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<h2 class="hd hd-2 unit-title">In Defense of Two-Boxing</h2>
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<p><span style="font-family: 'book antiqua', palatino; font-size: 12pt;"> Many philosophers believe that one-boxing is irrational, and that the form of decision theory I described above should therefore be rejected, however natural it may seem. </span></p>
<p><span style="font-family: 'book antiqua', palatino; font-size: 12pt;">Let me tell you about some of the reasons that have been set forth in defense of two-boxing.</span></p>
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<h2 class="hd hd-2 unit-title">Dominance</h2>
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<p><span style="font-family: 'book antiqua', palatino;">An important argument for two-boxing is based on the following observation. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">In a Newcomb case, there is one key matter you have no control over: whether or not the large box is full. And regardless of how this matter turns out, you will be better if you two-box than if you one box:</span></p>
<ul>
<li>
<p><span style="font-family: 'book antiqua', palatino;">If the large box is empty, you’ll be better off if you two-box than if you one-box.</span></p>
</li>
<li>
<p><span style="font-family: 'book antiqua', palatino;">If the large box is full, you’ll be better off if you two-box than if you one-box.</span></p>
</li>
</ul>
<p><span style="font-family: 'book antiqua', palatino;">Decision theorists sometimes summarize this by saying that two-boxing <strong>dominates</strong> one-boxing. (In general, one says that option <span class="math inline">\(A\)</span> (strictly) dominates option <span class="math inline">\(B\)</span> if however matters you have no control over turn out, you’ll be better off choosing <span class="math inline">\(A\)</span> than choosing <span class="math inline">\(B\)</span>.)</span></p>
<p><span style="font-family: 'book antiqua', palatino;">The fact that two-boxing dominates one-boxing is a powerful argument for thinking that you ought to two-box. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">One way to bring this out is to imagine that you have a friend who has your best interests at heart, and who knows whether the large box is empty or full before you walk into the Newcomb room. How would your friend want you to choose? If the large box is empty, your friend will be hoping that you two-box, so that you at least get the $1000. If, on the other hand, the large box is full, your friend will be absolutely delighted, because she knows you’ll be rich whatever you decide. But she’ll still be hoping that you two-box, so you get the extra $1000.</span></p>
<p><span style="font-family: 'book antiqua', palatino;">Actually, you needn’t bother asking your friend for advice. You know from the start that she’ll recommend two-boxing. For that matter, you don’t even need the friend. You know from the start that if you did have a friend who knew what was in the boxes and had your best interests at heart, she would recommend two-boxing!</span></p>
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<h2 class="hd hd-2 unit-title">Common Causes</h2>
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<p><span style="font-family: 'book antiqua', palatino;">I have given you an argument for two-boxing. Let me now say a little more about how the two-boxer thinks of Newcomb scenarios.</span></p>
<p><span style="font-family: 'book antiqua', palatino;">We begin with an analogy. You’re more likely to see wet sidewalks when there are people using umbrellas. But that’s not because umbrella use causes wet sidewalks (or because wet sidewalks cause umbrella use), it is because wet sidewalks and umbrella use have a common cause: they are both caused by rain. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">Two-boxers tend to think that something similar is going on in the case of Newcomb’s Problem. You’re more likely to find money in the large box if you one-box, but that’s not because one-boxing causes the large box to contain money (or because the contents of the large box cause your decision). It is because one-boxing and a full large box have a common cause: they are both caused by your psychological constitution.</span></p>
<p><span style="font-family: 'book antiqua', palatino;">One way to bring home the point is to consider a different example in which your constitution—in this case your physical constitution—causes two different effects. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">Suppose there is a gene with the following two features:</span></p>
<ol>
<li>
<p><span style="font-family: 'book antiqua', palatino;">Having the gene increases the probability of doing mathematics. (Perhaps the gene causes a certain hormone to be released, and the hormone causes one to enjoy doing mathematics.) </span></p>
</li>
<li>
<p><span style="font-family: 'book antiqua', palatino;">Having the gene increases the probability of suffering a terrible disease: <em>mathematosis</em>. (The symptoms of mathematosis are too horrible to describe here.)</span></p>
</li>
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<p></p>
<p><span style="font-family: 'book antiqua', palatino;">Mathematosis is much more prevalent amongst people who do mathematics than in the population at large. But this is <em>not</em> because doing mathematics causes the disease (or because having the disease causes one to do mathematics). It is because having the disease and doing mathematics have a common cause: they are both caused by the gene. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">Now suppose that you would very much enjoy doing mathematics. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">What should you do? Should you refrain from doing mathematics even though you would enjoy it? </span></p>
<p><span style="font-family: 'book antiqua', palatino;">Of course not! For there is a dominance argument. If you carry the gene, you’re likely to get the disease, but there is nothing you can do about it. Better to do mathematics, and enjoy life while you’re still healthy. And if you don’t carry the gene, there is no need to worry: you won’t get the disease, regardless of whether you do mathematics. So, again, better to enjoy yourself doing mathematics. Either way: you should do mathematics!</span></p>
<p><span style="font-family: 'book antiqua', palatino;"><em>Compare:</em> Suppose you don’t want the sidewalks to be wet, but you’d very much like to bring along your favorite umbrella. Should you refrain from bringing your umbrella, even though you’d enjoy it? Of course not! For, again, there is a dominance argument. If rain is on the way, the sidewalks will get wet regardless of whether you bring your umbrella. So better to bring it along, and get both the pleasure of holding your favorite umbrella and the ability to stay dry. And if rain is not on its way, there is no need to worry: the sidewalks will remain dry regardless of whether or not you bring your umbrella. So you’ll be better off bringing it, if it would give you pleasure.</span></p>
