A better way to divide the pie
insights.som.yale.edu
insights.som.yale.edu
However, a large number of negotiations in business happen with the same group of people over and over again. The example was a set of directors in a large org negotiating over budget. That kind of thing might happen every single business quarter between a stable set of peers.
Whenever I see strategies like these I consider those two cases since they have influence on how negotiations are done. In the car-sales case, there is an incentive to get the most out of the individual negotiation since you almost certainly will never see each other again. In the business case you are incentivized to prioritize the relationship with your peers over any individual negotiation.
So I don't agree with the simplistic conclusion in the article. It seems to only consider fairness within the context of a single transaction/negotiation. It does not consider what happens when this strategy is repeated between actors across multiple negotiations.
You may have been implying this already, but just to reinforce the message: it's an asymmetric event frequency.
For the buyer, it occurs once every few years. For the seller, it's occurring on a weekly or perhaps daily basis.
That means that the seller is fairly likely to know most of the common weaknesses and opportunities for buyers, and the ways in which those buyers communicate (or fail to communicate) them. Sellers can choose to do what they want with that information advantage.
To me the question is a broader one: why are Alice and Bob accepting to enter into some byzantine challenge where they have to co-operate in order to receive a larger amount of pizza? And why is there an entire book for sale on the topic, when at first-glance it seems to closely (~80%) resemble what can be defined as the prisoners' dilemma within a paragraph?
I think Alice and Bob should publish the ridiculous situation they've been faced with at the pizza restaurant and find somewhere else to go to eat, and I don't think they require a book to teach them that.
I’ve had to negotiate for my team at work before and one common thing I hear at private discussions with other parties when in planning for the meetings is that it’s backwards and toxic to have business politics and they want to leave the team over it. this feels like you’re take - and it misses the point that today, you have to accomplish some task. Even if you’re against politics at work, you’re beholden to them once they start. Tomorrow is for deciding if you should accept reality or make changes. And some things aren’t likely to go away.
In the context of workplace politics: again, these are all patterns that have been repeated for generations. Perhaps it's possible to document and make those patterns public, and then help people to view and decide upon the kind of workplace(s) they'd like to contribute to.
Very insightful point.
The biggest salary negotiation mistake I see is when people assume the negotiation is of the first type (one-off, never see people again) instead of the latter type (part of an ongoing relationship).
If a company works hard to minimize someone's compensation expectations and convince them to accept below-market salary, they're going to pay for it later when the person wises up and leaves for something better. This scenario is well-known.
The less discussed scenario is when a candidate aggressively negotiates a very above-average compensation but subsequently performs in a below-average manner. This is one of the most common complaint scenarios in a private manager forum that I'm part of: Managers who get wowed by people with excellent interviewing and self-selling skills who end up underperforming their lesser-paid peers later. It generates a lot of guilt and anxiety for managers when they realize they've been duped into inverting the contribution:reward relationship in their compensation structure.
These people are the first to go in any downsizing, reorgs, and layoffs (and rightly so), but they're often great at talking their way into the next highly paid job almost immediately. This is one of the main reasons experienced managers will go extra deep on reference checks for people with job-hopper resumes.
Isn't this more a failure of the management? What can justify having wide disparities in starting comp for the same role? Seems like the striving candidate should be bumped up a level & you just hold them accountable to the higher bar, rather than evaluating their performance based on comp.
Compensation does vary within a role, though. Even at organizations that publicly share salary info there is often a wide range within each band and the salary bands may overlap.
Paying everyone in perfect lock-step with each other sounds great in theory, but you end up either paying significantly more than you need to or locking yourself out of otherwise great hires that were just a few thousand short of your fixed salary. Obviously, not everyone within a role performs exactly the same.
That depends what you're negotiating. As a counterexample, if you negotiate a big raise upfront for your promotion and then "coast" for 5-10 years, you're still better off than negotiating a series of smaller raises every 2 years, because you forego the overhead of multiple negotiations. Personally, I'd rather just focus on the work.
Negotiation is costly if you're not good at it. It's easier to justify your value once, than multiple times. Due to anchoring, and people getting used to the increased output you bring, it will become harder and harder to negotiate as you go further.
Better to do it once, but do it right.
Sometimes people don’t do as much or as well for things that are none of your business and if that becomes an incentive problem for you, you’re the problem.
I think the author makes a good point in the article, but he should have at least mentioned future ramifications.
