[HN Gopher] A better way to divide the pie
___________________________________________________________________
A better way to divide the pie
Author : geox
Score : 58 points
Date : 2022-03-20 16:07 UTC (6 hours ago)
(HTM) web link (insights.som.yale.edu)
(TXT) w3m dump (insights.som.yale.edu)
| hackernewds wrote:
| Employee compensation would hilariously soar so much if this were
| the model. Currently employees in reality, are provided 0.00001%
| of the company.
| the_lonely_road wrote:
| Salary is often the single largest expense on the income
| statement, and especially so for service based companies. This
| expense will frequently massively outstrip the profit line
| item. So no employees are not getting 0.000001% of these
| companies, they are in fact getting the majority of the money
| flowing through these companies.
|
| 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.
| PragmaticPulp wrote:
| > Currently employees in reality, are provided 0.00001% of the
| company.
|
| 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.
| beowulfey wrote:
| I was trying to think of an alternative example; the initial
| condition (the fallback) seems kind of contrived.
|
| 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!
| paxys wrote:
| I actually think the method proposed in the article works
| perfectly in this case as well.
|
| 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.
| silisili wrote:
| This example system starts falling apart as the amounts shift.
| If one party has 5999, and the other 1 dollar, is that type of
| split still fair? It would never benefit anyone to be the
| higher of the contributors, a system of everyone looking for
| suckers.
| beowulfey wrote:
| No, of course not. That's why I pointed out that at the end
| of the day it comes down to what _seems_ fair, and what the
| two parties are willing to negotiate.
| tromp wrote:
| > let's say the value is guaranteed to increase, in this
| example by 200% to $12,000.
|
| Still kind of contrived:-(
| awestruckshoe wrote:
| Thanks for the more concrete example--the pizza situation in
| the article seemed really contrived and unintuitive to me! One
| question this leaves me with and I don't think the article
| addresses is what happens when losses are sustained when
| collaborating. Your stock example provides a good basis for an
| exploration of this question.
|
| 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!
| HWR_14 wrote:
| There is a whole subcategory of behavioral economics that can
| be summed up as "people treat potential losses and potential
| gains _very_ differently ". But what you're saying isn't the
| example that is being presented. You have A and B being equal
| partners with a loan from A to B of $1000. That's different
| from the kind of ultimatum style (with 100% certainty) game
| that is proposed.
|
| 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.
| eps wrote:
| If I were the $4000 person, I would reject the 7/5 split as
| unfair, because, conventionally, the expectation is that the
| return is proportional to the participation.
|
| 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.
| UnquietTinkerer wrote:
| This is a good line of questioning. I believe that the
| difference between the two situations is that the pizza deal is
| implied to be just for Alice and Bob. If either walks away then
| the deal is totally sunk, so they both have equal "leverage"
| over the deal.
|
| 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.
| beowulfey wrote:
| Definitely agree, a big part of this is also how badly the
| person putting more into it needs that other partner.
| [deleted]
| wyager wrote:
| Duh. The hard part is that negotiators will lie to make it seem
| like the difference is smaller than it is.
| hammock wrote:
| There is a whole book about this? The dark slices are each
| party's BATNA (best alternative to negotiated agreement, from
| Getting to Yes). Makes perfect sense that the negotiation is over
| the remaining pie
| stavros wrote:
| The point is that the remaining pie should be split evenly
| between the two parties, because they both have equal power in
| creating it.
| hammock wrote:
| In the simplistic example it could be argued that they have
| equal power. In a real scenario they likely don't.
|
| 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.
| tomcatfish wrote:
| Another formulation (unless I misread the article and it's the
| same thing here) is the Shapley Value [^sv], where you divide up
| the extra spoils according to the value added by each agent. This
| works pretty nicely with high numbers of agents too, as well as
| makes sure it's in everyone's interest to join your sharing
| scheme even if they're not already in it.
|
| [^sv]: en.wikipedia.org/wiki/Shapley_value
| reggieband wrote:
| One thing I learned in a class on negotiation was that many
| people look at negotiation as a one-time thing. Examples like
| buying a car happen for most buyers once every 5 to 10 years. It
| is also a negotiation that most often happens with a new sales
| agent / sales manager combo for every transaction.
|
| 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.
| WinterMount223 wrote:
| This is throughly discussed in game theory. Single games,
| finitely repeated games, infinitely repeated games.
| gpsx wrote:
| I like the way you say that. I was going to say that Ann can
| push to split the pizza 7-5 if it is OK that she is being an
| a@#hole. If not, she should split it 6-6.
|
| I think the author makes a good point in the article, but he
| should have at least mentioned future ramifications.
