Talk:Liberal paradox

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  • Cleanup : Ways out could be greatly improved: use Alice and Bob terms for clarity, as well as some formalism

"Liberal Paradox" is bogus[edit]

This "paradox" is saying that you cannot have the Pareto principle and have freedom, e.g. the exclusive right to control what is done with your loaf of bread. But this is just confusing people by using mathematical terminology to obscure an obvious fact -- you may benefit from choosing to sell your loaf of bread to someone else, if the price he offers is high enough. That ability to give up your freedom to use the bread in exchange for something better does not mean that you do not have the freedom. It is just one way of using the bread to benefit yourself -- you can eat it plain, make a sandwich, toast it, or sell it and use the proceeds. Where is the problem? There is no paradox. JRSpriggs 09:38, 24 March 2006 (UTC)

  • You don't quite get it.
  • It's not as bogus as you think — at least not for the reason you state. Without having grasped the issue in it's entirety, I would say that the personal liberty in your example would be something along the lines of being able to choose what to do with one's bread rather than keeping one's bread. —Bromskloss 19:50, 20 July 2006 (UTC)
  • It's not bogus, but I don't tend to think it's profound, either. Consider: people can do things that don't better themselves. If they're prohibited from doing these things, that's a restriction on freedom; if they aren't, they're being Pareto inefficient (hurting themselves and not helping anyone else). CRGreathouse 20:02, 20 July 2006 (UTC)
I don't think this is the same as the paradox, because the pareto principle operates on the individuals preferences - therefore even though you think it doesn't better them, it's still according to their preferences, so they aren't being Pareto inefficient. If the example below is a true indication of the meaning of the Liberal Paradox, the problem is that a group of people making decisions that have outcomes that only affect a subset of them will come up with results that weigh what the unaffected people think the affected people should prefer as important as what the affected people actually prefer. In many situations this will lead to pareto inefficiency (although it's possible that the preferences always coincide and so there is no problem...) Kybernetikos 10:15, 13 August 2006 (UTC)

If this is an excuse for government intervention then it is pretty pathetic one. The market doesn't have to be pareto efficient, it just has to be better at allocating resources than a central authority which it is. Also if there is pareto inefficiency then this no excuse for government to step in per regulatory capture. —Preceding unsigned comment added by Sabaton10 (talkcontribs) 09:13, 18 September 2010 (UTC)


I have a suggestion for how the example could be improved to be even more clear, but since I'm not familiar with the subject I want to post it here first to make sure I haven't messed anything up.

Suppose Alice and Bob have to decide whether to go to the cinema to see a chick flick, the possibilities being

  • both to go,
  • only Alice to go,
  • only Bob to go,
  • neither to go.

Suppose also that each has the liberty to decide whether to go themselves. If the personal preferences are based on Alice wanting to be with Bob and thinking it is a good film, and on Bob wanting Alice to see it but not wanting to go himself, then the personal preference orders might be

  • Alice wants: both to go > neither to go > only Alice to go > only Bob to go,
  • Bob wants: only Alice to go > both to go > neither to go > only Bob to go.

Clearly Bob will not go on his own. Futhermore, since Alice has personal liberty, the joint preference must have neither to go > only Alice to go. Likewise, Bob also has personal liberty so the joint preference must have Alice to go > both to go (as well as neither to go > only Bob to go). Combining these gives a joint preference neither to go > both to go, but this is Pareto inefficient given that both Alice and Bob think both to go > neither to go.

