One part of Canada's tax-transfer system increases inequality of wealth. That's not an unfortunate side-effect of the policy; it is deliberately designed that way. It would be very easy to design it differently so that it did not increase inequality.
The policy in question reduces the wealth of many people by a small amount, and makes a very small number of people very wealthy. Those who get wealthy as a result of this policy do so by sheer luck. Nobody argues that those who gain wealth are more morally deserving than those who lose wealth as a result of this policy.
Most government tax-transfer policies try to increase equality, even if there's a cost to doing so. We could scrap some of those tax-transfer schemes easily, and save on those costs, if we wanted to increase inequality. But this particular policy is designed to increase inequality, and has an administrative cost of doing so. By scrapping this particular policy we could increase equality at a negative cost.
The policy in question has cross-party support, at all levels of government. Some parties might want to modify this policy a little, but as far as I know none of the major parties wants to scrap it altogether. And the policy enjoys popular support as well. Anecdotal evidence suggests the poor are especially likely to support this policy.
Any outside observer who looked at this policy alone would conclude that Canadians wanted to increase inequality of wealth. And Canada is not alone.
I'm talking about lotteries. Lotteries redistribute wealth and increase inequality in a way that depends on sheer luck. Lotteries have an administrative cost, and so reduce average wealth. Sure, some part of the revenues are used to fund good things. But a simple lump sum tax on everyone could do the same funding, without increasing inequality at the same time.
A libertarian would find no paradox here. If people voluntarily join a club that increases the inequality of wealth of club members in some morally arbitrary way, the libertarian has no objection. Because it's a voluntary club. A libertarian would also not object to voluntary transfers from rich to poor that reduce inequality. As far as the pure libertarian is concerned, the only thing that matters is that it be voluntary. Whether it increases or reduces inequality is not what matters.
But very few people are libertarian.
Nearly all the rest of us say we value equality, and want the government to use its power to promote equality, providing the cost of doing so is not too great. The benefits of an extra dollar to the poor are greater than the benefits of an extra dollar to the rich. We argue only about which inequalities are morally justified, and how big the costs are of reducing inequality, and whether the costs are worth the benefits.
But when we buy lottery tickets our actions say that we want more inequality. When governments sell lottery tickets their actions say they want more inequality.
We do not begrudge the wealth of lottery winners. Even though we know they are not morally deserving of their wealth, and got it through sheer luck. Perhaps precisely because they got it through sheer luck, and so can't pretend they are more morally deserving than we are (which is what gets us really annoyed at the rich).
There's something paradoxical here. Are we really closet libertarians, despite what we say? Do we really support more inequality, despite what we say? Do we really believe the Utilitarian doctrine that says the poor benefit more from an extra dollar than the rich?
An ultra-quick Google says that one quarter of Canadians buy lottery tickets weekly. That means, at an absolute minimum, one quarter of Canadians want (have a revealed preference for) more inequality. They put themselves behind the Rawlsian Veil of Ignorance, and vote for more inequality.
None of this makes sense to me.
Worthwhile Canadian Initiative 
“Well, guess what, at least one quarter of the population go behind the Rawlsian Veil of Ignorance every week. And they don’t vote that way, even when the cost of equality would be negative.”
Sorry, I guess I still don’t see your point Nick. As Frances explained above, the impact of lotteries on inequality is just a side effect that none of the parties involved are really concerned with. The government isn’t promoting inequality, just collecting revenue. People aren’t supporting inequality, just giving themselves a bit of hope to escape their soul crushing job treadmill, ‘imagining the freedom’ as it were.
Behind a Rawlsian Veil of Ignorance, people would vote to have a society where nobody dies of a heart attack because they got high blood pressure from eating too many potato chips. And yet in reality, governments freely permit the selling of potato chips, companies go to great lengths to produce and sell them, and millions of people buy them, cutting years off their life in the process. Does that mean that governments support people dying of heart attacks, or that people themselves do? Or that it would be wrong to assume that if people were designing how society should look, they wouldn’t include unnecessary heart attacks in their utopian vision?
The existence of lotteries is a failure of our educational system.
Everyone should be required to have covered basic financial literacy – concepts like expected value and compound interest – before the end of grade 10. Even those who drop out of high school need this knowledge – if anything, they need it the most. A few simple math exercises will convince most kids that buying lottery tickets is a bad, bad idea.
