[Order] Global warming, the Expected Utility way

[Yvain Wintersong]

I'm so happy! In the thread on opinions, we've finally got a good debate going, on global warming!

In the original thread for the Order, I mentioned how, in my experience, people in internet debates usually just threw arguments at each other without changing their minds. I'm certainly guilty of that sometimes - I'm getting way too emotional about the global warming issue. I also mentioned I thought resolving these problems is very important, and might be possible. So let's bring in the big guns! I think (I'm only an amateur logician myself) that this is called an expected utility argument.

"Expected utility" is a method for calculating how good certain choices are. For example, you're in a casino with two slot machines. On Machine 1, you have a 1/100 chance of winning $100. Machine 2 gives a 1/1000 chance of winning $500. If you want the best odds of striking it rich, which machine should you play?

What if you play each machine a thousand times? On Machine 1, you'll win an average of ten times (1000 x 1/100), win $100 each time, and end up with $1000. On Machine 2, you'll win an average of 1 time, (1000 x 1/1000) and win $500. So, on average, you'll win twice as much money with Machine 1. This is true whether you play the machines 10 times, 1000 times or 1000000 times.

What if Machine 1 costs $2 per play, and Machine 2 costs only $1 to play? Let's try them a thousand times again. Machine 1 costs $2000 dollars and pays $1000. In the end, you lose $1000. Machine 2 costs $1000, and pays $500. In the end, you lose $500. So in this new case, playing Machine 2 is a better choice than playing Machine 1. Not playing either machine, you lose an average of $0 and win an average of $0, so clearly not playing either machine is the best idea of all.

We can generalize this strategy to find a way to decide between any two slot machines. Take the chance of winning times the payoff, and subtract the cost. This is the average dollar amount you can expect to win each time you pull the lever. This gives an easy way to decide which of any two slot machines is better. If it's negative, it also means that not gambling at all will, on average, give you a better result than using the slot machine. Of course, all real slot machines are negative - if they weren't, the casino would go broke.

But this doesn't just work for slot machines. It also works for all other games of luck - the lottery, roulette, et cetera. With a slight modification, it can be extended to games of skill. Consider a very simple blackjack game - we each bet $25, play one round against each other, and whoever wins keeps the $50. I'm twice as good at blackjack as you are, so there's a 2/3 chance of me winning (let's ignore luck for now). The expected utility for me of playing blackjack is now ($50 x 2/3) - 25 = 8 1/3. So on average, I win $8.33 each time we play - it's a good deal for me!

But this doesn't just work for games! It also works for almost any decision. How about this one? There's this really cute girl. I want to ask her out. If she says yes, I will be very, very happy. If she says no, I'll be really embarrassed and disappointed. How do I decide? First I quantify happiness. Maybe I predict I'll be really really happy if she says yes, but only moderately sad if she says no. I decide I'll be ten times as happy if she says yes as I will be sad if she says no. So we have 10 Happiness Units and -1 Happiness Unit respectively. It doesn't matter what the heck a Happiness Unit is, as long as I'm using it consistently.

I obviously don't know if she'll say yes or not. But I have a pretty good idea. If I'm rich and handsome, and she's desperate, there's probably a very high chance, around 9/10. If she knows I'm the sort of person who posts long essays about logic in micronational forums, there's a very low chance, around 1/10. Let's say, after considering my attractiveness level and her tastes, I estimate the probability of her saying yes at 1/4. So chance of success is clearly 1/4. And the payoff is clearly the 10 Happiness Units I mentioned. But what's the cost? The cost is the embarrassment and disappointment I get when she says no. There's a 3/4 chance of her saying no, so there's a 3/4 chance I'll have to deal with a cost of 1 Happiness Units. Plug that into the Expected Utility equation and we get (10 x 1/4) - (1 x 3/4) = 1 3/4. So on average, I gain 1.75 Happiness Units by asking her out. We don't know what the heck a Happiness Unit is, but since it's positive here, we know I'll, on average, be happier after asking her out. So our decision is...I should ask her out!

Playing around with the numbers shows that the equation fits common sense pretty well. For example, if there's a zero percent chance she'll say yes, the equation becomes (10 x 0) - (1 x 1) = -1. The Happiness Units are negative, and therefore I shouldn't ask her out - of course I shouldn't, I know she'll say no!

This equation does lead to one surprising result, though. It says I should ask her out...but we know that three times out of four, that decision will only lead to pain and suffering. What's up with that? Well, consider a lottery. Tickets cost $1. There's a 1/4 chance of winning. If you win, you get $1 million. I'd KILL for one of those lottery tickets, even though I know that three times out of four, it's a waste of a dollar. Clearly, whether a decision is good depends both on your chances of payoff AND on how big the payoff and the cost are.

Now we finally get to global warming! Yay! Consider any proposed solution to global warming - let's take the Kyoto Protocol, it seems pretty popular. Now we have a good mathematical way to determine whether the Kyoto Protocol is a good idea.

