Nudging People Towards Health

[a shorter post on the same topic is available here]

Operational Definitions

When we give something an operational definition, that means that instead of defining it in terms of other words, we define a procedure for determining whether something fits. For example, psychologists have struggled for a long time with coming up with a scientifically useful definition of intelligence. Their solution was to define intelligence operationally in the form of IQ tests.

Just like verbal definitions, an operational definition isn’t necessarily useful. The only reason people are interested in IQ is because it strongly predicts future life outcomes such as income, grades, propensity to commit (or at least be caught committing) crime, SAT scores (which are themselves useful for getting in to college), and a variety of other life outcomes.

On the other hand, if you define UQ (useless Q) as how many times someone can guess a coin-flip right out of 10 coin flips, this is an operational definition – just not one anyone cares about.


The reason I bring all this up is because I think that a wide variety of philosophical issues vanish once you start using operational definitions. In particular, I think we can resolve some of the issues surrounding the concept of identity.

As far as I can tell, when people talk about identity, they actually mean two distinct (though related) concepts. The first is that characteristics about you stay reasonably constant over time. Your intelligence, interests, personality, friendships, culture, and socioeconomic status next week are probably going to be very similar to today. The second is that you care about your future-self to a far greater degree than a stranger. Similarly, when we talk about the identity of a group of people, it’s usually in these same two ways: a degree of shared characteristics or shared sympathy for each other.

While I find the first definition quite interesting, I fear it’s hard to deal with formally. For instance, we can take things like your IQ, your personality scores, and your Facebook friends, and quantitatively measure the stability of these various measures, but it’s kind of unwise to try and compress these measures of stability down to a single number of identity-stability.

Instead, I’d rather look at the second type of identity: sympathy for your future-self.


Libertarianism is an ideology whose adherents are actually quite varied in their beliefs. Some simply interpret libertarianism as the belief that the government should keep interventions to the minimum. Other libertarians see government intervention as only justified when there are externalities (side effects) to actions such that the government should encourage or discourage those actions.

One of the classic examples is a lumber mill that pollutes a river, which harms farmers down-stream. Many (though not all) libertarians would be completely fine taxing the lumber mill and transferring the benefits to the farms as a way to “internalize the externality” – though they’d prefer a private solution negotiated via contract if possible.

It’s this second type of libertarianism that I want to address. It rests on a couple assumptions, though what exactly those assumptions are depends on who you ask. I’m going to pick apart two of them, and show how once you take into account these issues, you get a new type of political philosophy in which the government uses taxes and subsidies to “nudge” people into taking actions they, themselves, would consider good.

The first assumption I want to look at is the assumption that humans are rational. In particular, when most people make decisions, we know they don’t properly take into account the consequences to their future-selves.

We can actually measure this. According to one study, most people require between about 5 times as much money in 5 years as they do today to be indifferent (some of the evidence suggests the ratio is as high as 11, but I’ll be as conservative as possible) "title": "Discounting of delayed rewards: Models of individual choice".

You could argue that they’d invest the money, but there are two issues with that. First, Americans generally only save 5% of their income "title": "National Data: GDP & Personal Income". Second, even if you accept a generous 10% return on investment each year, that would suggest the “correct” answer is to value money today at 1.6 times the value in 5 years. So, if I take 1.6/5, I get about 0.3, suggesting that people only account for 30% of their future-selves utility.

Before going out, I’d like to point out that people probably operationally care even less about their future selves than this 30% figure. I’m being conservative in 3 ways:

  1. I’m taking the lower estimate of 5 instead of 11
  2. I’m assuming a 10% return on investment each year
  3. I’m assuming that for times longer than 5 years, this 30% figure stays constant, when it probably actually shrinks.

This means if you accept that (e.g.) exercise’s effects on future-you are largely a positive externality, then the proper response is to subsidize exercise by at least 70% of the your long-run benefits.


There are a whole host of actions that have long-term consequences for your future-self:

  • Saving for retirement
  • Exercise
  • Flossing
  • Eating healthy foods
  • Using drugs (tobacco, alcohol, etc.)
  • Owning guns

Before I explore a few of these, I want to address two potential sources of criticism.



Some people might be bothered, because I’m taking away people’s agency. However, I’d argue that I’m actually doing the opposite. People fall victim to well-known cognitive biases that stymie their ability to practice rational and good judgment "title": "List of cognitive biases".

What I’m trying to do is allow people to live better lives by their own standards. If anything, I’d interpret this as giving people agency.

To this end, I only take into account longevity in all my following analyses. I think we can agree that the vast, vast majority of people would prefer to live longer rather than shorter lives.

Smaller Government

Many people believe that the government is too big. However, I feel it’s crucial to recognize this is a really bad way to determine whether you should support a particular policy. Each policy needs to be judged on its merits, alone. Even if 90% of government policies are wasteful, this doesn’t mean a particular policy will be wasteful. If you disagree (e.g.) that the government should pay people to exercise, you should have a reason that this particular policy is bad.


One longitudinal study, tracked over half a million men and women over more than a decade "title": "Leisure time physical activity and mortality: a detailed pooled analysis of the dose-response relationship". For your convenience, I’ve converted the results to reflect an average American (i.e. one that weighs 175 pounds). If you’re a different weight, you can easily see how these results apply to you by dividing the left column by 175 and multiply by your weight. I’ve also taken the liberty of converting from mortality risk to life-expectancy gain "title": "Mortality and Life Expectancy".

