For reasons already stated (regarding willingness to pay), this can't be right. In your example, people are just buying a bundle of goods; one private and another public. The value people place on the associated private good is irrelevant to willingness to pay for the public good itself.

Yeah, I should say that I'm not really going to take an official stance on the whole combined good bundle question. I'd have to think about exactly how to handle it correctly, and I just don't feel like thinking about that right now.
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Though now that I think about it a bit, I think the problem with mjkidd's 'screw over others' example was that it dealt with utility, and didn't include a willingness to pay. That might be why you can talk about the two goods, but don't need to worry about saying the free-riders are 'buying' something to screw over others. But there is that difference between the two situations...

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further edit: That is why Scolar said to examine the easier case(s) instead of adding a lot of complicating factors. Sometimes the extra assumptions/goods hide what's going on a bit with the basic public goods allocation problem, and sometimes they add in a lot of theoretical complexity. Maybe I was just confused for a bit regarding how to handle the 'screw others over' pseudo-good, but I've seen other ostensibly simple problems be very confusing to even experts in the field.

His name is Sholar, not Scolar. Just want to get that out there.

Ah, crap. I try to remember his name as one letter missing from "Scholar", and obviously I omit the wrong letter...

Thanks for pointing that out though. I'm consistently misspelling his name. Hopefully not from now on.

This conversation, while interesting, may be near reaching some dead ends. Basically we are looking at the interaction between social institutions (i.e. organizations, laws), cultural practices, and the ability for various actors to coordinate their actions in a repeated but finite game (life). Ideally, we want to produce "socially optimal" outcomes, but how we define optimal is actually dependent on individuals and the cultures in which they are situated, so we're already going to stumble when it comes to trade-offs between equitable distribution of goods and efficient production of goods. I suppose an interesting place to start is trust / honesty, and how we might induce actors to trust one another in societies with large, heterogeneous, and relatively transient populations. That sort of analysis requires a more detailed understanding than I suspect we posses.

No. When you go to a store, you don't try to convince the shopkeeper that the candy bar has more utility to you than it does to him. You offer him more money than it is worth to him. (If you value is less than he does and purchase it, the difference between those values is the surplus that is generated.)

If you valued the candy bar more than he did, but still left the store without purchasing, then that would be an example of inefficiency. (Also inefficient: you valued is less than he did but the transaction still took place. This case would violate our assumptions about rationality and markets.)

For a public good, imagine a large group of people. They all have a price they are willing to pay for the good. If the sum of that money (not what they say they are willing to pay, but their actual private value) exceeds the cost of provisioning the good -- and yet the good is still not produced -- that is an example of inefficient underproduction.

I don't know that it makes sense to discuss your example before we agree on baseline definitions. What I will say is that in a quick reading, you had Tom bidding $50 secretly but $150 publicly. That suggests that the "pride" is worth at least $100 to him, not the $50 than you stipulated. But the entire exercise is a little tricky...

"Optimal" depends only on individual preferences and the cost of realizing their desires.

The question of equity doesn't enter into it at all, except insofar as the individual actors are willing to pay for it.

I am too tired to make the appropriate joke about the revelation principle. Which is, by the way, a wonderful idea in economics. (Briefly: "telling the truth" can be made to be the best strategy for a wide class of games.)

I think that more or less confirms what I was saying. Searching for the mechanism which induces this behavior is difficult when we are dealing with such complex games in practice. We need better social engineering, essentially.

Even with better social engineering, we still need better mechanisms. One looks to improve the world by changing preferences. The other looks to improve the world given those preferences.

Politics versus economics.

(The revelation principle relies on a trustworthy mediator, and basically says that we can simulate the optimal outcome under certain circumstances. It's better thought of as a tool for analyzing problems than as a universal salve; I don't agree that it has the philosophical implications you are drawing.)

Insofar as money is proportional to utility and actors will tend to maximize utility, the situation where the public good is produced in the optimal amount will tend to maximize the aggregate utility of the population, correct? Which is to say, a utilitometer might not be necessary to determine if a public goods situation is efficient, but it is certainly sufficient, right? I certainly admit that I've only taken three college-level economics courses, and those are ten years past now, so I apologize for any misunderstandings my ignorance might have caused.

I guess there's a third good in the example I described, shame. Not really a third good, just negative pride. In the private bid version Tom knowingly free rides for 50 dollars. In the public bid version if Tom were to bid 50 dollars then he would receive -50 dollars worth of pride (-$50 candy bars), the 50 dollars that he saves ($50 of candy bars), and -- assuming the rest of the town bids the same as he does -- 50 dollars worth of public good. However, we know that he is not indifferent between the 51st-100th dollar worth of public good produced and 50 dollars of shame or pride or candy bars.