Why was Alice being offered 4 and Bob 2? Perhaps Alice had done twice as much work as Bob to get the original pizza. Perhaps she had invested twice as many resources. In that case, why would the "fair" deal be one in which Bob is suddenly getting the same compensation as Alice?
The solution outlined in the article makes more sense.
Sheesh. What real world scenario is this supposed to model?
These types of situations happen all the time. Think of two businesses collaborating on a project, for example.
You've got great insights here. That said, I can't help but think that perception - that it is a one-time, transaction relationship - is a key difference between winners and losers. What I mean is, from the standpoint of the salesperson, they should be seeking a long-term win and not just a win in this transaction. We'll use your example of a car, but I can think of many other places where this also applies. In the the car situation - you really want to sell / lease them the car, but you also want there services business. You want them to tell their friends to come buy from you. You want them to come back in 5-10 years and buy/ lease their next car from you. None of that happens if they walk away feeling like it wasn't a fair situation.
Likewise, even in a seemingly "done" negotiation, things have a way of cropping up. Like the buyer comes to take possession of the car and decides that the tires look more worn than what they believe, and suddenly want to renegotiate. Or, maybe you've agreed on price already, have started signing the paperwork, but then the salesperson wants to upsell you on the truecoat. Point being - I think you were even more right than you may have intended, in terms of the ongoing nature of negotiations rather than a fixed-position scenario.
0. Given a prospective rental house. (And therefore a known set of rooms and a known total rent)
1. Each person "bids" by pricing every room in the house. Goal: each person should be looking for "break-even" pricing. Try to price such that all the rooms feel "equally good" at your given prices.
2. Just one restriction on the pricing: each bidder's room-prices must sum to the house's monthly rent.
3. Reveal all bids.
4. Choose the room-assignment that yields the highest total price. Because of the restriction in [2], we're guaranteed a surplus over the true total rent. (Unless everyone somehow put in identical bids)
5. Split the surplus evenly. Everyone gets a room at the price they bid for that room, minus 1/nth of the surplus. Effectively, everyone gets an identical surprise discount.
We lived together for over 10 years, through 5 different rentals. We split up when it came time to start families and buy houses.
1: One person who really wants a certain room bids $10 on it, and he assigns $0 to the nine other rooms. His roommates bid a neutral $1 on all rooms.
...
4: The person gaming the system gets his special room.
5: The surplus is $10 + 9*$1 - $10 = $9. Split evenly, $0.90.
Thus, the gamer pays $9.10 for his special room, and everyone else pays $0.10 for their rooms.
He has clearly made a terrible mistake. He's covering the cost of the entire rental nearly by himself.
Next time, he bids $1 + one gummy bear on his special room, and he bids $1 on the other rooms. He imagines that now he'll merely have to buy one gummy bear every month, split it in ten, and give everyone a slice. He's outwitted his roommates, he thinks.
However, much to his dismay, he overlooked that one of the rooms in this next rental was underground. Furthermore, the room was next to a leaky sceptic tank. Everyone else bid $0 on it. The gamer handily wins the sewage room, instead of his special room, and he hardly gets any discount for putting up with it. Oops, foiled again.
All of this is to say, your system seems robust. There's danger in over and underbidding on your assessment of a room's value. You want to be very careful in deciding how much a room is worth to you. I think I'll use this system for renting Airbnb's with friends in the future. Thanks!
As far as the 'sewer room' option goes, I think it would have to be priced at the cost of renting somewhere else; so a negative value.
For the split on the surplus rent there are a couple solutions to this.
IIRC it might be a dutch auction rule? The one where if N of a thing are available a there are N winning bidders all the winning bidders pay the lowest price? Take that rule except apply it to the lowest choice total among the set that yields a full rent.
There's also an argument about how to split the savings. In the 10 + 9 * 1 scenario the portion of the total rent the distribution of savings might be better split up as:
'refund' = SURPLUS * nROOM / (RENT + SURPLUS)
nRENT = nROOM - SURPLUS * nROOM / (RENT + SURPLUS)
If A = 10 and B..J are all 1
5.263... = aRENT = 10 - 9 * 10 / 19
0.526... = xRENT = 1 - 9 * 1 / 19
Rent (10) == A (5.26315789474) + Everyone else (4.73684210526)
Even in the pathological case offered this works well enough.
For example: suppose the total rent is $100 for 4 rooms of varying qualities. I have very little money, so I'm willing to take the terrible cupboard-under-the-stairs room for $15.
I have no way to arrange my bids to say that I can't afford more than $15, since the average of all my bids needs to be $25.
