Newcomb's paradox, voting, and carbon emissionsNewcomb's paradox
Newcomb's paradox is the following beautiful and famous thought experiment. A wizard arrives in town and claims to be able to predict the future. He then makes you the following offer. He has placed two envelopes in front of you and you have the option of either choosing just the envelope on the left (as you look at them) or choosing both envelopes. He, meanwhile, has put money into the envelopes according to the following rules: if he knows that you will just pick the envelope on the left, he puts in $1000 in that envelope and $100 in the envelope on the right; if he knows that you will pick both envelopes, he puts in just the $100 in the envelope on the right. When you've chosen your envelopes, you get to keep the money you find in them. What should you do?
There are two powerful lines of reasoning, and they give different answers. One argument is that the envelope on the right contains $100, so whatever the wizard has put in the two envelopes you will end up with $100 more if you choose both envelopes. The other argument is that if you choose just the envelope on the left, then you will end up with $1000 (since the wizard will have predicted this and acted accordingly), whereas if you pick both envelopes, then you will end up with $100.
Most people have a strong instinct one way or the other, but people's instincts differ. I, for example, am a one-envelope person, but I know several people who think that I'm just obviously wrong to take that view. The interesting thing about discussions of Newcomb's paradox is that they tend to be little more than repetitions of the above two arguments in louder and louder voices. (There are a few preliminary arguments to get out of the way, such as why you should have any reason to trust the wizard. A possible answer to that is that you are the 50th person that the wizard has made the offer to, and his predictions have been correct every time so far.)Voting
Several people argue that it is irrational to bother to vote, because the chance of your vote making a difference to the outcome is just too small to make it worth the effort. But others have a strong instinct that it is
worth voting, even if they can't quite explain why.Carbon emissions
There is a tempting line of argument that is quite similar to the argument against voting: it is that individual action to combat climate change, such as driving and flying less, insulating your house better, etc., is just a tiny drop in the ocean and therefore not worth taking. We just have to wait until our governments make deals that will have a global impact.Why these three topics in one post?
In the run-up to the last general election, I had the thought that Newcomb's paradox is related to the voting question as follows. Suppose that I regard myself as a reasonably typical person. Not necessarily an average person, but just a person with views that are similar to the views of a reasonably large number of other people.
For simplicity, let's suppose that I belong to a social group S and that people in S vote independently for party P with probability p. However, I don't actually know what p is. What can I say about it? One possibility is to look at it in a Bayesian way. I start off with some prior distribution on p (that is, a distribution that tells me the probability that p lies in any give range [a,b]). Then I use the additional information that I am intending to vote for party P. The conditional probability that I will vote for party P given that Probability[person in S votes for P] is p is, naturally, p, since I am a person in S. Using Bayes's theorem, I can get from that to a posterior distribution on p -- that is, a new updated probability distribution given the information that I plan to vote for party P.
The main point here is that the mean of the posterior distribution will be higher than the mean of the prior distribution. So if I vote for party P, then the expected number of people in social group S who will also vote for party P goes up. Similarly, if I don't vote for party P, it goes down.
To put all this less formally, if I assume that I am a reasonably typical member of group S, then the decision I make is likely to be mirrored by many other people in group S. So my voting power is amplified -- I really can make a difference.
Of course, to a two-envelope person all this reasoning will seem like a load of nonsense. Once I'm in the voting booth, my vote has no causal effect on anybody else's (assuming that I don't go out and campaign about it). But to a one-envelope person the "I am reasonably representative" hypothesis plays a role similar to the "the wizard knows what I'm going to do" hypothesis in Newcomb's paradox, and the reasoning is much more appealing.
I wondered whether anybody else had had this thought, and, not surprisingly, they had. I found it articulated very nicely in the following blog post: http://bleedingheartlibertarians.com/2012/10/the-one-boxer-argument-for-voting/And what about climate change?
For a while now I've felt guilty about taking the attitude that it is for governments rather than individuals to reduce carbon emissions. (I favour taxes on emissions that are high enough to change behaviour, coupled with subsidies for renewable energy.) And now I have a way of articulating my guilt. I just apply the same reasoning to another form of collective action: if I take steps to reduce my carbon emissions, it probably means that plenty of other people have reached their own tipping points, whereas if I don't, then it doesn't; so I should.
One of the things I have felt worst about is driving my children to school/nursery. But finally, after doing that for several years, I have invested in a Dutch bike (second hand, but still expensive) with a box on the front into which you can put two children, provided they aren't too big. A rough calculation suggests that it will pay for itself in a year or so, thanks to the petrol I will no longer buy, or less if I eventually sell it for a reasonable price. But my main motivation is not that I'll save money by not buying that petrol: it's that I won't then burn that petrol. And it will also mean I get more exercise. Today was the first day when I would have used the car but didn't. There are quite a lot of similar bikes in Cambridge these days -- so maybe I'm vindicating someone else's one-envelope decision.