I’m suddenly confused about the logic of imposing higher taxes as a way of calling a “truce” in positional races. Help me.
Suppose everyone has a strong preference for higher relative income. Arms race logic implies that people will increase their effort to move up position, but that, in order not to get passed, others will increase their effort to the same degree, and thus, there is a lot more expenditure of effort, but almost no one actually moves up. Since effort is expensive, everybody in the race would be better off if they could stay in position while spending less. A “truce” enforced by a credibly commited third part allows everyone to spend less, while losing nothing. That’s Pareto-fantastic!
Here’s where I’m getting stuck. How is a tax on income (or consumption) like a truce? I just don’t get it. OK. Think it through, Will. Suppose there’s a flat tax of 10 percent. You earn $10 and I earn $9. After tax, you earn $9 and I earn $8.1. Our relative positions have not changed, and neither have the ratio of our earnings. If we cared only about relative position, this would not be a brake on competition. Suppose the tax is progressive. You are taxed at 15 percent, and I’m taxed at 10 percent. Now you’re at $8.5 after tax, and I’m at $8.1. Woo hoo! I’m catching up! If I’m not seeing your tax rate, just your level of consumption, it may seem that you are within my sights, and that the cost in terms of effort of passing you has gone down. And if you care as much as I do about relative position, you’ll find this unnerving. In order keep the pretax gap between us at, you’d now need to make about $11. Where is our reduced incentive to work?
This stuff is confusing because the point is that there’s no particular taste for the marginal dollar, except insofar as it plays into the positional race. In the position game, I’m no longer trading work for dollars, such that fewer dollars leads me to work less. I’m trading work for position in the race. But I think the tax-as-truce literature is equivocating. One the one hand, we are motivated to work by our taste for relative position, not absolute income. But on the other, if the state reduces the amount of income to be gained from work, we’ll work less because we’re motivated by absolute income?
It seems to me that a flat tax leaves the position game totally unchanged. If people don’t care about absolute income, and you reduce income by the same proportion through the distribution, then, well, no one cares.
Suppose we each have some function that takes the subjective value to us of moving up (or not moving down), multiplies it by the perceived probability of moving up (or down) a position, gives the expected value of spending a unit of effort, and thereby determines the effort we put into the race. The claim of Frank, Layard, and others is that we are all built such that the value to us of moving up and not moving down is high. Anyway, when the probabilities of moving up or down go up, we put more effort into the race. Now, suppose we represent the probability of moving positions as partly a function of our representation about how much effort others are planning to spend, but also as a function of the size of the gap between us and the positions ahead and behind. If there is a huge gap between me and the next guy, my effective motivation to compete for that position may be next to nil, even if I like higher position very much. And if the guy behind me is way behind, I’ll know he won’t be very motivated to catch me, and so I won’t be very motivated to speed up. In this case, a truce would amount to maximizing the size of the gaps in the income distribution. In which case, couldn’t a progressive tax work something like the opposite of a truce. Wouldn’t an increase in inequality, or something else that dispirited people about mobility, be what we are looking for?
At first blush, then, it seems a truce might require something like a caste system, with very large gaps in income between castes. But then, of course, people will start caring only about the within-caste race. The income distribution as it is is fairly continuous until the upper reaches, where it starts getting gappy. (There may be no one, for example, who earns anything between $18 and $20 million, for example, though you can be sure that someone earns between $180 and $200 thousand.) Would it be possible to have a optimally discountinuous system? Perhaps there could be a government-mandated payscale. You either earn $10K, 20K, 40K, 80K, 150K, $500k, $2mil, $10mil, or $100mil. I’m pretty sure that would work as an effective truce. In reality, of course, it would just move positional competition to margins other than income. And you’d lose a massive amount of productivity. (If your labor is worth 35K, tops, you’ll probably produce only about 20K, because what would be the point.) But that’s the point, right? We produce too much and it does us no damn good. Anyway, ugly, ugly, idea.
So, real economists, am I really screwed up? How exactly is it that Frank-style progressive consumption taxes, say, are supposed to amount to a truce in the positional race if it is the position signaled, rather than the number of dollars spent, that matters to us?