The example really helped me get a first idea of what it is all about, and I hope it will be even better now. —Bromskloss 21:17, 20 July 2006 (UTC)

I don't like "(as well as neither to go > only Bob to go)", "Furthermore" or "Likewise" (or the border) but apart from that it looks fine. --Henrygb 17:11, 21 July 2006 (UTC)
The border exists only here in the talk page to indicate where the example begins and ends. —Bromskloss 09:15, 22 July 2006 (UTC)
In both the original and this proposed alternative, there's a non-trivial leap, at least for me. Specifically, I would like a clearer explanation for "Futhermore, since Alice has personal liberty, the joint preference must have neither to go > only Alice to go." Why does Alice's personal liberty lead to this joint preference? This should be clarified. Anomalocaris 18:14, 8 August 2006 (UTC)
As I imagine it, Alice has the power to change the joint preference from neither to go to only Alice to go because that change involves only herself, and she has the right to decide over herself. However, I don't dare say so in the article, because I'm not sure it's correct. —Bromskloss 10:51, 10 August 2006 (UTC)
Very helpful example, but I agree with Anomalacaris. I think a more clear definition of personal liberty is necessary. It looks like this problem has arisen only because Bob has chosen to think that Alice should go even under circumstances that she believes she doesn't want to. Assuming Bob and Alice talk about this and discuss the options before voting, we've created the problem because Bob believes Alices stated preferences are not a true reflection of her real preferences. If we allow this kind of thing, surely it throws the whole concept of voting into question. Does it mean that for voting to make sense all participants must believe that all other participants will vote according to their true preferences? If we assume that, does the paradox go away? If Bob assumed that, then he would leave the option for Alice to go alone unrated. Am I right in thinking that in this case the paradox doesn't occur? Perhaps this would turn into a paradox of pareto efficiency vs religon, parenting, government, any system where others believe they know better than you your best interests. Kybernetikos 09:59, 13 August 2006 (UTC)
Reasoning backward from the example, the definition of personal liberty would be something like this: For any two results where the only difference between them is the actions of an individual, the final community agreed outcome must contain the same preference as that individuals preference between those results.
This rapidly becomes complex though, because although the difference between only Bob going to the film and both Bob and Alice going to the film consists solely in the actions of Alice, her actions clearly affect Bob and his preferences.
Useful link
Feel free to add the link. Your suggested definition of personal liberty is slighty too wide: it should be that in some area the personal choice of a particular individual should be decisive. In the example it is whether the individual goes to the film, but it does not have to be. --Henrygb 16:25, 15 August 2006 (UTC)
I don't know what my problem was before, and I now understand why Alice's personal liberty leads to the joint preference must have neither to go > only Alice to go. Anomalocaris 17:38, 20 August 2006 (UTC)
Nice to hear that. No we only hope that it actually is correct! ;-) —Bromskloss 21:44, 20 August 2006 (UTC)
The presentation of this example is unclear and flawed. The problem is that the example constructs a preferential order between Alice and Bob, but yet this runs into issues of Arrow's Theorem and the Voting Paradox. So you can't really construct a combined order without referring to a specific decision procedure, and Sen's Liberal Paradox is independent of any given method of constructing a combined preferential order. (e.g. borda count, single transferrable vote, or a condorcet-like methodology) Obscuranym (talk) 04:13, 15 December 2009 (UTC)
I agree with the "it seems bogus" position, but for a different reason: The examples in the article proper seem to rely on malicious desire to inflict harm as being valid uses of resources. I think these examples don't reveal a "liberal paradox" so much as they reveal that valuing harm of others over self-satisfaction leads to sub-optimal resource allocation. That is, if the social members disrespect others' rights to pursue happiness, you get this paradox. The Alice & Bob example is better, but still relies on an assumption on Bob's part that he knows better than Alice what she wants in order to come to this paradox. The classical liberal tends to assume that seeking to control others' behavior for one's own gratification is an evil, and this evil is demonstrated in this paradox because it is required to create it.Segev Stormlord (talk) 14:51, 31 May 2017 (UTC)

This looks a lot like the voting paradox[edit]

How is this different from the Voting paradox? —The preceding unsigned comment was added by Beefman (talkcontribs) .