There is nothing you study in high school math more important than this. Throw out algebra, geometry, statistics, almost anything else if you have to for the weaker students, but don’t leave vulnerable kids at the mercy of predatory lenders, credit cards, casinos and government lotteries.
There is a social function to lotteries, they are a way for some people to save, who have wrong time preferences. For example if you would like to save for a home, but when presented with a temptation you can’t resist, but after the fact you regret a lottery is a way to commit yourself in a way that removes the option to be tempted.
Declan: the heart attacks are a contingent side-effect of chips. We can imagine chips that don’t cause heart attacks. People don’t eat chips because they cause heart attacks; they eat chips because they taste good, despite the heart attacks.
A lottery that didn’t cause increased inequality wouldn’t be a lottery.
Playing cards with friends can be fun. Playing for money can add to the excitement. But it’s not all about the money. The money is just the salt on the chip.
You could explain lotteries the same way, but it’s harder to.
The main economic case for government policy to increase equality goes like this: the marginal utility of wealth decreases with wealth. As evidence for this statement we point to people’s risk aversion. People with diminishing marginal utility of wealth who maximise expected utility will buy insurance (if it’s not too costly, in the expected payoff sense). People do buy insurance, therefore MU must diminish with wealth. Therefore redistribution from rich to poor (if it’s not too costly) will increase total utility, and therefore the government should do it.
But when we observe a quarter of the population buying lottery tickets, even when it’s costly (because the total payoffs are less than revenue from ticket sales), that very same argument gets stood on its head. They must have increasing MU of wealth. Therefore redistribution from rich to poor will reduce total utility, even if there’s no cost of doing so.
Or, forget about expected utility maximisation altogether. Suppose we observe the government converting people’s grape juice into wine, and losing some juice in the process. (That’s Arthur Okun’s “leaky bucket” metaphor, to represent the costs of redistribution). Then we observe a quarter of the population joining a club to convert their wine back into grape juice, and losing still more wine in the process. That might make us wonder if those people really wanted the government to convert their grape juice into wine.
OT: if instead of buying the lottery ticket and waiting for the draw to find out if it was a winner, you had to commit to paying a loser fee if the ticket you had did not win. Would people still play?
Patrick: my hunch is that “degenerate gamblers” (Mario Puzo’s phrase) would buy still more.
TGGP – I didn’t suggest that a win would necessarily “represent real change”. I didn’t even assume that there was something special about poverty that made the purchase of lottery tickets more rational for poor people than for anyone else. I just did not believe that buying lottery tickets was at all irrational or even incompatible with risk-aversion. I’m in the top half of the income distribution, I have insurance policies and I buy pretty much one lottery ticket a week. And BTW I work with statistics, have a masters degree in economics and am not at all impressed by the “stupidity” assumptions or the preference for inequality arguments.
This being said, I do think that there are inconsistencies between reality and the simplified “rational idiot” type of framework that is used, correctly I think, for analyzing most economic choices. There are puzzles, and this is one when you assume away all non-income related advantages, but I think it still dissolves when you give a little more flexibility to your definition of rationality. In fact, what I suggested is that if you allow for loss aversion to explain some of the risk-aversion (as opposed to leaving it all to diminishing MU of wealth, which is just too ad hoc for my taste), and if that aversion only kicks in beyond a certain threshold, then there is no reason that you would need to treat this as some weakness of the poor schmo’s will, and thus you would not see it a priori as a problem, i.e. as a socially imposed loss of income instead as just another available consumption good, when you put yourself “behind the Veil of ignorance” for ethical purposes.
Also, I have no quarrel at all with Karelis’ theory – it does look quite interesting.
I’m sympathetic to Yvan’s view above. It’s how I want to think. But I still think we are cheating a bit.
We have this preconceived view that: MU diminishes; and equality is good. And when people buy insurance we take this as unproblematic evidence confirming our view. But we refuse to treat people buying lottery tickets as unproblematic evidence of the opposite view. We try to explain away that disconfirming evidence. We add epicycles. We cheat.
Maybe people buy insurance for fun. Maybe they are irrational, in some narrow expected utility sense.
Yep. Maybe people drastically overestimate the risks of an accident (the odds of winning a lottery). Maybe people lay awake nights dreaming of all the bad things that could happen without insurance (dreaming of all the good things they could do if they win the lottery). That’s why they buy insurance. It’s got nothing to do with E(U) maximisation with diminishing MU.