Well, OK. Let’s see if I can think how a Frank tax works. A progressive consumption tax adds to the price of everything, and expensive things most. So people hit their budget limit faster. So the biggest house the richest guy can afford to buy is smaller than it would otherwise be. It’s all about the “frames of reference” within which we evaluate the adequacy of our consumer goods. My 1500 sq ft house seems less inadequate when compared to a 3000 footer than with a 5000 footer. So smaller (and cheaper) objectively adequate houses are more likely to seem subjectively adequate by reducing the size of the biggest. More people will be happy with what they have got, and they will have spent less to get it. Sigh… I’ve spent too long on this… But aren’t the best positional goods frame of reference busters? Won’t some people, with the strongest taste for status, be willing to pay the tax to send the status signal? What if, ala Zahavi’s handicap principle, the tax itself becomes a signal. (“Do you know how much tax that guy had to pay for that boat… He must be loaded!“) If we are primarily interested in signaling position, not money, then won’t the demand for signaling be price insensitive? If I have to work longer hours to afford the house that sends the signal, then won’t I just work longer hours? Again, it seems like what we need is a kind of gappiness that reduces peoples’ perceived probability of successfully signaling a position higher than the next closest guy. Anyway, your turn…
I think your objections are well taken, if not quite rigorous yet. But if I wanted to construct a simple model that supported a tax, I think I would assume agents have preferences over *both* absolute income *and* relative income. When deciding whether to exert additional effort, I will compare the marginal benefit, in terms of both absolute and relative position, to the marginal cost in terms of exertion and time. Now, what does a tax do? It will reduce the marginal benefit absolute income, even if it has no effect (in equilibrium) on relative income. Therefore I will tend, on the margin, to exert less effort. So will the other guy. As a result, we’ll both work less than before, with little change in our relative positions.
I think your objections are well taken, if not quite rigorous yet. But if I wanted to construct a simple model that supported a tax, I think I would assume agents have preferences over *both* absolute income *and* relative income. When deciding whether to exert additional effort, I will compare the marginal benefit, in terms of both absolute and relative position, to the marginal cost in terms of exertion and time. Now, what does a tax do? It will reduce the marginal benefit absolute income, even if it has no effect (in equilibrium) on relative income. Therefore I will tend, on the margin, to exert less effort. So will the other guy. As a result, we’ll both work less than before, with little change in our relative positions.
I think your objections are well taken, if not quite rigorous yet. But if I wanted to construct a simple model that supported a tax, I think I would assume agents have preferences over *both* absolute income *and* relative income. When deciding whether to exert additional effort, I will compare the marginal benefit, in terms of both absolute and relative position, to the marginal cost in terms of exertion and time. Now, what does a tax do? It will reduce the marginal benefit absolute income, even if it has no effect (in equilibrium) on relative income. Therefore I will tend, on the margin, to exert less effort. So will the other guy. As a result, we’ll both work less than before, with little change in our relative positions.
I am not an “economist”, but I have an ear for verbal obfuscation and unexamined premisses. This whole gap analysis seems to me typical technical jargon intended to intimidate discussion instead of clarifying it. While I admired your economical way of presenting the problem, I finished without the slightest interest in solving it.
The unexamined, or unmentioned, premiss is the belief that whatever tax is chosen must have the effect of increasing overall productivity. But what if that is not the province of taxes at all. What if taxes are just that — taxes, or levies, in order to allow the society as a whole to do things it needs to? George Lakoff prefers to call taxes “dues” which we pay to society (our predecessors) to enjoy the conveniences (infrastructure) it has already provided for us.
I am not an “economist”, but I have an ear for verbal obfuscation and unexamined premisses. This whole gap analysis seems to me typical technical jargon intended to intimidate discussion instead of clarifying it. While I admired your economical way of presenting the problem, I finished without the slightest interest in solving it.
The unexamined, or unmentioned, premiss is the belief that whatever tax is chosen must have the effect of increasing overall productivity. But what if that is not the province of taxes at all. What if taxes are just that — taxes, or levies, in order to allow the society as a whole to do things it needs to? George Lakoff prefers to call taxes “dues” which we pay to society (our predecessors) to enjoy the conveniences (infrastructure) it has already provided for us.