Take the chance global warming's manmade. Multiply that by the benefits of implementing the Kyoto Protocol. Subtract the cost of the Protocol. That's your expected happiness after implementing the Kyoto Protocol. (I'm starting to realize I've done this all very inelegantly and the signs are messed up, but too late now.) But the benefit of the Kyoto Protocol is not having global warming happen...so it's equal to whatever the cost of global warming would've been. The cost of the Kyoto Protocol is the economic cost of closing down polluting factories and that sort of thing.

So...if (Probability that global warming is real x Global warming's costs) - Cost of Kyoto Protocol > 0, we should implement the Kyoto Protocol. Or, since seeing it look all nice and proper gives me a warm glow, (P x G) - C > 0 implies Kyoto is a good idea.

P, the probability that global warming is manmade, is the most complicated part. The best way to do it would probably be a prediction market like InTrade. I should really explain that more, but this post is already too long (that always happens!) Another good way would be looking at the percentage of intelligent scientists who believe each view.

G is the cost of global warming IF it really exists. We could try giving a cost in dollars, based on how much property would be destroyed by flooding, extra strong hurricanes, and stuff like that, and adjusting for the cases when global warming would actually create value - the new tropical vacation paradises in Canada But this approach has one problem - how do we factor in the cost in people killed? What about human suffering - maybe people starve, or lose their jobs, or something. The standard way to do this is to convert dollars, lives, and suffering into a common currency called "utils", which are pretty much the Happiness Units I posted earlier. This is easier than it sounds...sort of. I'll explain it later.

C is the cost of implementing the Kyoto Protocol. Nice and straightforward - a few hundred billion dollars in lost economic growth because there aren't enough coal plants to power factories and that sort of thing. I'm sure someone's done the calculations, so again, let's look for the least biased group. There might also be some human suffering involved here too, so convert it all into utils and you've got utils on both sides of the equation.

My question for everyone involved in discussing global warming on the other thread is: do you think this will work? If so, let's - all of us who are interested - try to find numbers for all three of these variables. Let's plug them into the equation and see whether the Kyoto Protocol is a good or bad idea. If the equation says it's a bad idea, I promise to very seriously reconsider my support. If the equation says it's a good idea, I'd hope you would do the same thing. Are you game?

[Yvain Wintersong]

[I edited that pretty substantially, and I might've missed a sentence or two. If something makes NO sense or has NO context, that's probably why. Sorry.]

[Jacobus Loki]

I don't make too much noise about GW usually. Getting off fossil fuel is a good thing. We can't ever get to warp drive while we are still burning concentrated dead plankton to make our cars move.

I just refuse to feel guilty about it. I hate to be manipulated by a cause celebre du jour.

I'll believe it more when the guys in Hollywood and Washington give up their private jets and start flying coach. Or going Amtrack.

And trade the limos and big SUVs for Prius's.

And give up their mansions to live in efficiency housing.

Oh, crap, a black helicopter just landed across the street.

Al Gore and a couple of guys in black suits are getting out.

No.

NO
NO

I BELIEVE

AGGGGGhhhhhhh

(transmission terminated)

[Bayen]

Wow, I LOVE this decision-making model! Next time I take one of those "Wellness" classes, and they talk about "good decision making," this is coming out!!! ^-^

And yes, I would like to find out the numbers for Global Warming... just let me know how I can help!

[Jacobus Loki]

What is a "wellness class"?

asked the old guy with no kids.

[Yvain Wintersong]

O, Jacobus, thrice and four times happy art thou, that the abomination of a "Wellness Class" never crossed your innocent eyes, nor violated the happy calmness of your brain! May all the gods of this Multi-Temple keep you safe from such a monstrousity, that many decades hence you may go peacefully to your grave still ignorant of its true horror...

...I had to take a class like that when I was 13 or so. Didn't much care for it. If Bayen's was anything like mine, it's a class where they make you sit there for an hour each day while they say "Don't do drugs. Don't have unprotected underage sex. Don't eat lots of really bad food." And then you have to do lots of homework every night, like write essays on topics like "Should you take lots of drugs and have unprotected underage sex or not? What about eating really bad food? Write five pages explaining your answer."

I suppose I MIGHT have tolerated it if they had presented research and discussed the issues rationally. If they had taught the fundamentals of good decision-making, like Expected Utility, I might have loved it. Instead, they presented obvious propaganda created by someone who drastically underestimated the mental capacities of thirteen year olds. A typical "lesson" would be a video showing a handsome guy who's a great athlete being tricked into smoking a joint by evil, heavily accented "friends", and then dying alone in a back alley at age 30 all because of that one smoke.

The sad part was that it wasn't until I was twenty or so that I learned that some illegal drugs are actually both safe and even extremely beneficial if used correctly. I think many people eventually figure this out, and then dismiss their wellness classes as complete lies. The problem is, some drugs really are as bad as the classes make them out to be. Without any education as to which ones these are, my guess would be a whole lot of people get hurt. If wellness classes were to honestly teach which recreational drugs kill you, which ones hurt you, which ones are mostly neutral, and which ones reveal Ultimate Holy Reality unto you, they'd save a lot of people from getting messed up while finding it out for themselves.