The problem with game-theorist economists is that they always neglect long-term externalities because they're messy. Having a reputation as a decent human being is a long-term externality that's very messy.
So let's say there's some investment opportunity where someone has $4,000 to put in and I have $2,000. The investment requires $6000, so neither of us can access it alone. If we agree to invest, let's say the value is guaranteed to increase, in this example by 200% to $12,000. The power analysis way of distributing that increase would be that the other person gets $8000 and I get $4000. Using this pizza analysis, it would instead be distributed as $7000 and $5000 -- splitting the increase of $6000 equally.
It's an interesting concept. Certainly I, with only $2000, would be more inclined to contribute. And the other party would certainly benefit more than if we had decided to not go through with it at all.
I think it comes down to how much the person with the weaker power is likely to want to contribute. It's a good way to convince them if the power is fairly offset, but when they are close it's not really necessary to convince them.
I think this is partially touched on in the article itself, and it makes sense. It comes down to what seems fair to the parties involved!
Still kind of contrived:-(
What you're seeing in this hyperbolic "counter-example" is that the assumptions of that model don't hold; the person providing 1 rather than 5999 is probably very replaceable and would be willing to settle for much less profit due to market forces, the person providing 5999 probably has the means to at least temporarily acquire another 1, the deal probably wouldn't fall through in the first place if it were for slightly less than 6k, and so on.
Say A puts $4000 in and B puts $2000 in with the expectation that they will double their money, but instead they lose it all. By the procedure outlined in article, the “pie” worth -$6000 would be evenly distributed, meaning both A and B would have to pay $3000. So A ends up with $1000 and B ends up with -$1000. This seems especially punitive to B, and they end up in a worse place than they would have with what the article calls the “power” arrangement, under which they would have $0 after losing only $2000 instead of $3000.
I’m curious about how many weaker parties continue to favor the “pie” method when losses are divided the same way as gains—-my intuition is that a “pie”-style deal is typically reached only when there is an almost-certain probability of gain, but I’m curious about how negotiators actually behave!
I would say a better example is that A owns 66% of a startup and B owns 33%. They decide to sell the tech for X dollars. However, they are offered a 2X buyout if both of them agree to work for 3 years at the acquiring company. There's no "partial" offer though, it's both partners or neither. How is the 2X split up?
The contrived example fails because of the 33% and 66% wouldn't be assigned randomly.
When you frame it as an investment question, the implication is that if either person walks away then they can be replaced by a third party who is willing to stake the cash. Since it is easier to replace someone when their stake is lower, the person putting up the $2k has less leverage in this case.
If you explicitly limited the investment to two specific people (imagine a crazy term in a will or something), then I think you'd end up back with a $7k/$5k split.
Consider an extreme sceanrio - $5990 and $1. As per the article the return should be $8999 and $3001. That's not going to fly in the real world.
If you found a magic investment that was guaranteed to return 200%, but were some money short so couldn't invest at all, if I made up the difference and said we had to split the gains evenly it would still be in your best interests to say yes.
Of course the obvious response is that investments aren't guaranteed to return money. Going by this method, the losses would be "split" evenly as well rather than in proportion. So if the company could only return 50% of the initial investment, you would claim extra money towards your principal, thus reducing your overall risk at the expense of the person who invested less money.
Also note that it's two humans agreeing on a deal, and the way of looking at things described in the article might not be shared by both. If your other party is convinced that 6/6 is the most fair distribution, it is to your advantage to agree with that notion, at least if you are Bob. If you are Alice, then you should absolutely make the case. Of course if the game is repeated and you don't know the future game's distributions, this might come back at you, if the roles are switched and the other party goes into the game with that memory.
[^sv]: en.wikipedia.org/wiki/Shapley_value
In a real scenario, the dark slices may or may not be irrelevant; Bob must also consider making a deal with Charlie, who was left out of the example and has 6 dark slices of his own, or with David, who has 3 dark slices.
There is also the pizzeria across the street to consider which gives Alice and Bob each 3 dark slices.
It is also called as BATNA - Best Alternative to a Negotiated Agreement (BATNA). This is evaluating what is your best alternative if the deal does not get through. In a negotiation, you would want to strengthen your BATNA and weaken other's BATNA. The course was amazing.
How about this way of dividing the pie: Alice and Bob describe theirs needs to a third party, and the third party gives each one what is needed. Or if no third party: just describe and justify your needs in an envelope, open both simultaneously, and share the pie.