I am not an “economist”, but I have an ear for verbal obfuscation and unexamined premisses. This whole gap analysis seems to me typical technical jargon intended to intimidate discussion instead of clarifying it. While I admired your economical way of presenting the problem, I finished without the slightest interest in solving it.
The unexamined, or unmentioned, premiss is the belief that whatever tax is chosen must have the effect of increasing overall productivity. But what if that is not the province of taxes at all. What if taxes are just that — taxes, or levies, in order to allow the society as a whole to do things it needs to? George Lakoff prefers to call taxes “dues” which we pay to society (our predecessors) to enjoy the conveniences (infrastructure) it has already provided for us.
Dammit Will, I’m a philosopher, not an economist!
Noting that, let me lay out some thoughts and about the tax and creating a disincentive to relative position competition. I’m on a time limit so I will write another comment later, but here is a start.
1) People are motivated by combinations of preferences for absolute wealth, working less and relative wealth.
2) People will exchange work for absolute wealth and/or relative wealth in the proper amounts, but not for amounts which are too small.
3) Through taxation, you can decrease the amount of absolute wealth that is gain from work exchanges.
4) Therefore, People will have less incentive to work. If the problem is needless production, this may reduce it. We assume that generally the more necessary things will still be purchased and therefore produced, and less necessary things will not be.
This leaves us with the following problem: although work/production will be down, there may still be the same amount of production due to desire for relative position.
If relative and absolute wealth are seen as linked however, this may change the level of desire for relative wealth. Let me clarify.
I desire to be the richest person in the world. Why? Because I saw a show which talked about all the stuff he has. I also read some statistics about all the stuff that people in the top 10% of income holders have. It is a lot of stuff! This makes me totally want to be in that class of people.
To the extent that absolute wealth is decreased at the top, being at the top is less desirable. I will not claim that this applies in all cases. For example students for example compete with test scores even at levels where the score will not affect their end grade and no one will ever notice outside or after the class. But there are a lot of marginal cases, and often when the difference between top and bottom is minimized, people just don’t care (as much) where they fall.
I’ll suggest that this applies particularly to progressive taxation, as it makes it that much harder to have increadable differences in wealth. I will consider further my thought that people don’t just want to have some more than others, it is often wanting to have ‘significant’ amounts more than others. I want to make 50 times as much as you, not $50 more than you. I would only do so much to get that though, so the harder it is for me to be many times richer than you, the less likely I am to think that it is worth doing.
Just some thoughts to start with while I work out others.
Dammit Will, I’m a philosopher, not an economist!
Noting that, let me lay out some thoughts and about the tax and creating a disincentive to relative position competition. I’m on a time limit so I will write another comment later, but here is a start.
1) People are motivated by combinations of preferences for absolute wealth, working less and relative wealth.
2) People will exchange work for absolute wealth and/or relative wealth in the proper amounts, but not for amounts which are too small.
3) Through taxation, you can decrease the amount of absolute wealth that is gain from work exchanges.
4) Therefore, People will have less incentive to work. If the problem is needless production, this may reduce it. We assume that generally the more necessary things will still be purchased and therefore produced, and less necessary things will not be.
This leaves us with the following problem: although work/production will be down, there may still be the same amount of production due to desire for relative position.
If relative and absolute wealth are seen as linked however, this may change the level of desire for relative wealth. Let me clarify.
I desire to be the richest person in the world. Why? Because I saw a show which talked about all the stuff he has. I also read some statistics about all the stuff that people in the top 10% of income holders have. It is a lot of stuff! This makes me totally want to be in that class of people.
To the extent that absolute wealth is decreased at the top, being at the top is less desirable. I will not claim that this applies in all cases. For example students for example compete with test scores even at levels where the score will not affect their end grade and no one will ever notice outside or after the class. But there are a lot of marginal cases, and often when the difference between top and bottom is minimized, people just don’t care (as much) where they fall.
I’ll suggest that this applies particularly to progressive taxation, as it makes it that much harder to have increadable differences in wealth. I will consider further my thought that people don’t just want to have some more than others, it is often wanting to have ‘significant’ amounts more than others. I want to make 50 times as much as you, not $50 more than you. I would only do so much to get that though, so the harder it is for me to be many times richer than you, the less likely I am to think that it is worth doing.