| svilen_dobrev wrote:
| this reminded me of: Evolution of trust
|
| https://ncase.me/trust/
| jka wrote:
| > One thing I learned in a class on negotiation was that many
| people look at negotiation as a one-time thing. Examples like
| buying a car happen for most buyers once every 5 to 10 years.
| It is also a negotiation that most often happens with a new
| sales agent / sales manager combo for every transaction.
|
| 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.
| vineyardmike wrote:
| I can't quite tell if you're missing the point. The pizza
| analogy is just some simple case that's easy to explain in a
| paragraph. The book is on negotiations, so they need some
| easy case to negotiate.
|
| 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.
| jka wrote:
| Generally I think my perspective on the issue is that a lot
| has been written already, and that people have a tendency
| to rewrite and bring-to-market content that is a rehash of
| existing knowledge, as opposed to gathering people together
| towards consensus (and expansion, and critique) of existing
| best-known information. Perhaps writing books is an
| expression of that; and perhaps my frustration is because I
| wonder whether we could do better in the digital age.
|
| 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.
| PragmaticPulp wrote:
| > 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.
|
| 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.
| antisthenes wrote:
| > 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).
|
| 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.
| rkk3 wrote:
| > 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.
|
| 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.
| PragmaticPulp wrote:
| That's the point - If you bring someone in at the wrong
| level (higher comp = higher level) then you have a major
| problem.
|
| 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.
| sharkjacobs wrote:
| this is game theory 101 too. The prisoner's dilemma is a simple
| game, like tic tac toe, and the only correct move is to betray
| the other player every time. But repeated prisoners dilemma is
| a much more complicated game about trying to get as much out of
| your opponent as possible without breaking down cooperation
| altogether.
| zasdffaa wrote:
| [deleted]
| chociej wrote:
| Did anyone think to ask "who's hungrier?"
| littlecosmic wrote:
| As you say, Alice is not in desperate need of pizza, so she'll
| just wait for a deal that gives her the most. The power to say
| no to deals is the true advantage of greater wealth.
| NAR8789 wrote:
| This reminds me of how I used to split rents with my roommates:
| Identify surplus value, and split that value evenly.
|
| 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.
| exo-pla-net wrote:
| 0: Total rent is $10, for ten rooms, to be split among ten
| people.
|
| 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!
| thenerdhead wrote:
| I've always come to the same conclusion that "tit-for-tat"
| strategies are the simplest and most effective.
|
| 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.
| gnicholas wrote:
| I'd be curious how many people were surprised to be greeted by a
| picture of a pizza after clicking a link that refers to dividing
| pies.
|
| 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?
| [deleted]
| joshuajomiller wrote:
| This is not a new idea. It was written about thousands of years
| ago in the talmud:
| http://www.talmudology.com/jeremybrownmdgmailcom/2016/9/27/b...
| rishabhjain1198 wrote:
| Absolutely incredible! I haven't felt the feeling of insight
| after just reading 3 paragraphs in a long time.
| ulucs wrote:
| So... Uhh... Just Nash bargaining? Or Shapley values result in
| the same outcome too in this case.
| gondo wrote:
| Reading the title, I thought this will be about a fair splitting
| of home cooked pie (or any dish). My go-to method for this is to
| divide the responsibilities. One party cuts (or decides where to
| cut in the case children are involved), the other party picks.
| Does anyone use a better, fairer method?
| papandada wrote:
| For 2 people that's fair. It only gets a bit more complicated
| with more people or other variations.
|
| https://en.m.wikipedia.org/wiki/Envy-free_cake-cutting
| 11235813213455 wrote:
| Reminds me of https://www.google.com/doodles/celebrating-pizza
| m3kw9 wrote:
| This example seem like a lesson for bob on how to not get screwed
| by Alice's seemingly higher leverage by focusing on what is
| actually at stake to negotiate, the 6 extra slices. And also
| recognize Alice does not actually have more leverage just because
| the fallback is to her advantage, she would still have lost out
| up to 6 slices, making any type of deal would be better for her.
| delgaudm wrote:
| Perhaps I got lost in the explanation, or the example is overly
| simplified, but isn't this just "splitting the difference"?
| nerdponx wrote:
| The example is overly simplified.
|
| 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.
| karmakaze wrote:
| I imagine in many contexts, the more 'relative status-quo'
| outcome to the original would be 4+4 to 2+2, double-or-no-
| change. Bob wanting more than to double could be spiteful
| bargaining power which Alice could answer with spite.
| HWR_14 wrote:
| I saw it in the article and literally thought it was a
| straw man. I believed the author was arguing against a 6-6
| division and introduced a more unbalanced shift to try to
| make their position seem reasonable.
|
| 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?
| HWR_14 wrote:
| No. Splitting the difference could be a term invented to
| describe this, but it already has a different meaning. It's use
| is if I offer you two slices and you counter with a demand for
| six slices, then "splitting the difference" just refers to
| using the average value of four.