The logic that "of course, everyone should take as much as they can" is an impasse. It doesnt make anyone truly happy, makes the person with the worse fallback an inferior to the other party during the negotiations, doesnt guarantee fairness, etc. And worst of all: it doesnt allow for human values such as empathy.
This article is an algorithm between programs, not any reasonable way to treat a person, valuing their feeelings and needs.
Would my village be a happier, better place if the one or two families who already own most land used it as an leaverage to extort as much resources as they could from the others? Quite definitly not.
The idea here is that the individual cannot trust the group to consider their needs. This is not a theory it is a collective lifestyle choice. There are countries and regions where the opposite (people looking out for each other depending on their needs) works out just fine.
In German we speak of something called the Gesellschaftsvertrag — the implicit contract each individual has with society. It can be extremely enlighting think about whether someone subscribes to this contract and if not, why. E.g. someone who has been convicted for years of prison for a minor drug charge while bankers who steal billions go free, might just stop to believe it pays off to honor the rules of the contract. Someone who thinks everybody else is just a fool to extract money from probably even thinks of society as something with implicit rules.
However every human society, even societies with slavery, genocide, etc had these implicit rules of what a wealthy person was expected to provide, what a poor person was expected to endure. Break the contract on a large enough scale and you get a violent change of power or a revolution.
It's not clear what everyone's utility function is. If a sales person is nearing a quarterly target, their utility function might have a giant kink in it, or if they're at the start of a period it might be very linear. The marginal pie, more often than not, has multiple dimensions which different agents care different amounts for.
Thankfully I've never been in a negotiation without a decent BATNA and so just chat about it until either we decide it's not going to work out, or we are both happy. People who negotiate too hard by playing stupid games and trying to max out themselves without any quarter given are tiring and push me to the first option. Why would I want to work with you if you're a pain to deal with before we even start?
He holds that such theory is useful to know in general, but that real-world negotiations are carried out by emotional, irrational humans. As a result, these rational theories often break down in the face of hubris, anger, fear, love, shame, etc, and as such, relying solely on these theories will not get you the results you want. Thus, you should "never split the difference."
Instead, he then goes on to suggest a whole variety of ways one can achieve better negotiation results, starting with the most obvious: really, truly listening to the needs of the other. The book is fascinating. Highly recommended.
Imagine if it was a 24-slice pizza. The argument is that the "original" 6 slices should be divided according to the original preferences of 4 and 2, and the "extra" 18 slices should be divided evenly into 9 and 9.
You're the first person I've seen suggest that this is a thing and I'm kind of shocked. What reasoning would there be for unequal division of the additional slices in A's favor?
As an edge case, let's say A has 1M, and B has 1k and there's 500k new units. Should B get 250k same as A? Would A go for that? Would B be happy with 100k?
There's also a question of if there is any value to clam pizza beyond the initial four slices. That sounds like a lot of food that reheats poorly.
Now, if you want to say this applies to something in the real world as a concept, I would say it's not a novel concept. No one expects a new employee to capture 100% of the value they add, nor do people expect the new employee to work for free.
I propose the Imperial/English pizza theorem. The optimal number of slices for a pizza is equal to the size in inches.
Another kind of situation is if there are 3 people, Alice, Bob, and Charlie, with fallbacks x, y, z respectively. Suppose they all need to reach an agreement to get n slices. Then g=n-(x+y+z) and Alice, Bob, and Charlie should get x+g/3, y+g/3, z+g/3 respectively.
Another possible situation is if there are 3 people, but they have unequal roles. Alice only needs to make a deal with at least one of Bob or Charlie, to get n slices. If Bob and Charlie both agree to the deal, then the total is still n slices. Intuitively, this would make Bob and Charlie less important, so they should get less of the gain. The split here should be x+2g/3 for Alice, y+g/6 for Bob and z+g/6 for Charlie, if they're all in on the deal. The reasoning there is that if we're adding games together, then we should also add the payoffs together. We can make a Alice&(Bob|Charlie) game by adding together Alice&Bob + Alice&Charlie - Alice&Bob&Charlie. Similarly, the payoffs should add like this: (g/2, g/2, 0) + (g/2, 0, g/2) - (g/3, g/3, g/3) = (2g/3, g/6, g/6)
I'm from California, where "pie" refers exclusively to the dessert variety. I expected the article wouldn't be specifically about pies, but rather about negotiation in general.
Did anyone (from areas where "pie" can mean pizza) think that this was going to be an article in which pizzas were used to illustrate the point?
You are noting that the employee line item is split up amongst 50,000 employees and the smaller profit number is behind split up among 50 owners. So an individual owner makes massively more money than an individual employee but missing that employees as a class are still getting more of the money than the owners.