I started this line of argument because I objected to a party being part of an assurance contract still being called a free rider; I said that it was simply a matter of the assurance contractor demanding the wrong price. I'd like to modify that objection somewhat and say that the free rider problem is instead a subset of a larger problem of the voluntary funder of a public good not enjoying the effects of his contribution. While perhaps this phenomenon would more often lead to underproduction of the public good rather than overproduction, in certain circumstances this problem could lead to the overproduction of the public good.

I have a feeling that when you say "proportional" you are secretly thinking "equal" (e.g., that is what is driving your intuition, even if you don't think so). When I buy a candy bar for $1, the resulting utility to me must be worth at least $1, but could be more. $1.33, say. I imagine that you'll agree with that statement when you read this, but the way you write suggests that's not how you're thinking about things.

For the rest...you are just making life complicated with all of these additional considerations (they don't help to explain anything), layered on top of some very arbitrary assumptions (which exclude the possibility of diminishing marginal utility, for example). It's probably best to abandon that edifice and start over. Forget psychology. Forget extra goods. Start simple.

Money and one good. That's all you need.

I don't agree with this. Equity considerations don't (or needn't) enter into the calculus. For most social policy considerations that nominally involve equity, a lower level economic justification exists. Many social welfare policies can be framed as responses to tendencies in human behavior that pose systemic risks to social stability (the minimum wage as bulwark against bread riots).

Moreover, I'm not sure it's possible to articulate a non-arbitrary standard for equity. How can we neutrally decide the definition?

I agree with Dr. Modern here...the socially optimal level of production just has to do with people's individual desires for the good. Nothing with society's norms or equity or anything like that. It's purely an efficiency argument.

That is not to say that equity isn't an important consideration. It's just that one ought to know what happens to the efficiency side of things when making informed decisions. Most policies that increases equity decreases efficiency. So for those policies, there are gains (assuming equity is a good thing) and there are losses, from the decrease in efficiency. To determine if the tradeoffs from the policy are overall beneficial, you need to look at both the gains and losses.

And, as Dr. Modern said, talking about equity is tricky--who's definition? Or, how do we combine definitions as a society? Efficiency is a lot easier to discuss since it isn't open for interpretation. That might make talking about efficiency less 'sexy', but just as important, as talking about equity.

I think you folks are talking a level above me. I'm just saying we want a lot of goods, but we also want those goods to be spread out somewhat "fairly". That we can put both of these under the umbrella "maximize utility" does not negate that these are two separate considerations in maximizing utility, each of which has the distinct advantage of being measurable.

Now I just have no idea what you're talking about. Fairness ≠ efficiency (an efficient outcome can seem even grossly unfair), and efficiency is not defined in terms of utility. I also have no idea how you propose to measure fairness.

That's true... "fairness" per se is difficult to measure, though I'd posit it's easier to measure than utility, if only by asking people how "fair" they think distributive schemes/outcomes are. At any rate, we can just look at something like a GINI measure of wealth inequality.

This measurement method seems likely to become hopelessly mired in cognitive biases and self-serving answers.

Could you give me a brief primer on Gini coefficients? I read the Wikipedia entry, but want to make sure I understand the operative terms before going further with this line of discussion.

True, doesn't mean it can't tell us something useful.

My understanding is less good than Wikipedia's. It's just a mathematical measure of how unequal a distribution is (which is not the same as how spread out it is) found by figuring out how far people are from average.

The problem, generally speaking, is that people are terribly inaccurate when they estimate inequality (based on surveys of Americans, at least).

I also imagine that, whatever people say, talk is cheap. More concretely, I think there is a lot of tension between seeking an equitable process versus equitable outcomes.

For Gini coefficients: imagine ordering people from most destitute to wealthiest [x-axis], and then plot their accumulated wealth [y-axis]. If we label both axes with percentiles, then pure equality is a line with slope 1, from the origin at (0,0) to (1,1) -- the accumulated wealth of everyone is 100%, and pure equality means that the poorest X% of people control exactly X% of the wealth. The actual curve will have nonnegative second derivative ("concave up") and lie beneath that line of pure equality. If the curve passes through, (.8,.2), this would mean that the poorest 80% control only 20% of the wealth.

The area under the curve then varies between ~0 (for pure inequality -- 1 person out of billions controls all of the wealth) to .5 (everyone is equal). The Gini coefficient then is 1-[area]/2 -- so 1 is pure inequality and 0 is pure equality. One can do this for all anything, really, not just wealth...it's a now-standard single measure of discrimination (in the sense of how well some model predicts something) as well. Although it is, of course, not magic (one number describing a distribution contains only so much information) it is pretty handy.