We're going to apply what we learned about dividing the pie to a real world problem of sharing costs. What makes this tricky and what makes this interesting is that nobody goes out there and says to you, this is the pie. You have to go and figure it out. The problem I have in mind came up as a result of a speaking tour. Sal, who's based in San Francisco was scheduled to give a talk in New York, and another talk in Houston. He's a busy guy. Instead of having to do two round trips, he was able to do a triangle route. That is, he flew from San Francisco to Houston, and from Houston to New York, and then back home to San Fran. He could have done two round trips, but he was fortunate that the groups in the two cities were able to coordinate the timing so that he could do a triangle route. And thus, the negotiation question, how should the two hosts divide up the airfare? The cost of each leg was as follows. San Francisco to Houston cost $666, Houston to New York costs $909, and New York back home to San Fran costs $1,243. When you add up the three legs, the total comes out to $2,818. So here's the negotiation. The folks in New York and in Houston are jointly responsible for the $2,818. They know that and they agree to it, yet each of them would like to pay as little of that amount as possible. Imagine the two of them on the phone trying to work out a solution. New York might start out by proposing what looks like a really simple solution. They say to Houston hey, let's just split it evenly, 1409 and 1409. That sound fair right? The likely response would be, Houston, we have a problem. Houston would point out that the round trip airfare from San Francisco to Houston is only $1,332, twice the $666. So, why should Houston end up paying more as a result of the triangle route? Okay, New York recognizes that's a problem. So they come back with the following more reasonable counter. You have to fly south to Houston in any case, so the $666 is all on you. We have to fly him home in any case, so the $1,243 is all on us. Thus, the real question is how to divide up the $909. Let's just split that amount, $454.50 and $454.50. What matters here is the principle, but if you’re doing the numbers, that means Houston pays a total of $666 plus $454.50, or $1,120.50. Again, as Houston, I wouldn’t be persuaded. Why should Houston pay half of the New York to Houston leg? They could say hey, Houston's on the way to New York. I got Sal part of the way there, you can get him the rest of the way. Even if you pay the full $909, that's still a lot cheaper than the $1,243 it would have cost you to fly him to New York. New York doesn't think that's fair, but they see some merit in Houston's argument, so they come back with let's divide the $909 in the same proportions the legs were each responsible for. In other words, New York was responsible for $1,243, and Houston's responsible for $666. So we'll divide the Houston to New York leg in the same ratio, namely 65, 35. That means Houston will pay 35% or $317 to the $909, and New York will pay 65% or $592 of the $909. Let's recap for a moment. New York first proposed that Houston pay half the total, or $1,409, but that was a nonstarter. Then they suggested the two of them split the Houston to New York leg. Houston countered with the idea that they should just pay $666 as that is already getting Sal closer to New York. Lastly, New York countered that the two of them should split the Houston to New York leg in the same ratio as what they would have paid if there had been two round trips. This last proposal is exactly the same as just splitting the total $2,818 airfare from the triangle route in proportion to the cost of the two round trips. Some of you may be thinking, where's this all going to end, is there a right answer? We're looking for something that's fair and we're looking for a principled argument. I think our notions of fairness all come down to the same thing, and that is equal treatment. The question is equal treatment of what? The idea of splitting the $2,818 in proportion to the cost of the two round trips can be justified as treating each dollar of airfare in the same fashion. Both parties are getting the same proportional savings. I'm guessing that this is a solution most of you would have settled on before the session, especially if you hadn't watched the first video. Another common answer is to divide things based on miles. How far is New York and how far is Houston from San Fransisco, and then use that as the ratio to divide up the $2,818. In this case, we'd be treating each mile the same way. But I don't think there's anything fundamental about dollars or miles that says we should treat them equally. We can use fairness to make a principled argument. But, what is it that we treat fairly? It isn't dollars or miles, it's people. We want to treat people the same way. I think this all becomes clear If we go back to basics and ask, what is the pie? All the arguments so far have been struggling to find some focal point. But we've ignored the big lesson of why it is that the two parties are having this negotiation. So let's take a step back and think about what is the pie in this circumstance. And to do that, all you need to do is consider what will the two parties do if they reach an agreement versus, what will they do if they don't reach an agreement? Remember how A and B can get one and two on their own, but if they come together they could create nine, so the pie is six. In this case the two parties, here Houston and New York, come together so they can fly south to both cities for $2,818. But if they don't come together, then they'll have to buy two round trips. $1,332 for Houston and $2486 for New York, which when you add up, comes to $3,818. So by doing the triangle route rather than the two round trips, the two hosts can save $1,000. That 1,000 is exactly what the pie is, and it's what the negotiation is all about. Of course, each of the two parties is gonna want to get as much of that $1,000 as possible. What's the most they could ask for? $1,000. Houston could say, New York, you were willing to pay $2,486, you should still pay $2486! In which case the full thousand dollars goes to Houston, and they end up paying only $332. If Houston, said that, New York should respond, hey, Houston, you were willing to pay $1332, so you should still pay $1332, and I'll keep all the savings. In other words, New York would pay $1,486. I think each of these arguments is equally reasonable and equally unreasonable. The sensible solution is to meet halfway. That is both parties end up saving $500 dollars. Why is this the case? The reason is that each of the two parties is equally powerful. If Houston says to New York, you know that Monday doesn't really work for me, I need to move the meeting to Thursday, well the $1,000 disappears. If New York says that Tuesday doesn't work for me, I need to move Sal to Friday, once again, that $1,000 disappears. Only by having Houston and New York come together, agree and coordinate, can they create the $1,000. Each of them is needed equally to make that happen. So therefore, I think you split it 50, 50, or in this case 500, 500. And what that means is that Houston pays a total of $1,332 minus $500, or $832, and New York pays $2,486 minus $500, or $1,986. I'm willing to bet that is not your first response when you saw this problem. But, I hope it's something you now think is the most reasonable answer. Once you see the pie is the savings the two parties create, and that they're both needed to create that savings, then splitting it evenly makes perfect sense. The hard part is seeing the pie. It's what the two can create by working together compared to what they would each do on their own. Does the pie have to be split 50, 50? No, if I were New York, I might well start off by proposing the two sides split the total in a fashion that's proportional to the two round trips. That way New York will get 65% of the savings, rather than half. But if I were negotiating with someone who had seen this video, I don't think I'd succeed. Houston could well come back and ask for 65% of the pie and offer me 35%. Any argument that leads to one party getting more than half, can be literally turned on its head. And so while there's no rule which says it has to be 50, 50, I don't think there's a valid argument that will lead to one party getting more than half. I don't expect you to be fully convinced at this point. We're still starting, but you can see the challenge of turning a real world problem into figuring out what the pie is, and we'll have a few more examples. The next one we'll look at is how to split the cost of a taxi, and then we'll turn to some problems from the talmut. And finally we'll turn to some questions where people aren't quite sure what the pie is, and figure out how we go about splitting the pie even when the two parties have different views where there's some uncertainty about what the pie is. The key take away If you start a negotiation by calculating the pie. Once the conversation is focused on the pie, in this case the $1,000 savings, all the clutter and irrelevant detail fall away. Then, since you're essential to make that pie, you should get at least half.