| tromp wrote:
| It is splitting the difference between Alice offering to take
| the whole negotiation pie at 10-2 and Bob counter offering to
| take the whole negotiation pie himself at 4-8.
| HWR_14 wrote:
| Yes, if each originally maximally said "I want all 6 new
| slices" then it would be splitting the difference in their
| asks. However, in the case where Bob counters with an offer
| to split 6-6, it is no longer splitting the difference.
| hackernewds wrote:
| Now it has been bastardized by "Never Split the Difference"
| which is what you now hear from a desperate car salesman now
| HWR_14 wrote:
| How would a desperate car salesman use that phrase?
| nhod wrote:
| "Never Split the Difference" is also the name of an
| outstanding book by Chris Voss, the former head of FBI
| hostage negotiation. For shorthand, Voss refers to all biz
| school rational-actor negotiation theory (as espoused by
| the parent post, for example) as "splitting the
| difference."
|
| 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.
| zw123456 wrote:
| maybe a little off topic, but....
| https://yaledailynews.com/blog/2021/10/14/yales-endowment-re...
|
| 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.
| HWR_14 wrote:
| Education doesn't scale. Great professors don't scale. The
| endowment _is_ used for funding the tuition of people who
| cannot afford it.
|
| And, to the degree it does scale (Edx, coursera) well endowed
| universities were at the forefront of putting classes online.
| zw123456 wrote:
| OK, so if I am understanding your point correctly, education
| does and doesn't scale, and big universities with huge
| endowments have done enough because they put classes online
| and subsidizes tuition for a small number of lucky people.
| So, it's OK for them to hold onto $42B endowment fund, for...
| something?
| HWR_14 wrote:
| Some parts of education scale, some parts don't (see
| Customer Service and 100 other examples). Universities are
| doing a good job using tech to scale when they can. It's
| unreasonable to expect in person attendance to be able to
| even double and maintain close to the same quality.
|
| Yale give a scholarship for any students, with any part 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.
| gondo wrote:
| The naive 6:6 split tries to compensate for the original
| unfairness. In real life, starting positions are mostly hidden
| and therefore this problem is avoided.
| [deleted]
| est31 wrote:
| The base case, in which Alice and Bob don't reach an agreement,
| has a specific name: BATNA.
| https://en.wikipedia.org/wiki/Best_alternative_to_a_negotiat...
|
| 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.
| huynhhacnguyen wrote:
| If we can ignore the utility value of the negotiating pie (e.g.
| Alice may not want a 5th slice anyway), it is an interesting
| perspective. If only there were more examples and less
| explanation.
| c1ccccc1 wrote:
| In general: Suppose the fallback positions are x slices for
| Alice, and y slices for Bob, and they get n slices total if
| they reach a deal. Then we can figure out the split by defining
| the gain, g, as the additional pieces they get if they reach a
| deal. So g=n-(x+y). Then the fair split should be x+g/2 for
| Alice and y+g/2 for Bob.
|
| 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)
| HWR_14 wrote:
| It's a modestly interesting point, but it certainly doesn't make
| sense in the concept of pizza. The author tries to appeal to
| fairness, but where the fallback positions are knowingly arranged
| randomly. Therefore, the naive 6-6 solution is just refusing to
| adjust for a superior random arrangement in the experiment, which
| was unfairly assigned. Therefore, I would expect the naive 6-6 to
| be chosen the plurality of them time.
|
| 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.
| davidmanheim wrote:
| Also, why is any pizza ever getting cut into 12 slices?
| rootusrootus wrote:
| Aside from small pizzas, I generally cut pizzas into 12
| pieces. 8 slices ends up with unwieldy slices, 16 makes for
| overly narrow ones. Cut it however you want, of course, but
| for most average sized pizzas 12 makes for a nice sized
| slice.
| NeoTar wrote:
| That's very much a cultural thing. An average European
| pizza is more of a 'personal' pizza and 8 or 10 inches in
| diameter. Twelve slices would be too much.
|
| I propose the Imperial/English pizza theorem. The optimal
| number of slices for a pizza is equal to the size in
| inches.
| HWR_14 wrote:
| A giant pizza cut so that each slice is a full meal
| (maybe two if very hungry) is optimal.Eating a slice of
| pizza should be enough.
| hexane360 wrote:
| Unfortunately, that guarantees the arc length of the
| slice to be constant (at pi inches), but not the total
| area (= d * 1/2 in). I believe this is why larger pizzas
| make more sense to cut into squares, as long thin pieces
| are harder to slice and to eat.
| rootusrootus wrote:
| Yeah, that's my exclusion for small pizzas. We only do
| personal pizzas for the kids. The rest of the family
| shares a larger one (or two, or however many).
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