Nick, I think it’s true there is probably something like the opposite of the precaution principle going on here (i.e. giving more weight to extreme events in calculating the expectation, which is not the same as overestimating probabilities) – call it the dream principle, I guess. But what rattles me in your notion of cheating is that you seem to hold to some monotonically decreasing MU as a real heliocentric hypothesis. And I don’t see why the “good” of equality is at all at stakes here anyway – maybe one very specific notion of equality is threatened, but then it’s the one that is closely knit with decreasing MU anyway.
So why should it be cheating to entertain the idea of a globally decreasing MU for most people, although you would have lots of local peaks and valleys, depending on your anticipated projects and/or specific fears on that day? Also, what do we do with real-world loss aversion, i.e. this “bias” we have that makes use lose more utility from losing our 101st dollar than we gained from earning it in the first place? You can’t even have an MU function with this, right? But is it irrational? Is decreasing MU an index of rationality per se?
Jim Sentence got it.
It has to do with increasing equality of opportunity.
But Lotteries don’t sell real improvement (most studies suggest winning the Lottery is a mixed blessing) they sell dreams. Looking at the fact that some people win, is missing the point.
There is another way of looking at it. People are balancing their investment portfolios. There is an unsupply of very high reward, very high risk investments for small investors.
@Tom West – It’s kind of a math game. Us occasional lottery buyers justify buying a bunch at once because given the choice between spending $3 every week vs spending $18 every six weeks, the latter has better odds.
Still not significant, but better.
I buy lottery tickets much less than every six weeks, but usually buy $5 or $10 worth when I do. Usually I’ll walk away with one of the smaller prized ($2-$5, or at least a free play). I also have a policy of not checking my ticket until long after the draw, keeping the dreams alive for free for several weeks.
Lottery pools are the worst. You effectively have to buy in, because being the one person in the office who didn’t participate in a win is so much worse than being out few dollars every week. Even the fantastically low odds make it a good investment.
I have no major insight to offer, but I shall offer some Orwell:
“The existence of lotteries is a failure of our educational system.
Everyone should be required to have covered basic financial literacy – concepts like expected value and compound interest – before the end of grade 10. Even those who drop out of high school need this knowledge – if anything, they need it the most. A few simple math exercises will convince most kids that buying lottery tickets is a bad, bad idea.”
Well, I agree that our education system does a lousy job of teaching basic financial literacy (although I’m curious when that became the responsibility of the school system instead of being something imparted by parents).
But I disagree that the existence of lotteries has to do with ignorance. I think for most lottery players, lotteries sell hopes and dreams. At $5 for a week’s worth of dreams of being a millionaire, that’s not an irrational or poorly thought-out spending choice, that’s a bargain.
Moreover, for someone who wants to be a millionaire (understood as someone who will never have to work again in their life – which nowadays probably means you actually have to be a mutli-millionaire), you’re probably no less likely to achieve your goal by playing the lottery every week than by saving up an extra $5 a week in your investment account (and you’re probably more likely to achieve it sometime soon. Moreover, lottery winnings, unlike investment income, is tax-free). Granted, in either case, the incremental effect of your $5 investment decision on your likelihood of being a millionaire is almost, but not quite, zero, but it’s the “no quite” that keeps people hoping.
Nick, I appreciate you taking the time to elaborate your position. I follow what you’re saying, I just don’t see there’s that much of a connection there. If the winning condition for the lottery was that everyone would become wealthy enough to not work again (leaving the macro problems with that scenario aside for the moment 🙂 people would still play. It’s not the inequality that people want (in my opinion), it’s the wealth, the ability to live their life without having to turn the other cheek to a bunch of jerks every day because they have to stay on the job treadmill or fall through the cracks in society. In fact, given a choice, many if not most people would probably prefer it if everyone else could join them in a life of ease. Of course, this is challenging from a macro perspective to pull off, but then so is making a healthy potato chip that still tastes good.
People aren’t really equipped with a natural instinct for continuous variables (at least that’s one of the things I took away from Steven Pinker’s ‘The Stuff of Thought’ and it matches well with what I see day to day). I think the internal model most lottery ticket buyers have is one where their current state is ‘unhappy’ and buying a lottery ticket gives a very small chance of ‘happy’ with a near 1 probability of ‘unhappy’ Given this internal model, they have nothing to lose by buying a ticket. (Insurance is similar, but in reverse – people see a possibility of two outcomes, ‘No Change’ and ‘Disaster’, buying insurance converts the situation to one where the only option is ‘No Change’ so it makes sense.)
