12 Dec 08
2 edits
Originally posted by KazetNagorraYou can repeat it all you like, but that's not a PD. A PD is about the presence of a dominant strategy that leads to an equilibrium where everybody defects.
The wealthy are better off by having healthier and better educated poor people, but they are even better off if they don't have to fund it themselves. There is no decision of a poor person involved here.
12 Dec 08
Originally posted by PalynkaThe equilibrium is that all the wealthy people defect and no one is left to pay for health care and education for the poor, even though the wealthy are better off paying for it collectively.
You can repeat it all you like, but that's not a PD. A PD is about the presence of a dominant strategy that leads to an equilibrium where everybody defects.
12 Dec 08
Originally posted by KazetNagorraIs this thing on? *tap tap tap* It's not a PD.
The equilibrium is that all the wealthy people defect and no one is left to pay for health care and education for the poor, even though the wealthy are better off paying for it collectively.
Where's the dominant strategy?
12 Dec 08
Originally posted by KazetNagorraTo make this clear, you then believe that the prisoner's dilemma applies to this if the two agents are rich and decide by themselves what to contribute for a third party (the poor), which is not directly in the game. Is that it?
The dominant strategy is not contributing to the health care and education of the poor. I don't understand why (you think) it's not a PD.
12 Dec 08
1 edit
Originally posted by PalynkaThere don't have to be two agents, there can be many, which is the case here since there are many "wealthy" people. The dilemma is as follows: there are arbirarily many rich people, such that the contribution from one individual is neglegible. The options are:
To make this clear, you then believe that the prisoner's dilemma applies to this if the two agents are rich and decide by themselves what to contribute for a third party (the poor), which is not directly in the game. Is that it?
Cooperate: contribute to health care and education of the poor.
Defect: don't contribute.
The best option for the wealthy collectively is to cooperate, so that crime is lower, social cohesion is improved, productivity of the poor is increased, democracy is improved through more informed choices, etc. This more than offsets their modest decline in material wealth on the short term (on the long term, this is also increased to the productivity gain). The best outcome for an individual is to defect and have all the others play cooperate. But if all the others defect, the better choice is also to defect since the individual contribution is neglegible, making defect strictly dominant, and the only way out of the PD is a mandatory tax, taxing up to the point where further increasing the tax causes too much losses in material wealth and too few gains in health care and education quality.
12 Dec 08
Originally posted by KazetNagorraThe thing is that there are never arbitrarily large amounts of wealthy people. The marginal contribution of each individual is not zero and, even if it's extremely small, then it leads to progressive increases in the contribution (as the aggregate contribution increases with each iteration).
There don't have to be two agents, there can be many, which is the case here since there are many "wealthy" people. The dilemma is as follows: there are arbirarily many rich people, such that the contribution from one individual is neglegible. The options are:
Cooperate: contribute to health care and education of the poor.
Defect: don't contribute. ...[text shortened]... s too much losses in material wealth and too few gains in health care and education quality.
The strong assumption of zero marginal benefit from contribution is required, but that then requires an infinite amount of players. Even if it's finite and extremely large, the result breaks down.
12 Dec 08
Originally posted by PalynkaI don't see how it breaks down because the contribution of one individual to all tax revenue is neglegible.
The thing is that there are never arbitrarily large amounts of wealthy people. The marginal contribution of each individual is not zero and, even if it's extremely small, then it leads to progressive increases in the contribution (as the aggregate contribution increases with each iteration).
The strong assumption of zero marginal benefit from contribution ...[text shortened]... n infinite amount of players. Even if it's finite and extremely large, the result breaks down.
12 Dec 08
How is it that the wealthy would be better off if they all contributed? It seems this is just an adverse selection market failure, not a prisoner's dilemma.
Regardless of the PD issue, I do think an argument can be made that universal health care is on net a welfare improvement (according to a utilitarian social welfare function) because it solves the adverse selection problem. Forced entry means all the risk is pooled so that the law of large numbers can work its magic.