0.00001% of Amazon's entire revenue (not profit, but revenue) last year would be about $14,000.
Fortunately, every one of their full time employees is paid more than that. Entry level engineers make 10X that amount and the best engineers make 50X that or more.
At some of the most highly paid companies like Uber, paying employees according to the value they create would actually make salaries go down in every scenario, because the company is still fueled by investor funds and can't self-sustain on revenue alone.
After round-tripping from IC to manager and back a couple times, I've come to realize that the value given to engineers especially is extremely high. Many initiatives in the tech industry don't ever turn a profit for the company or investors, yet we get paid six figures all the same.
If anything, I would expect such a hypothetical initiative to redistribute more of the wealth away from engineers like us and toward people like the customer support team who are fixing all of the problems created by products that don't work quite right. The person on the phone with grandma walking them through a support issue arguably contributes more to the LTV of that customer than anyone else.
Stepping outside of tech, I think people imagine profits to be much higher than they are in reality. Grocery stores are a common example of a business that has very narrow profit margins (some times a couple percent) that don't actually have large amounts of leftover profit to distribute to employees.
Regardless, it's all hypothetical. The employment market is supply and demand, and that's why engineers are paid so highly. End of story.
You agree to cooperate at the start. Then you follow whatever choice your opposition made the previous move. The even better approach is to add in generosity randomly as a means to "forgive" misunderstandings.
Maybe just me, but this article seems to add more complexity to the problem.
I am thinking maybe t yale could spend a little time on finding a fairer way of slicing up that pie? It seems like they could easily educate a lot more people who cannot afford their tuition. And I am not just picking on Yale, Harvard and a lot of others could add to a fund, what if all those schools with multi-billions dollar endowments could give half of it to fund the education of anyone who wants it?
This is not a meant to be a rant just a humble suggestion that occurred to me when they were talking about giving away half a pizza.
And, to the degree it does scale (Edx, coursera) well endowed universities were at the forefront of putting classes online.
Yale gives a scholarship to any students for the amount in between the expected family contribution and full cost of tuition/room/board/books/activity fees/small spending stipend. More than half of Yale students get such a scholarship and the average value of that scholarship is higher than tuition and books alone would be, meaning most students are only paying for housing and food. (Okay, it's an average and an average, so it's possible only like 40% of people are having their entire tuition covered, but also their entire room and board and another 17% are getting a dollar.)
But, yes. In general you summarized my points correctly. But I take issue to "small number of lucky people". And, of course, with the sarcasm clearly coming from your post.
More interesting IMO, is the question of whether or not great professors can scale, and whether online can do it. Or whether the real value add for "elite" universities is their quality of education, and whether great professors are required for it.
My beliefs (totally unfounded), is that yes, "great" professors _can_ scale, because the mark of the "great" professor would be their ability to explain things in lecture. This of course, ignores any personal attention you can glean, but for most undergrad courses you're not getting much of that anyways.
I don't think that great professors solely exist at prestigious schools, but there's definitely a greater density of them there. Just like FAANG has a greater density of competent programmers than competitors outside their tier.
I agree that not everyone needs a great professor. But, by definition, they are better. But yes, not everyone needs an elite education.
Ivy League schools have nowhere near a trillion dollars in endowment money. They have $1XX billion, I don't recall exactly how much.
I think that's all of the points, but I may have missed one.
I have listened to the Feynman lectures before, they are great for sure. But there are thousands of people haven't, and yet they still have benefited from a good college education.
If you want to figure out how to scale an elite Ivy league education, I think you cannot, I think the elite part is what trips you up. But if you want to see how to scale a good college education, you need look no further than the state university system, which for over 100 years has done exactly that. Unfortunately, the costs of that have gone up to the point that many young people are saddled with unmanageable debt. Some progressives, who are themselves the product of said elite education, talk about taxing billionaires and large corporations to pay for universal affordable college but somehow conveniently overlook the pile of money sitting in those endowment funds, far more than what those schools will ever need.
We should have universal affordable college for all that want it, billionaires and large corporations should contribute to that and so should the elite schools with outsized endowments. A good start would be to add a little tax to all those and increase the subsidies to state and community colleges.
And this comes from someone who is a product of said elite schools and was lucky enough to have it paid for. But not everyone is so lucky. I have also been lucky to have worked with young people who served their country and used those benefits to pay for college and, in my view, they are every bit as capable as anyone that attended an elite school.