One of the reasons your juice-wine-juice analogy is flawed is because it assumes, by analogy, that all inequality is the same, whereas for most people, the inequality of a random lottery winner getting rich is quite different from the inequality of a system that gives them 0 chance of succeeding while a bunch of jerks get rich because they chose the right parents when they were born or because they were more willing/able to bend the rules and screw people over than other people were (you know, the type of person that the business press calls ‘innovative’). It’s much like the difference between a democracy vs. a dictatorship. Both systems end up creating an inequality of political power, but in one case it is considered legitimate and in the other it is not, because of the difference in the process that generated that inequality.
You can see this in the studies that show how people’s support for redistribution is heavily contingent on whether they believe the current inequality is the result of a fair process or not.
Tyronen: “A few simple math exercises will convince most kids that buying lottery tickets is a bad, bad idea.”
That’s a nice dream. Meanwhile many of my co-workers (all of whom are pretty mathematically literate, some of whom have masters degrees in statistics) can often be found purchasing lottery tickets.
One thing I think I could add here as something to think about, is the point often made by Chris Dillow – for most people a pure meritocracy is just as bad a deal as oligarchy/plutocracy. Even if the system is not necessarily rigged against them, it gives them no chance of “winning”. To go back to Rawls, a lottery (where not played by addictives) makes relatively little difference to the balance of society – but it does make the mind experiment in Rawls (that your position in society is unknown) real.
Declan: interesting. You are coming at this from a more “proceduralist” perspective (a perspective I tend to associate more with libertarians, though it doesn’t have to be, I suppose).
Let me expand a little:
Most economists (e.g. in optimal tax theory models) see the distribution of income as being determined by: choices; and luck. Some luck can be insured against, and people will insure against it. But some can’t (because of moral hazard, adverse selection, or because the luck happened before you could insure against it (you were born that way). An optimal tax system is designed to try to insure people against the uninsurable luck (to remove the effects of luck), while recognising that there’s a moral hazard problem because this will distort people’s choices, and tries to do the best it can on the trade-off between removing luck and creating moral hazard (disincentives).
So if you start from that perspective, and then see a lot of people deliberately re-introducing luck, and undoing all your costly attempts to try to remove some of the effects of luck, you start to wonder: why the hell did we bother!?
Nick,
see my post and lots of posts by Chris Dillow. One element of luck people can’t possibly insure against, is being born untalented. Lotteries of their way of being able to “win” in life anyway.
But surely you see the point here – popular lotteries (those that make sense to me anyway) are always those with very large rewards at very low probabilities – whereas what the tax system tries to do is put a floor under losses. They are two very different animals. If people were going in lotteries that were expensive and only every second player lost everything, then I could understand your concerns.
When we think about gambling addicts, I also think the type of games they will concentrate on are not the sort of lotteries we are talking about. Gamblers go in a game in order to enjoy the kick of winning. Going in a lottery where you in all probability will NEVER win, cannot be their thing.
Seriously!
reason: yep. It’s uninsurable risks, like being born untalented, that the tax/transfer system is supposed to be trying to deal with. And yes, I see that the risk created by a lottery isn’t exactly the same as the risk removed by the tax/transfer system. But it does suggest that people don’t want the luck of super-high earners completely redistributed, because that’s exactly what they try to re-create in the lottery.
Nick: I have to confess respectfully that I’m somewhat amused by your frustrated paternalism… But obviously, you’re going to see anomalies all over the place when you take simplifying assumptions seriously, including when it comes to normative economics. Yet, you could still rescue your personal ideals by assuming that what you see as revealed preferences are conditional on the presence of inequality, so that people buy lotteries given they have to put up with inequality anyway (why should they be the victim of such a mean society!), but they would so much more want to live in the world that you want for them… Would that perspective be heart-warming enough?
Yvan: Yep, but that sense of “frustrated paternalism” is I think exactly how an optimal tax theorist would think.
Yep, there will always be anomolies. But one quarter of the population (and that’s certainly an underestimate, given people who play the lottery less frequently, and who do negative sum gambles in other ways) is a big one. Do more people gamble than insure (not counting compulsory insurance)?
I can see how your “rescue” might work. But the preferences you would need to assume to make it work would be a long way from those assumed in optimal tax theory.
The lesson I’m groping towards is this: there might be a case of redistributive taxation. But that case, and the sort of tax system that would be justified, might be very different from the case made by optimal tax theory.
