insurance than under perfect information.

This could be the case in a very simplified economy where the endowments are two different antivirals and only one virus (state) will attack (realize in) our fantasy world. But I have read also a conceptually very similar example on the insurance market in the book that I cited.

EDIT 2: Taking back Mas-colell book I have found this: enter image description here you could look into Spence (1973) signalling model where even if the signal is not costly could create such a problem!

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    $\begingroup$ I have read the second book (several years back), but I still do not understand what you mean. Why is it bad that the insurance possibilities are destroyed? If you already know everything, you don't need ex post insurance? And ex ante insurance is not destroyed. $\endgroup$ – Giskard Feb 25 at 20:41
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    $\begingroup$ In your example total welfare might decrease, but the situation with information on the state of nature doesn't seem to be Pareto inferior to the one without information. The agent with the "good" good is not made worse off by revealing the state of nature. $\endgroup$ – VARulle Feb 26 at 9:38
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    $\begingroup$ This comment really surprises me. Total welfare may be in doubt (it will depend from the exact curvature of the utilities), but for sure the certain situation is a pareto deprovement. The "bad" agent has utility of zero so is obviously worse off and it is not a pareto improvement. $\endgroup$ – KArrow'sBest Feb 26 at 9:49
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    $\begingroup$ @KArrow'sBest: Well, for being Pareto inferior compared to the certainty situation both agents would have to be strictly worse off. $\endgroup$ – VARulle Feb 27 at 9:07
  • $\begingroup$ @VARulle, I know the definition. I believe, that also the agent with the "good" good would be worse off if both states at t=0 (before the signal) have p=.5 he will loose half of the time and will end-up with expected utility lower than the case with full insurance. $\endgroup$ – KArrow'sBest Feb 27 at 10:56
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Cases where the information increases perceived value but not real value

Information that can only be used for harming others and/or self are generally not helping the broad public.
The ongoing efforts to pursue 3D printed guns is one of such topics; while you may argue that some people in certain cases benefit from them, they are generally undesirable as knowledge.
Even more so, public information on nuclear devices can ruin a person's life while not likely making anyone better off.

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  • $\begingroup$ So basically the fact that everyone is better off when nobody has guns than when everyone has a gun (even though every individual person is better off having a gun), but where the source of the guns is information? Yeah, that works. $\endgroup$ – user253751 Feb 27 at 13:54
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Not an exact example but here's a case when omniscience is a disadvantage.

Suppose I'm playing a game of chicken where I'm driving straight at an opponent and whoever swerves first loses. If I know my opponent is omniscience or can read my mind [and doesn't have a death wish], then I can confidently conclude that I need never swerve. My opponent will read my mind and realize that I will never swerve, and hence realize he be the one who has to swerve.

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    $\begingroup$ In your example, more information does not make everybody worse off. $\endgroup$ – Herr K. Feb 24 at 22:54
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    $\begingroup$ @HerrK. Ok, what if both you and your opponent are omniscient? $\endgroup$ – Andy Feb 25 at 1:12
  • $\begingroup$ @Andy: Then one of the Nash equilibria will be played. But I still don't see how that hurts both players. $\endgroup$ – Herr K. Feb 25 at 6:16
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Cortisol

Cortisol is a hormone similar to adrenaline that is used in emergencies. One of its effects is to shut down the immune system for a short period (while that emergency lasts) to save energy (there's no need for that when the lion chases you).

(Mis)using this effect, long-term stress can cause your immune system to be reduced, and make you sick. Panicking about a situation over which you have no control but plenty of information (e.g. the Covid-19 pandemic where the only defence is your immune system and reducing the risk of getting it) could cause more harm than less information.

Sleeping more helps the immune system, but stress could disrupt that as well.

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  • $\begingroup$ This seems at least analogous to world economics, but would benefit from some sources to back it up. $\endgroup$ – ti7 Feb 26 at 18:50
  • $\begingroup$ What does this have to do with information? $\endgroup$ – user253751 Feb 27 at 13:52
  • $\begingroup$ @user253751 Knowing about a pandemic can cause your immune system to be less capable of fighting the infection off. However, it's a weak argument - it also means you can be more careful with hygiene, avoid sick people, take disease more seriously (instead of e.g. going to work) etc. Those can be behaviors that aren't usually worth their costs, but are much more worthwhile with a dangerous pandemic around. My post-com country has plenty of history with officials preventing the spread of information for similar non-reasons, resulting in e.g. toxic chemicals remaining in foods for decades. $\endgroup$ – Luaan Feb 28 at 7:50

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