Just some thoughts to start with while I work out others.
Dammit Will, I’m a philosopher, not an economist!
Noting that, let me lay out some thoughts and about the tax and creating a disincentive to relative position competition. I’m on a time limit so I will write another comment later, but here is a start.
1) People are motivated by combinations of preferences for absolute wealth, working less and relative wealth.
2) People will exchange work for absolute wealth and/or relative wealth in the proper amounts, but not for amounts which are too small.
3) Through taxation, you can decrease the amount of absolute wealth that is gain from work exchanges.
4) Therefore, People will have less incentive to work. If the problem is needless production, this may reduce it. We assume that generally the more necessary things will still be purchased and therefore produced, and less necessary things will not be.
This leaves us with the following problem: although work/production will be down, there may still be the same amount of production due to desire for relative position.
If relative and absolute wealth are seen as linked however, this may change the level of desire for relative wealth. Let me clarify.
I desire to be the richest person in the world. Why? Because I saw a show which talked about all the stuff he has. I also read some statistics about all the stuff that people in the top 10% of income holders have. It is a lot of stuff! This makes me totally want to be in that class of people.
To the extent that absolute wealth is decreased at the top, being at the top is less desirable. I will not claim that this applies in all cases. For example students for example compete with test scores even at levels where the score will not affect their end grade and no one will ever notice outside or after the class. But there are a lot of marginal cases, and often when the difference between top and bottom is minimized, people just don’t care (as much) where they fall.
I’ll suggest that this applies particularly to progressive taxation, as it makes it that much harder to have increadable differences in wealth. I will consider further my thought that people don’t just want to have some more than others, it is often wanting to have ‘significant’ amounts more than others. I want to make 50 times as much as you, not $50 more than you. I would only do so much to get that though, so the harder it is for me to be many times richer than you, the less likely I am to think that it is worth doing.
Just some thoughts to start with while I work out others.
I take it you’ve read Layard’s “Rethinking Public Economics: The Implications of Rivalry and Habit”? Did you understand the maths? If so it should serve to answer your question fairly straightforwardly. Layard uses a subtractive form for consumption reference effects, embedded in a Cobb-Douglas utility function – which I’m not sure is the best way of doing it, but it probably still captures the essence of things.
The most intuitive way to think about it is simply as an externality: my consumption harms you by reducing your satisfaction with what you have; but I don’t take that cost into account when choosing how much to work and consume. The tax is a standard Pigouvian one, intended to internalise this externality.
The reason I think you’re ending up with a different intuition is essentially Glen’s: the utility function assumed by Layard, Frank etc. (and supported by the data) is one in which both absolute and relative income matter. On the other hand, you seem to be assuming that only rank matters (though to be honest, it’s a little difficult to tell exactly what you’re assuming. I think this is definitely a situation where the maths is useful in enforcing clarity). If it were the case that only rank mattered, there would be no externality at the margin – and the tax (which affects marginal incentives) wouldn’t necessarily have the desired effect. But that’s a rather implausible case to have to make.
I take it you’ve read Layard’s “Rethinking Public Economics: The Implications of Rivalry and Habit”? Did you understand the maths? If so it should serve to answer your question fairly straightforwardly. Layard uses a subtractive form for consumption reference effects, embedded in a Cobb-Douglas utility function – which I’m not sure is the best way of doing it, but it probably still captures the essence of things.
The most intuitive way to think about it is simply as an externality: my consumption harms you by reducing your satisfaction with what you have; but I don’t take that cost into account when choosing how much to work and consume. The tax is a standard Pigouvian one, intended to internalise this externality.
The reason I think you’re ending up with a different intuition is essentially Glen’s: the utility function assumed by Layard, Frank etc. (and supported by the data) is one in which both absolute and relative income matter. On the other hand, you seem to be assuming that only rank matters (though to be honest, it’s a little difficult to tell exactly what you’re assuming. I think this is definitely a situation where the maths is useful in enforcing clarity). If it were the case that only rank mattered, there would be no externality at the margin – and the tax (which affects marginal incentives) wouldn’t necessarily have the desired effect. But that’s a rather implausible case to have to make.