This one deals with (minimal) liberty; the other is more about democracy and the independence of irrelevant alternatives. So they are similar but not the same.--Henrygb 09:22, 23 August 2006 (UTC)
But isn't the cause of the paradoxes the same (cycles in combinations of ordered tuples)?—The preceding unsigned comment was added by Beefman (talkcontribs).
In plain English, the cause of the paradoxes is indeed that sometimes group decision making with many choices produces strange results when people disagree. But one case points out issues with democracy while the other points out issues with libertarianism. --Henrygb 23:24, 23 August 2006 (UTC)


is something wrong here?

In the article, it says there are 2 pareto optimal solutions. But I could only find one. Did I do something wrong? See photo. __earth (Talk) 10:52, 31 October 2006 (UTC)

Yes, as you seem to think that the only optimal solution is both going. Pareto optimal means roughly that you cannot make one person happier without making another person unhappier. Moving from Alice goes alone either to both go or to neither goes makes Bob unhappier, while moving from Alice goes alone to Bob goes alone makes both unhappier. So Alice goes alone is Pareto optimal (as is both go, since it is Alice's first choice and any change makes her less happy). --Henrygb 17:28, 31 October 2006 (UTC)
I'm really bad at doing it in words. If you're familiar with game theory, could you show me how it is possible to obtain the second pareto optimal in normal form as in the photo? I can't see how Alice goes alone can be an equilibrium. __earth (Talk) 10:37, 1 November 2006 (UTC)
It is not an equilibrium, but it is Pareto optimal - and that is part of the liberal paradox. How do we know? Well, it is Bob's first choice, so it must be Pareto optimal (anything else makes Bob unhappier). But it is not an equilibrium because if Alice goes though the door alone then Bob will not follow her, and so she will turn round and come home. But both go is also not an equilibrium, as if they both go through the door together, Bob will turn round and come home (and then Alice will follow). So the only equilibrium is the non-Pareto-optimal solution of neither going (unless one of them gives up liberty in exchange for the happiness of the other - also called true love). In your photo, presumably a two player game where they do not know what the other will do, Bob goes is dominated by Bob does not go since Bob prefers Alice goes alone to both go and prefers neither goes to Bob goes alone. So Alice can only choose between Alice goes alone and neither goes and prefers the later. --Henrygb 18:02, 1 November 2006 (UTC)
Okay. Let me get this straight. There are two Pareto efficiencies because Bob does not go is a dominating strategy. However, there's only one equilibrium which is both go. So, the paradox is the fact that those efficiencies are not at equilibrium. Do I get that right? __earth (Talk) 01:59, 2 November 2006 (UTC)
No, and no. The reason there are at least two Pareto efficient results is because there are different first choices for the overall result, and in fact there are exactly two. Both go is not an equilibrium, because as they set off together, Bob will turn round and go home (and then Alice will follow). The equilibrium is neither goes since neither alone will make a move for the door, but it is not Pareto efficient (since both go is better for both, but there is no way of achieving it).--Henrygb 09:39, 2 November 2006 (UTC)
Maybe I can help understanding with a diagram I made to understand it myself:
        Bob:            goes     doesn't

   goes                 4,3   >    2,4
                         ^          v
doesn't                 1,1   >    3,2
With the arrows I represent the "movement" each of them (Alice verticals, Bob horizontals) would make in each of the possible states. The Nash equilibrium is evidently only in neither goes, as Henrygb explained.
Both states "Alice going alone" (2,4) and "both going" (4,3) are Pareto optimal because if you are in one of these states, you cannot move to another state without making one of them less happy. This will always hold for the states wich are strictly prefered by one party.
It's noteworthy for me that, at least in the example (I've just discovered the topic with this article), the problem arises only if none of the parties consider what the other parties would do is she changes her strategy. For example, if in the state of "both going", Bob would not rationally choose to switch his strategy and stay in home (thus benefiting) because he'd knew that Alice would then stay too (and he prefers both going to neither going). Considering that, I don't quite understand the relevance of the paradox... Maybe that's a peculiarity of the example, and doesn't happen in other worthy circumstances? --euyyn 16:25, 15 November 2007 (UTC)
The parties can and do consider each other's strategies. However, the example you give, "...Bob would not rationally choose to switch ... because he'd know that Alice would then stay too (and he prefers both..." doesn't lead to a rational decision by Bob, since if he reasons that Alice thinks he will choose to go with her (being better for both), he should then choose to stay since that is better for him. Likewise, if he reasons that Alice will recognize his dominant strategy of staying, she will also stay, and his best choice is to stay. Without communication or cooperation, Bob has a dominant strategy of staying, and Alice recognizes this and chooses to stay as well (maximizing her utility given Bob's strategy), leading to the single Nash equilibrium of both staying. So basically, the Pareto optimal outcome of both going is only possible with cooperation. These games only consider strategies by parties seeking to maximize their utility without cooperation between them. So the dilemma is that the best outcome given individual self-interested choice is not Pareto optimal. --cwh —Preceding unsigned comment added by (talk) 21:11, 11 November 2009 (UTC)