The exchange with Declan was interesting. At first I couldn’t see how he could fail to see my point. Then I realised he genuinely didn’t see it (though I’m still a bit miffed at him accusing me of “pretending”). Because he didn’t see an egalitarian tax system as trying to partially remove the effects of luck. He saw it as doing something quite different. Something like trying to remove the effects of procedural unfairness?
If real people don’t want the tax/transfer system to do what optimal tax theorists think they want it to do, maybe it shouldn’t try to do it.
Nick: 1/4 of the population is not 1/4 of a relevant economic variable. You give a bit too much importance, I think, to something that is the adult equivalent of a kid throwing a penny in a fountain. But all I’m saying is that optimal tax theorists could simply accept that their utilitarian framework is at best an imperfect yet useful work hypothesis, and just go on doing their thing. Isn’t that really what they end up doing anyway, at least once they’ve tamed their inner central planner?
Nick: I’m not seeing the need to distinguish between “luck” and “procedural unfairness.” The world is rife with procedural unfairness: inheritance, monopoly rent, preexisting division of finite resources. Luck (other than winning the lottery) is just landing on a particularly juicy piece of rent.
This passage from a favourite Kurt Vonnegut novel always comes to mind for me:
This kind of world view is, at least for me, the principal justification for redistributive taxation.
I should have referenced where I found that version of the Vonnegut quote: http://blawgletter.typepad.com/bbarnett/2009/03/should-law-firms-have-to-disclose-partner-pay.html
I don’t think that the existence of lotteries necessarily invalidates the assumptions of optimal tax theory. For instance, if Karelis’ theory is correct, then poor people have S-shaped utility functions, but it is still optimal to redistribute income if this places them above the inflexion point.
K, interesting point, but I see no reason to conflate luck with rent seeking. Yes, if rent seeking by those with higher income (which is obviously a negative externality) outweighs their positive effects on the rest of society, then an income tax can increase efficiency, if only by discouraging everyone.
Clearly, it’s better to avoid rent in the first place by improving policy, and to capture remaining rents for public use. Even then, this would not substantially decrease uncertainty, since ‘honest’ profit seeking is also subject to risk, much of which is uninsurable. And lottery winnings should be untaxed, since playing the lottery is a profit-seeking activity, although a rather trivial one.
anon: I mostly agree. Public policy (including taxes) ought to directly target the existence of rents (e.g. land tax). My point was that it is the existence of rents that is the principle cause of extreme inequality. Therefore luck (i.e. whether you happen to be a payer or receiver of rent and how much) accounts for vastly greater dispersion of wealth, than it would in an economy without private rents. So I do think think that collection of rents for public purpose would have a significant impact on reducing uncertainty.
And I also agree that honest profit seeking (including lotteries) ought to be as untaxed as possible (ideally not taxed at all).
“An ultra-quick Google says that one quarter of Canadians buy lottery tickets weekly. That means, at an absolute minimum, one quarter of Canadians want (have a revealed preference for) more inequality.”
No, it doesn’t. Meaning is not preserved across logical inference. What it means is that people value their increase in hope and excitement over the cost of the lottery ticket. They don’t do the probabilities, or, if they know that the odds are against them, not only in terms of money but in terms of the utility of the money payoff, they don’t care. (And for many the utility of the money payoff is seen as more than the money itself. It means a lifestyle change. As one woman said, “The lottery is my pension plan.” Sure, the odds are that she would have a more comfortable old age if she saved the money instead of playing the lottery, but her odds of having a comfortable old age at all are better with the lottery.)
As for the fact that having a lottery at all makes for inequality, I think that you are right that people want inequality. But you don’t need the lottery to conclude that. Look at the popular fascination with celebrity and wealth, even with royalty. People want the fairy princess to live happily ever after (or to be in rehab ;)).
Nick,
you think too linearly. Embrace non-linearity.
Min: you are right. But, if people don’t understand lotteries, they don’t have a hope of understanding the tax/transfer policies of the political parties they vote for!
reason: but the Utility function of a risk-averse agent, as assumed by optimal tax theory, is non-linear!
Nick Rowe: ” if people don’t understand lotteries, they don’t have a hope of understanding the tax/transfer policies of the political parties they vote for!”
You said it! 🙂
Ah,
but but is it S-shaped?
And Nick, I thought it was clear that EXPECTED utility maximisation is besides the point here. People are spending a small amount of their income in order to be able to dream. It is cheaper than going to the movies. Actually winning the lottery (a bit like winning the girl) is almost a let down compared the dream.