I take it you’ve read Layard’s “Rethinking Public Economics: The Implications of Rivalry and Habit”? Did you understand the maths? If so it should serve to answer your question fairly straightforwardly. Layard uses a subtractive form for consumption reference effects, embedded in a Cobb-Douglas utility function – which I’m not sure is the best way of doing it, but it probably still captures the essence of things.
The most intuitive way to think about it is simply as an externality: my consumption harms you by reducing your satisfaction with what you have; but I don’t take that cost into account when choosing how much to work and consume. The tax is a standard Pigouvian one, intended to internalise this externality.
The reason I think you’re ending up with a different intuition is essentially Glen’s: the utility function assumed by Layard, Frank etc. (and supported by the data) is one in which both absolute and relative income matter. On the other hand, you seem to be assuming that only rank matters (though to be honest, it’s a little difficult to tell exactly what you’re assuming. I think this is definitely a situation where the maths is useful in enforcing clarity). If it were the case that only rank mattered, there would be no externality at the margin – and the tax (which affects marginal incentives) wouldn’t necessarily have the desired effect. But that’s a rather implausible case to have to make.
You guys are awesome. Thanks. Yeah: duh. It looks like the relative strength of our preference for relative and absolute income is going to do a lot of work. I think part of what I’m groping at is that these arguments have the most force when the preference for relative income is extremely strong–which makes the zero-sum aspects of the game seem irremediable. But when the relative preferences are strongest, willingness to pay in effort is going to be pretty insensitive to price. That just might mean that the tax needs to be high. But in that case, in which relative preference is very strong, the tax isn’t exactly calling a truce so much as pushing the fight to another battle field–displacing the status race to another dimension of competition. The relevant question then is really whether the net externalities from the substitute positional race are more or less than the income or consumption race.
Layard seems to argue that (1) people have an extremely strong taste for relative position and (2) if you push them off the income/consumption race, the competition won’t just pop up on another, possibly more harmful, dimension. He implies the only alternative to income/consumption-oriented labor is leisure, and argues that people don’t race on the leisure dimension. Maybe. But that’s not the only relevant dimension. (1) implies that people won’t stop competing just because competition on one dimension has become too expensive. All the tax will have done is lower the relative cost of competing on another dimension. So, an argument for tax-as-truce that involves (1), requires an additional argument identifying the most likely substitute dimension, and showing that competition on this dimension will be more benign. An argument without (1) will have a hard time sustaining itself against “you can always just choose not to care about relative material position” least-cost avoider arguments.
You guys are awesome. Thanks. Yeah: duh. It looks like the relative strength of our preference for relative and absolute income is going to do a lot of work. I think part of what I’m groping at is that these arguments have the most force when the preference for relative income is extremely strong–which makes the zero-sum aspects of the game seem irremediable. But when the relative preferences are strongest, willingness to pay in effort is going to be pretty insensitive to price. That just might mean that the tax needs to be high. But in that case, in which relative preference is very strong, the tax isn’t exactly calling a truce so much as pushing the fight to another battle field–displacing the status race to another dimension of competition. The relevant question then is really whether the net externalities from the substitute positional race are more or less than the income or consumption race.
Layard seems to argue that (1) people have an extremely strong taste for relative position and (2) if you push them off the income/consumption race, the competition won’t just pop up on another, possibly more harmful, dimension. He implies the only alternative to income/consumption-oriented labor is leisure, and argues that people don’t race on the leisure dimension. Maybe. But that’s not the only relevant dimension. (1) implies that people won’t stop competing just because competition on one dimension has become too expensive. All the tax will have done is lower the relative cost of competing on another dimension. So, an argument for tax-as-truce that involves (1), requires an additional argument identifying the most likely substitute dimension, and showing that competition on this dimension will be more benign. An argument without (1) will have a hard time sustaining itself against “you can always just choose not to care about relative material position” least-cost avoider arguments.