Both your explanations are excellent and the diagram and anecdotal description of the Alice and Bob walking in and out of the door greatly helped my understanding of the example. I think it would be helpful to add them to the article. --I (talk) 12:08, 8 June 2008 (UTC)


The provided link to a blog where some pseudo-discussion about the issue at stake is totally irrelevant. Not the least piece of useful information can be gather from there. I would suggest its removal.

anon-- 12:59, 26 March 2007 (UTC)

I agree. Brad DeLong's blog post misses the fact that the term Liberal is used to denote personal liberalism in Waldman's article (non-interference by the state in personal decisions -- like reading porn). He confuses it with economic liberalism. Liberalism means that no individual will be forced to act against their personal wishes. --sam 23:17, 13 April 2007 (UTC)

What kind of liberalism?[edit]

I removed this sentence from the introduction:

Note that this refers to liberalism in the sense of new liberalism.

This was my (not logged in) attempt to make NPOV this sentence:

Note that this uses the modern, or Socialist definition of the word Liberalism, and not the original definition of Classical Liberalism.

That in turn was written by on July 4.

It doesn't seem to be born out by the article, where the only sort of socialism comes in as a desire for Pareto optimality. The liberalism itself is strictly about individual freedom. Perhaps people who know more about this (I just stumbled across the article looking up stuff about Sen) can decide whether this sentence is wrong, or whether instead the rest of the article needs to explain the background in liberalism better. For now, I'm going with the rest of the article. —Toby Bartels 03:01, 12 July 2007 (UTC)

Involving Pareto efficiency unnecessary to create paradox[edit]

Consider a matching pennies game, with each player preferring win results over lose results. Using the same logic as used in the article, player A's personal liberty means that that the joint preference must have both choose heads > A chooses tails and B heads and both choose tails > A chooses heads and B tails. And player B's personal liberty means that that the joint preference must have A chooses heads and B tails > both choose heads and A chooses tails and B heads > both choose tails. It is logically impossible to construe a joint preference which satisfies all of these. Thus, liberalism as described is not only incompatible with Pareto efficiency, but just plain impossible.

Another problem came to me as well. Consider the situation where both Alice and Bob actually have the exact same preference order, namely both to go > neither to go > Alice to go > Bob to go. It would seem obvious that this should also be their joint preference. Yet if one considers only personal liberties (both to go > Bob to go, neither to go > Alice to go, both to go > Alice to go, neither to go > Bob to go) and logical deductions thereof, there is no way to come up with the relationship both to go > neither to go, nor with Alice to go > Bob to go. So even though both have the same desires, by this logic, they'll never come to a decision, each wanting to wait and see what the other does first. -- Milo