<p><span style="font-family: 'book antiqua', palatino;">Two-boxers think the dominance argument of the preceding section is analogous. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">If you want to be rich, it makes no sense to one-box. For if the large box is full, it will be full regardless of whether you one-box or two-box. So better to two-box and get the extra $1000. And if the large box is empty, there’s nothing you can do about it now: better to keep the extra $1000 as a consolation prize.</span></p>
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<h2 class="hd hd-2 unit-title">The pull of one-boxing</h2>
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<p><span style="font-family: 'book antiqua', palatino;">Even if you are a committed two-boxer, it can be difficult to escape the temptation to one-box. Imagine that a billionaire comes to town, and offers everyone the chance to participate in a Newcomb case. After the first day, your one-boxer friends are absolutely delighted. They have each found a million dollars in the large box, and they have spent the night celebrating with caviar and champagne. Your two-boxer friends, on the other hand, are all crestfallen. They all found the large box empty. There’s nothing wrong with getting a thousand dollars, but it’s not quite the same as a million.</span></p>
<p><span style="font-family: 'book antiqua', palatino;">You get your chance to participate the next day. When the time finally comes, you decide to two-box, and, predictably, you find nothing in the large box. Your one-boxing friends can’t stop laughing. “What a fool!” they cry. “What on Earth possessed you to two-box!?” Are they right? Did you make a mistake? Although philosophers are not all in agreement about this, my own view is that you did not make a mistake when you two-boxed. The billionaire came to town with the intention of rewarding irrational behavior (i.e., one-boxing). So it would have certainly been in your interests to somehow make her <em>believe</em> that you are irrational, since that would cause her to reward you. But by the time you entered the room it had already been decided that you would not be rewarded: your large box was empty from the start, and there’s nothing you could have done to change that. Leaving the thousand dollars behind would certainly not have helped.</span></p>
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<h3 class="hd hd-2">Video: Two conditionals</h3>
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<h4><span style="font-family: book\ antiqua, palatino;">Some Exceptions</span></h4>
<p><span style="font-family: book\ antiqua, palatino;">I have been arguing that one ought to be a two-boxer. But I'd like to mention a couple of special cases in which I think one-boxing would be rational. </span><br /><br /><span style="font-family: book\ antiqua, palatino;">First, consider a Newcomb scenario in which the predictor has a time machine. She travels to the future, observes whether you one-box or two-box, travels back to the past and makes her prediction in accordance with what she observed. In ordinary Newcomb scenarios, your choice has no causal effect on the contents of the large box. But in the case we are considering your choice has an effect on what the predictor observes when she travels to the future, and therefore a causal effect on the contents of the large box. I see no reason to think that one-boxing would be irrational under such circumstances.</span></p>
<p><span style="font-family: 'book antiqua', palatino;">Next, consider a predictor who is <em>perfectly accurate</em>: there is no possibility of her issuing the wrong prediction. Under such circumstances, there are really just <em>two</em> possible outcomes, rather than the original four:</span></p>
<table>
<thead>
<tr class="header"><th align="center"></th><th align="center"><span style="font-family: 'book antiqua', palatino;">Large box full</span></th><th align="center"><span style="font-family: 'book antiqua', palatino;">Large box empty</span></th></tr>
</thead>
<tbody>
<tr class="odd">
<td align="center"><span style="font-family: 'book antiqua', palatino;">You One-Box</span></td>
<td align="center"></td>
<td align="center"><span style="font-family: 'book antiqua', palatino;">NA</span></td>
</tr>
<tr class="even">
<td align="center"><span style="font-family: 'book antiqua', palatino;">You Two-Box</span></td>
<td align="center"><span style="font-family: 'book antiqua', palatino;">NA</span></td>
<td align="center"></td>
</tr>
</tbody>
</table>
<p><span style="font-family: 'book antiqua', palatino;">Against such a background, one-boxing is <em>equivalent</em> to one-boxing with a full large box, and two-boxing is <em>equivalent</em> to two-boxing with an empty large box. So your options are actually these:</span></p>
<table>
<thead>
<tr class="header"><th align="left"><span class="math inline" style="font-family: 'book antiqua', palatino;">\(\mbox{Option 1}\)</span></th><th align="left"><span class="math inline" style="font-family: 'book antiqua', palatino;">\(\mbox{Option 2}\)</span></th></tr>
</thead>
<tbody>
<tr class="odd">
<td align="left"><span style="font-family: 'book antiqua', palatino;">Take the contents of a full large box</span></td>
<td align="left"><span style="font-family: 'book antiqua', palatino;">Take the contents of the small box (plus the non-existent contents of an empty large box)</span></td>
</tr>
</tbody>
</table>
<p></p>
<p><span style="font-family: 'book antiqua', palatino;">And if these are your options, you should certainly choose Option 1!</span></p>
<p><span style="font-family: 'book antiqua', palatino;">Notice, incidentally, that perfect accuracy requires more than just a 100% probability of success. For perfect accuracy requires <em>no possibility of failure</em>, and 100% probability of success concerns not the possibility of failure but the probability of failure: it requires only that <em>if</em> there is a possibility of failure, then the probability of such a possibility is so small that any positive real number is be too big to measure it. (Imagine, for example, that a dart with a point-sized tip is traveling on a random path towards a line of length 1. What is the probability that the dart lands exactly on the line’s midpoint? As we’ll see in chapter 7, this is an event of probability 0. But it’s certainly not impossible, it’s just incredibly unlikely.) The discussion above supports the conclusion that one should One-Box in the case of a perfectly accurate predictor, but not the conclusion that one should One-Box in the case of a predictor who is not perfectly accurate but nonetheless has a probability of success of 100%. For in the latter case we still have the original four possible outcomes.</span></p>
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