You guys are awesome. Thanks. Yeah: duh. It looks like the relative strength of our preference for relative and absolute income is going to do a lot of work. I think part of what I’m groping at is that these arguments have the most force when the preference for relative income is extremely strong–which makes the zero-sum aspects of the game seem irremediable. But when the relative preferences are strongest, willingness to pay in effort is going to be pretty insensitive to price. That just might mean that the tax needs to be high. But in that case, in which relative preference is very strong, the tax isn’t exactly calling a truce so much as pushing the fight to another battle field–displacing the status race to another dimension of competition. The relevant question then is really whether the net externalities from the substitute positional race are more or less than the income or consumption race.
Layard seems to argue that (1) people have an extremely strong taste for relative position and (2) if you push them off the income/consumption race, the competition won’t just pop up on another, possibly more harmful, dimension. He implies the only alternative to income/consumption-oriented labor is leisure, and argues that people don’t race on the leisure dimension. Maybe. But that’s not the only relevant dimension. (1) implies that people won’t stop competing just because competition on one dimension has become too expensive. All the tax will have done is lower the relative cost of competing on another dimension. So, an argument for tax-as-truce that involves (1), requires an additional argument identifying the most likely substitute dimension, and showing that competition on this dimension will be more benign. An argument without (1) will have a hard time sustaining itself against “you can always just choose not to care about relative material position” least-cost avoider arguments.
In ragards to your statements: “the tax isn’t exactly calling a truce so much as pushing the fight to another battle field–displacing the status race to another dimension of competition.” and “identifying the most likely substitute dimension, and showing that competition on this dimension will be more benign.”
The very difficulty of coming up with the substitute may be reason to suspect it would be a truce of sorts. Let me put it the following way. When I gave up competing for relative wealth, I started competing for (hypothetically) intellectual debates or some such. Al Gore, when he lost the election, instead of relative wealth decided to compete with rugged outdoorsmanship, and after that decided to compete for top environmental advocate. You may compete along the dimension of how much you love liberty (“Give me liberty or give me death.” That is how much I love it!) or along the demention of best dressed in a philosophy department. Some may even suggest that you would try to have a better blog than others.
Now, money is an obvious competition, and physical stuff is sometimes, but note that people compete physically along different dimensions.
To this extent, we are not in the same sort of competition as with relative wealth. The problem with relative wealth is that too many people are competing on the same field so there are not enough winners. When we disperse and all compete for different things, our winning is not mutually exclusive. No matter how much better your blog is than Gore’s, he is a better environmental activist than you, and you can both be happy and prideful about it.
In ragards to your statements: “the tax isn’t exactly calling a truce so much as pushing the fight to another battle field–displacing the status race to another dimension of competition.” and “identifying the most likely substitute dimension, and showing that competition on this dimension will be more benign.”
The very difficulty of coming up with the substitute may be reason to suspect it would be a truce of sorts. Let me put it the following way. When I gave up competing for relative wealth, I started competing for (hypothetically) intellectual debates or some such. Al Gore, when he lost the election, instead of relative wealth decided to compete with rugged outdoorsmanship, and after that decided to compete for top environmental advocate. You may compete along the dimension of how much you love liberty (“Give me liberty or give me death.” That is how much I love it!) or along the demention of best dressed in a philosophy department. Some may even suggest that you would try to have a better blog than others.
Now, money is an obvious competition, and physical stuff is sometimes, but note that people compete physically along different dimensions.
To this extent, we are not in the same sort of competition as with relative wealth. The problem with relative wealth is that too many people are competing on the same field so there are not enough winners. When we disperse and all compete for different things, our winning is not mutually exclusive. No matter how much better your blog is than Gore’s, he is a better environmental activist than you, and you can both be happy and prideful about it.
In ragards to your statements: “the tax isn’t exactly calling a truce so much as pushing the fight to another battle field–displacing the status race to another dimension of competition.” and “identifying the most likely substitute dimension, and showing that competition on this dimension will be more benign.”
The very difficulty of coming up with the substitute may be reason to suspect it would be a truce of sorts. Let me put it the following way. When I gave up competing for relative wealth, I started competing for (hypothetically) intellectual debates or some such. Al Gore, when he lost the election, instead of relative wealth decided to compete with rugged outdoorsmanship, and after that decided to compete for top environmental advocate. You may compete along the dimension of how much you love liberty (“Give me liberty or give me death.” That is how much I love it!) or along the demention of best dressed in a philosophy department. Some may even suggest that you would try to have a better blog than others.