I like what you've said and thougth, it has made me think. Considering that the paradox has to have some insight, or it wouldn't carry the name of it's discoverer, I've come to some deductions about what the paradox must be about.
You present two cases:
heads, heads  >  heads,tails
      ^               v
tails, heads  <  tails, tails
in which the "horizontal strategy switchs" (represented by < and > arrows) would be made by player B, and the "vertical switchs" would be made by player A. As you well say, there's no way to construct a joint preference. It is evident from the diagram that no order relationship can be made with the states (keeping individual freedom), as there's no transitivity (in other words, the graph has a cycle). There's no Nash equilibrium, either. There aren't Pareto optimal states, either, as one can move from (heads,heads) to (tails,tails) and viceversa without anybody caring (and the same for player B winning conditions).
But suppose that player A prefers (heads,heads) over (tails,tails). This added preference doesn't change the diagram, nor therefore what we've said about joint preference and Nash equilibria. But it does create a Pareto optimal state in (heads,heads).
So I guess (I don't really know) that the paradox comes to say something like "even if a joint preference can be constructed, it may be incompatible with Pareto ordering".
Your second case is:
both go  <  Alice goes
   ^            v
Bob goes >  neither go
here you can make an order relationship, but, as you point out, it's not a total ordering but a partial ordering (there are state pairs which you cannot sort). I don't see where's the problem you have with this case. There are 2 Nash equilibria, both going and neither going, so if both are at home, they'll stay there, and if they are in their way to the cinema, they'll keep going. The Pareto ordering (which in this case is a total order, as both Alice and Bob have the same preferences) is perfectly compatible with the joint preference order. The possibility of them being stuck in a Nash equilibrium which is not Pareto optimal (neither go, in this case) is not as strong an assertion as saying that the Pareto efficiency orders two states differently from the joint preference order. That's what I think the paradox must be about. In any case, I've never studied the paradox, so maybe I'm wrong. --euyyn 17:51, 15 November 2007 (UTC)


Tafor correcting me. Thecurran 00:56, 10 August 2007 (UTC)

The section on ways out of the paradox[edit]

I wanted to read more about some of the proposed solutions but none of them contain citations, so I've added citation needed tags. The summarizing sentence of that section reads a little like original research, or at least synthesis. 12:35, 2 September 2007 (UTC)

I have problems understanding the first and third ways out:

  • 1: In the first way out, the solution seems to imply the states of the problem aren't {x, y, z} but {x, y, z} x {x, y, z} = {(x,x), (x,y), ..., (z,z)}, that is, that both A and B can chose among "their own" x, y and z. But the preference relationship given is a relationship among x, y and z (and not the tuples, which are the states). Do I have to deduce that the preference of A is (x,x) > {(x,y),(y,x)} > {(y,y), (x,z), (z,x)} > {(y,z), (z,y)} > (z,z) , with no preference defined for the states between curly brackets?
If that is the case, the state (x,z) is already Pareto optimal and the better state in the joint preference (with full personal liberties), so there'd be no paradox in this case... (the states (x,x), (z,z) and (z,x) would also be Pareto optimals, although not Nash equilibria, as (x,z)).
  • 3: I don't understand wether A and B can choose their own w, x, y and z or not. --euyyn 19:01, 15 November 2007 (UTC)

I don't have any citations, but I think one obvious "way out" that we've missed is simply changing preferences. If society wants someone to bike and he wants to drive, then perhaps taxing driving and making the person want to bike instead will be a pareto efficient (and liberal) outcome. Scott Ritchie (talk) 13:54, 30 May 2008 (UTC)

I think that can't be possible by definition, since taxing the driving to force the driver to go by bike makes the driver worse off compared to the original position and is therefore not pareto optimal. --I (talk) 12:06, 8 June 2008 (UTC)


Would someone who understands the language that this article is written in please scrap it and do a complete rewrite in English? Thank you.