Anyways, here are the results.

As you can see, the first 600-or-so calories get you a majority of your longevity benefits. Indeed, it turns out that more research reveals that diminishing returns are probably more extreme in real life than this particular study found. You can see here for a more in-depth analaysis.

Anyway, we see a benefit of about 3.3 years if you follow the minimum guidelines. Recall, that we’ve been using the conservative “1 year of life equals $50,000” estimate, so in dollars, this becomes 165,000. However, because present you does take future-you into account by 30%, the externality become $115,000. Divide that by 80 years of working out about an hour each week, and you find that the positive externality of 1 hour of aerobic exercise is about $28 per hour. Recall this is still a conservative estimate.

So, in order to internalize this externality, the government should pay you $28 for the first hour you exercise in a week. This would also, presumably, lower health-care costs. The evidence for additional benefits is kind of weak (see tangent above for details).

If everyone exercised an hour a week, such a program would cost nearly half a trillion dollars per year, about 2.5% of our nation’s GDP "title": "National Data: GDP & Personal Income". On the other hand, we’d all live 3.3 years longer, catapulting us to the top of the HDI rankings [feel free to double check my math "title": "Human Development Index" "title": "List of countries by Human Development Index"]. Of course, in reality, the cost and benefits would be significantly but proportionally smaller (not everyone would exercise an hour each week).

The question becomes, then, are you willing to sacrifice 2.5% of your income (most of which you’d get back if you exercised) in order to live 4% longer? Assuming you never exercised, such a reduction in income would reduce your happiness by about 0.04 points "title": "Happiness" on a 10-point scale. If you consider the fact that this reduction in income would not be particular to you, but would affect everyone you know, your happiness is not likely to be affected at all "title": "Will raising the incomes of all increase the happiness of all?" "title": "the happiness-income paradox revisisted" "title": "Happiness and Growth the World Over: Time Series Evidence on the Happiness-Income Paradox". So, all thing considered, I think a 4% longer life is the better choice – especially if you believe that running makes the years you do live healthier as well.

Aerobic exercise could be tracked via running apps or at the gym. Sure, some people would illegally cheat; this is true of everything. You can argue that this expands government, but we’re talking about the potential to add 3.3 years of life to 320 million people – that’s equivalent to saving over 10 million lives. I don’t think a generic argument against government encroachment holds a candle to that.

Some people have reacted to this conclusion by saying something along of lines of “but who cares if I live a few more years in my eighties?”. All I can say, is that, contrary to popular belief, older people tend to be happier than younger people "title": "The effect of age on positive and negative affect: A developmental perspective on happiness", so this apathy towards extending life in old-age tends to be broadly unfounded. Of course, individual circumstances matter a great deal, but we can only ever play the game of maximizing expected value anyways "title": "Von Neumann–Morgenstern utility theorem".


We already tax cigarettes. The reasoning goes that we need to discourage smoking to reduce healthcare costs and reduce second-hand smoke. However, the chief cost of smoking is to the smokers themselves.

The analysis here is pretty straightforward. The average cigarette costs you 11 minutes of life "title": "Time for a smoke? One cigarette reduces your life by 11 minutes". Using our $50,000 conversion rate, this comes out to about $1 cost per cigarette. Multiply by the 70% we’ve been using, means the government should tax each cigarette by 70¢. Since most packs contain 20 or 25 cigarettes, this implies a tax of about $16 per pack. Currently cigarette taxes range from $0.17 to $4.35 per pack.

In the US, about 263 billion cigarettes are smoked each year "title": "List of countries by cigarette consumption per capita" "title": "How many adults live in the USA?", for a total revenue of $180 billion. If you’re worried that this is a regressive tax, then simply use that revenue to increase welfare.

Gun Ownership

Now, for a controversial one. I previously wrote a piece on gun control in which I argued that the real cost of guns was their increase of the suicide rate (the evidence for a net-increase in homicides is not very strong).

I did gloss over a detail though: I argued that the entire increase in suicide-risk should be treated as an externality. Instead, we now know that only 70% of it should be [or, since we were conservative, the amount should really be between 70% and 100%]. So, we have the following tax on gun-ownership per year:

Gun TypeFee Per Year

Sorry for misleading you, but I didn’t want to make that post even longer by getting into a tangent on operationalization and identity. If you recall though, I made conservative assumptions throughout that probably more than made up for this 30% off mishap.


Of course, there are a wide variety of things that affect people in the long-run in positive and negative ways. This was not meant as an exhaustive list. Things like the government matching people’s savings up to a limit, the subsidizing and taxing of foods based on healthiness, and the government sponsoring of standing desks all have a place in this political philosophy.

All my examples look only at longevity, but there are other things that are almost universally valued too like happiness, the ability to walk and take care of oneself unassisted, and avoiding cognitive diseases as one ages. This justifies yet more policies. For instance, even though the evidence that anaerobic exercise boosts longevity is weak, we do have evidence that it prevents cognitive diseases, so I’d be perfectly fine subsidizing that too.

The main point here is that we don’t hit people over the head with laws, we encourage them to leave lives more in tune with their own values. No one is perfect. We have well-known cognitive biases that make us act in ways we wish we didn’t. This approach can’t solve all the world’s problems, but it can make the world more forgiving of imperfection.

Works Cited [show]