Bayen, I'm glad I've finally found someone who finds these topics as interesting as I do. Finding the numbers for global warming is going to be harder than I thought, because I've discovered there's no prediction market on global warming. Since I can't think of another good way to get unbiased numbers, and no one except you has expressed interest in this subject, I might just give it up.

[Bayen]

Completely apart from the Global Warming, I have a few observations on your equation. First, the purely mathematical on some other possibilities:

What if there's an additional problem when an unfavorable outcome occurs? Then it would be (P * G) - (P * B) - C

Or it could just be for each block of outcomes, you have a (Probability * Payoff) where payoff can be negative...

And also, sometimes it will give you unwanted results.

Those 1/4 million dollar lottery tickets, for example. What if they didn't cost one dollar, but costed 100,000 dollars, but pay one trillion dollars? (Just for an example, of course... a trillion's just a REALLY big number )

So 1/4 * 1,000,000,000,000 - 100,000 = 249 999 900 000, which is a VERY positive number. But what if your life savings are only 60,000 dollars, you have to sell everything you own for 40,000 dollars. Three in four times, you will be left with absolutely nothing.

Money, even a trillion dollars, can't necessarily buy happiness, but lack of money sure can bring misery, especially in this case where you have not a dollar left. What if you have a family to support?

Personally, even with the possible amazing payoff, I would not buy one of those tickets...

[Yvain Wintersong]

I tried to address the possibility of the negative outcome in the example with the girl. But your equation (P * G) - (P * B) - C is more elegant than the one I used because it keeps fixed costs and costs of a negative outcome separate. Thanks.

The unwanted results problem is a VERY good point. Do you know a lot about economics? Because what you're talking about sounds kinda like the Law of Diminishing Marginal Utility. My GUESS would be that we could probably fix the problem by working with utility (technically measured in utils, but same as the happiness units I used above in the girl example) rather than money.

So for your example, you'd have to quantify the amount of happiness winning one million dollars would give you, and then quantify the amount of happiness that having savings and goods rather than being completely broke gives you right now. Then you can plug those happiness units into the calculations and come up with the right answer. If you're like me, the amount of happiness that not being broke gives you is a lot more than the amount of happiness that winning a million dollars would give you.

Of course, this is much less elegant than the original formulation, because dollars are easily quantified whereas happiness units are not. There are tricky ways to quantify happiness units, but they lack the simplicity of the original. So my hope would be that the original calculations in dollars are valid when the amounts are low enough that diminishing marginal utility doesn't have an effect, but for higher values you'd have to go through the really difficult process of calculating happiness.

This would hopefully not affect the original global warming example, since it seems to be dealing with billions of dollars among entire nations, at which point the value of money seems pretty constant.

Do you accept that as a good solution to your objection?

[Bayen]

Ooo... The Law is very interesting... I know next to nothing about economics, but it's an intriguing topic that I look at sometimes.

And it wasn't so much of an objection as just an... observation? Clarification? I don't know... But yes, the Diminishing Marginal Utility solves it quite nicely.

[Jacobus Loki]

Yvain,

We had a thing called "Health class". They skipped lightly over the "don't do drugs", ignored the sex part (except a line drawing description of what bodily part did what), touched briefly on the now obsolete "food pyramid " (sponsored by the cattle growers association) and then proceeded to teach us the U.S. Civil Defense Manual about how to survive a nuclear war.

How to hide, what rotten food might be safe afterward, emergency first aid because all the doctors might be dead. The best part was that a quorum of our Supreme Council of what is now called a micronation had the same class, and we could sneak some time to plot the downfall of our enemies.

[Maksym Hadjimehmetov]

Sorry, but the UK's Geography Syllabus + ESL Debates about global warming = me pretty full of hot air about the subject anyway (excuse the bad pun)

As far as I see it, the battle is preparing for the worst rather than spending millions convincing every Texan oilman who still refuses to believe that global warming theory is almost a certainty by now.
Either way, even if global warming doesn't exist, it still can't hurt for us all to cut back on all the resources we use. Whether there's global warming or not, resources are finite (contrary to Boserup's theory for any Demographers out there ) and we must find alternatives to fossil fuels and learn to recycle better.

[Jacobus Loki]

Either way, even if global warming doesn't exist, it still can't hurt for us all to cut back on all the resources we use. Whether there's global warming or not, resources are finite

Amen. And if worse comes to worse, we still have all of this lovely uranium and coal.

[hypatias mom]

To say nothing of all the unexploited, thousand-year oil reserves off our coasts and up in Alaska.

[Jacobus Loki]

But if we can buy all of what the other people have, and use it up before we use up or own

Then there are all the hydrates.....

If we go to coal, the U.S. has enough to last 30,000 years at the current size of the economy. There's enough oil shale in the Rockies for hmmm, 5,000 years, I think.....

But thats messy, and if we go nuclear, we can use it all to make plastic.

And coal won't work on a starship! (Just ask Admiral Quirk!)

Nuclear would. A pretty slow starship, .25c perhaps. Proly multi-generational. Alpha Centauri in 20-25 years earth time.

[hypatias mom]

Sounds good to me, Captain.

[Jacobus Loki]

You know, since we annexed Absentia, the "Improvise " belongs to us now.