Possible way out?[edit]

Suppose Bob pays Alice one util for her to go alone. Then the payoff matrix would look like this:

Bob: goes doesn't

  goes                 4,3   <    3,3 (instead of 2,4)
                        ^          ^

doesn't 1,1 > 3,2

Would this work? (talk) 17:26, 13 February 2009 (UTC)

Yes, side-payments (as they are known) are one way out. But not all problems allow side-payments! CRGreathouse (t | c) 17:51, 13 February 2009 (UTC)
So the Coase theorem basically takes care of the liberal paradox, then? (talk) 00:58, 14 February 2009 (UTC)
I'm not sure how to respond to that. The Cose theorem assumes that trade is possible and cost-free; the liberal paradox assumes that trade is impossible (infinite transaction costs, if you will). In a sense the two show the effect of lowering trade barriers.
But formally, the two can't coexist because of their assumptions exclude the other's.
CRGreathouse (t | c) 17:03, 16 February 2009 (UTC)
A more nuanced Coasian view would say that transaction costs are non-zero and non-infinite, and if the expected benefits from a transaction exceeded these costs, a transaction would occur. At the least, I think the article needs to explicitly mention the unrealistic assumption of infinite transaction costs. This assumption leads to just as impossible of conclusions as the "Coasian" world where markets can deal with all externalities because transaction costs are zero. -- (talk) 13:50, 14 April 2009 (UTC)
Of course here you get into the problem of hidden and immeasurable utilities; this verges on social choice theory. CRGreathouse (t | c) 14:29, 14 April 2009 (UTC)

What if they can decide together?[edit]

What happens, if they could decide together? Not individually... but, let´s say they call each other... Would that solve the problem? I mean, that is the theoretical way to solve externalities in free economy - assumed the negotiations costs are zero you solve externalities in the most efficent way. So, if the part of this article on externalities is the same problem as the paradox, than this could solve the paradox as well... —Preceding unsigned comment added by (talk) 00:18, 22 April 2009 (UTC)

Solving the paradox[edit]

At present, there are three 'solutions' listed to the paradox: (1) restrict the domain, (2) allow contracts, and (3) allow contracts. I think that we should follow the formalism of the paradox more closely. (Of course, this will require adding a formal definition to the article!) The solutions would then come from changing the framework or denying at least one premise. Examples of the former: allow side-payments or contracts; examples of the latter: restrict the domain, allow non-Pareto-optimal outcomes, restrict liberalism. Restricting the domain seems harsh, but Sen puts a good spin on it; restricting liberalism seems bad under that name, but when it goes by its usual name (dictatorship-over-pairs) it's not odd to restrict it in some way; Pareto seems fundamental, but a solution might not be 'far' from optimal. So this seems to be at least five 'natural' solutions.

CRGreathouse (t | c) 19:54, 15 December 2009 (UTC)

The Paradox Arises Because of Irrational Actors[edit]

It seems to me that the paradox only arises because Alice has an irrational order of preferences (of course she does, she's the female! :D) Specifically, if Alice wants to be with Bob primarily, but also thinks it's a good movie, then her order of preference can't rationally be this:

Alice wants: both to go > neither to go > Alice to go > Bob to go

The problem is that "neither to go > Alice to go" is not in Alice's best interest. She should prefer "Alice to go > neither to go", because after all, she DOES think it's a good movie. How can she rationally choose to deprive herself of that when neither scenario affects Bob?

So, if we re-draw the issue using rational actors, their orders of preference should look like this:

Alice wants: both to go > Alice to go > neither to go > Bob to go

Bob wants: Alice to go > both to go > neither to go > Bob to go

Or graphically...

                  Bob Goes    Bob Stays

 Alice Goes          4,3    >    3,4
                      ^           ^
 Alice Stays         1,1    >    2,2

You can see clearly that the equilibrium state is that Alice goes and Bob stays, which is also Pareto Optimal. Therefore, the paradox has been mischaracterized, in that it's not so much a Liberal Paradox as it is an Irrational Actors Paradox. —Preceding unsigned comment added by Kpresidente (talkcontribs) 13:42, 18 December 2009 (UTC)