Note that I'm not advocating UHC. I would like to see more research done on the problem (very difficult to model by the way). I'm saying that it is not clearly welfare reducing like some people presume.
13 Dec 08
Originally posted by PalynkaThat's not what negligible (just found out I've been spelling it wrong the whole time) means. A drop of water is negligible for the purposes of a swimming pool, yet if you take a very large number of drops of water out of the pool, it will be empty. Likewise, for the purposes of tax, the contribution of a single person is negligible, yet if no one contributes the excrements will hit the air dispenser. There is no contradiction or breakdown here.
It's not zero.
13 Dec 08
8 edits
Originally posted by KazetNagorraWhether or not this is a PD depends critically on the degree to which improved health for the poor increases the utility of a rich person compared to how much private consumption does.
I gave some arguments for this a few posts back.
Consider the following game. If both pay for health care (P) then, following your assumptions that the rich benefit from a healthier poor, both get a payoff of 4. If one pays and the other does not (DP), then health care is underprovided and the poor are not as healthy so both players have a lower payoff. The player who defects however gets a bit higher payoff because he can gets more private consumption. Finally if neither contributes, then the poor get no funding and both players get low payoffs (despite having more private consumption).
. . . . . . . . . . . . .Rich 1
. . . . . . . . . . . P . . . . . DP
Rich 2 . P . . . 4,4 . . . . . 3,2
. . . . . .DP . . 2,3 . . . . . 1,1
This game is not a PD. In fact, the dominate strategy is for both to pay. The key reason is that the benefit of a healthier poor is high to the players relative to private consumption.
If we instead assume that the benefit of a healthier poor is small relative to private consumption, then we get a payoff matrix with this structure:
. . . . . . . . . . . . .Rich 1
. . . . . . . . . . . P . . . . . DP
Rich 2 . P . . . 3,3 . . . . . 5,2
. . . . . .DP . . 2,5 . . . . . 4,4
This is also not a PD. Although here the dominate strategy is for both players to not pay, the equilibrium where both don't pay gives more utility to each than the one where they both pay. Even though the both play outcome gives each a healthier poor, the don't pay gives each more private consumption (which they value relatively higher than helping poor).
This final game has a PD structure. The key is to justify the payoff matrix.
. . . . . . . . . . . . .Rich 1
. . . . . . . . . . . P . . . . . DP
Rich 2 . P . . . 4,4 . . . . . 5,0
. . . . . .DP . . 0,5 . . . . . 1,1
Here if both reduce private consumption and pay for healthcare they get a pretty good payoff. The health of the poor must be highly valued by the players. If one player defects, then the one who pays get 0 so the reduction in public health has a big effect on the players' payoffs. Meanwhile the additional consumption afforded to the defector hardly changes his payoff. So far it is clear that providing additional healthcare is highly valued relative to additional consumption. In the both defect equilibrium, however, healthcare is not provided and both get increased private consumption. The payoffs however are too high to be consistent with the story we've built so far. In this case there is not healthcare to the poor, which should have a big decrease in payoffs. It does, but not by anymore than when healthcare was only underprovided.
Can you construct a payoff matrix with a prisoner's dilemma for which the payoffs seem consistent with the implied relative values of private consumption and healthcare?
16 Dec 08
2 edits
There are not just 2 players in this particular game. The dominant strategy will always be to defect, even if the gain in material wealth is very small en the gain in health care quality is very high, as long as the individual contribution is small enough to be negligible. The loss of the material wealth remains constant, but the individual gain in wealth through better health care scales inversely with the population of the wealthy.
16 Dec 08
Originally posted by KazetNagorraThe number of players is really not important. The effect that you describe could just as easily be embedded in the payoff matrix.
There are not just 2 players in this particular game. The dominant strategy will always be to defect, even if the gain in material wealth is very small en the gain in health care quality is very high, as long as the individual contribution is small enough to be negligible. The loss of the material wealth remains constant, but the individual gain in wealth through better health care scales inversely with the population of the wealthy.
Basically you've presented the free rider problem which can be thought of as a PD.