Now, money is an obvious competition, and physical stuff is sometimes, but note that people compete physically along different dimensions.
To this extent, we are not in the same sort of competition as with relative wealth. The problem with relative wealth is that too many people are competing on the same field so there are not enough winners. When we disperse and all compete for different things, our winning is not mutually exclusive. No matter how much better your blog is than Gore’s, he is a better environmental activist than you, and you can both be happy and prideful about it.
Will — as conchis points out, the precise mathematical way in which we model preferences matters quite a bit. Math in economics is a pain sometimes, but the alternative is worse.
Can’t we understand the Layard “tax as truce” concept within a prisoner’s dilemma-type framework? IIRC, the key feature of the model isn’t that it is Zero-Sum, but rather that it is Negative Sum. That’s the arms-race analogy.
Suppose there are 2 choices: slack (S) or rat-race (R)
The payoff matrix is
S R
S 10, 10 6,12
R 12, 6 8, 8
Without a tax, the dominant strategy is to rat-race.
But then the government comes in and puts a tax on rat-racers, possibly redistributing the proceeds to slackers, or at least lowering the tax burden slackers would otherwise bear. So the payoff matrix becomes:
S R
S 10, 10 8,10
R 10, 8 6, 6
Now the dominant strategy is to slack.
It’s easy to write down a model where Layard’s policy recommendations are Pareto improving. I just did it in 5 minutes. Go me! But I can also write down a model which gives everyone negative infinite utility if they don’t give Layard the Nobel Prize.
As I think I read on Tyler Cowen’s site: “It’s easy to lie with statistics, but it’s a lot easier to lie without them.” (With theory, for example)
Will — as conchis points out, the precise mathematical way in which we model preferences matters quite a bit. Math in economics is a pain sometimes, but the alternative is worse.
Can’t we understand the Layard “tax as truce” concept within a prisoner’s dilemma-type framework? IIRC, the key feature of the model isn’t that it is Zero-Sum, but rather that it is Negative Sum. That’s the arms-race analogy.
Suppose there are 2 choices: slack (S) or rat-race (R)
The payoff matrix is
S R
S 10, 10 6,12
R 12, 6 8, 8
Without a tax, the dominant strategy is to rat-race.
But then the government comes in and puts a tax on rat-racers, possibly redistributing the proceeds to slackers, or at least lowering the tax burden slackers would otherwise bear. So the payoff matrix becomes:
S R
S 10, 10 8,10
R 10, 8 6, 6
Now the dominant strategy is to slack.
It’s easy to write down a model where Layard’s policy recommendations are Pareto improving. I just did it in 5 minutes. Go me! But I can also write down a model which gives everyone negative infinite utility if they don’t give Layard the Nobel Prize.
As I think I read on Tyler Cowen’s site: “It’s easy to lie with statistics, but it’s a lot easier to lie without them.” (With theory, for example)
Will — as conchis points out, the precise mathematical way in which we model preferences matters quite a bit. Math in economics is a pain sometimes, but the alternative is worse.
Can’t we understand the Layard “tax as truce” concept within a prisoner’s dilemma-type framework? IIRC, the key feature of the model isn’t that it is Zero-Sum, but rather that it is Negative Sum. That’s the arms-race analogy.
Suppose there are 2 choices: slack (S) or rat-race (R)
The payoff matrix is
S R
S 10, 10 6,12
R 12, 6 8, 8
Without a tax, the dominant strategy is to rat-race.
But then the government comes in and puts a tax on rat-racers, possibly redistributing the proceeds to slackers, or at least lowering the tax burden slackers would otherwise bear. So the payoff matrix becomes:
S R
S 10, 10 8,10
R 10, 8 6, 6
Now the dominant strategy is to slack.
It’s easy to write down a model where Layard’s policy recommendations are Pareto improving. I just did it in 5 minutes. Go me! But I can also write down a model which gives everyone negative infinite utility if they don’t give Layard the Nobel Prize.
As I think I read on Tyler Cowen’s site: “It’s easy to lie with statistics, but it’s a lot easier to lie without them.” (With theory, for example)
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