"Alice wants to be with Bob primarily, but also thinks it's a good movie"
"She should prefer Alice to go > neither to go"
No, I think you've contradicted yourself here. If she "wants to be with Bob primarily", that means she want to be with Bob more than she wants to see the movie. So she prefers staying at home with Bob rather than going alone to the movie.Kavafy (talk) 13:38, 10 February 2010 (UTC)
Your objection is that the description doesn't match the preferences, not that the preferences are per se irrational. I don't agree with the objection -- I think that if she primarily wants to be with Bob, it's rational to prefer to be home with him rather than leave him at home. But even if I did agree, that's a problem with the description, not with the paradox.CRGreathouse (t | c) 13:41, 11 February 2010 (UTC)
of course she does, she's the female! :D -- You lost me with this. Beginning a logical argument with a sexist joke is not a good way to give yourself credence. - Sikon (talk) 11:30, 19 June 2014 (UTC)
But women are irrational. Witness their voting behavior in recent presidential elections! But I'm a male and what do I know?😉😎. (mlg666666contribs) Mlg666666 (talk) 08:33, 18 May 2015 (UTC)

A New Solution Through Dynamism[edit]

Hello again wiki community. I've submitted this solution before but the original paper wasn't yet published so it couldn't appear on the Article (: Welcome to Wikipedia. Sorry to rain on your parade, but I'm afraid we can't use your solution until it is published in a reliable source. Happy editing otherwise. Paradoctor (talk) 19:50, 6 July 2014 (UTC)). Now it is published, and I've tried to rewrite my original post to make it easier to read:

Description: There is a copy of a book and it must be given either to Lewd to read (L), to Prude to read (P), or disposed of unread (U). In decreasing order of preferences: Lewd: P, L, U | Prude: U, P, L.

Equilibrium: If Lewd knows Prude decides to read, Lewd won’t read. If he knows Prude decides not to read, Lewd will. So there’s no dominant strategy for Lewd, he decides what to do depending on Prude’s decision. If Prude knows Lewd decides to read, Prude won’t read. If he knows Lewd decides not to read, Prude won’t either. So “not to read” is a dominant strategy for Prude, no matters what Lewd decides, he won’t read. Lewd know Prude decides not to read, and Lewd prefers to read it himself rather than have it disposed of, so he decides to read. The outcome is “Lewd reads”.

Paradox: “Lewd reads” is regarded as worse than "Prude reads" by both Prude (U > P > L) and Lewd (P > L > U), and the chosen outcome is therefore Pareto inferior to another available outcome—the one where Prude reads the book.

Dynamic Solution (my new proposal): Instead of both deciding what to do at the same time, they should do it one after the other. We've seen Lewd have a dominant strategy in no reading, no matters what Prude does, Lewd won’t read, so if the first one to decide is Lewd, we’ll end with the same outcome: “Lewd reads”. What if Prude moves first? If he decides not to read, then Lewd will decide to read, same outcome. However, if Prude decides to read, Lewd won’t. “Prude reads” is preferred by Prude (and also Lewd) than “Lewd reads”, so he will decide to read (with no obligation, voluntarily) to get this Pareto Efficient outcome.

Theorem (my new proposal): If there's, at least, one player without dominant strategy, the game will be played sequentiality (one after the other) where players with dominant strategy and need to change it (if they are in the pareto optimal they don't have to) will be the firsts to choose, allowing to reach the Pareto Efficiency without dictatorship nor restricted domain (so respecting conditions) and also avoiding contracts' cost such as time, money or other people. If all players present a dominant strategy (as prisoners' dilemma), contracts may be used.

Publication: I guess that the need for the reliable source is twofold. First, attest to the accuracy of the solution. Second, prevent someone stealing someone else's work. Today it has been published at University webpage: (the paper is available in Spanish; You can check the poster to see it just looking at top right and down left to see the two pay-off matrices ( Given the fact it is a simple and logical solution, you don't have to blindly trust me (that's the reason why I wrote the example and the dynamic solution and not just the theorem). To check the authority, I hope you can trust a well-known Spanish University, 'Universitat Autònoma de Barcelona'.

Roomfordessert (talk) 00:04, 30 August 2014 (UTC)