Dore: Ogre


Obviously, not every man can marry his first-choice woman, and not every woman can marry her first-choice man. Life sucks that way. So, let's try for something weaker. Given a way of pairing off the men and women, say that it's stable if no man and woman who aren't married to each other both prefer each other to their spouses. In other words, you might despise your husband, but no man who you like better than him likes you better than his wife, so you have no incentive to leave. This is the, um, desirable property that we call "stability".
-- Scott Aaronson "Quantum Computing Since Democritus"
Чот я не вкурю - это же переусложнённое определение оптимальности по Парето, нет?
Вроде нет. Если A уходит от B к C, то B может стать более несчастен, то есть такой переход по Парето запрешён, а вот в соответствии с этим определением вполне может быть возможен, если A и C предпочитают быть друг с другом, а не со своими текущими партнёрами - даже если их текущие партнёры при этом станут намного несчастнее.

То есть любое "стабильное" состояние является парето-оптимальным, но обратное, вообще говоря, не верно
Мне кажется, определение плохое. Если мы говорим про "incentive to leave", то мы уже работаем не со статическим snapshot'ом, а с динамикой во времени. Чтобы использовать это определение, нужно предположить, что отношение "like" константное (стабильное) во времени, а это далеко не так. Восприятие одной и той же женщины, увиденной со стороны, и увиденной в результате многолетнего сожительства, это очень разные восприятия.
Ух ты! Это ведь не значит, что Скотт Ааронсон самый несчастный человек на земле?
Desirable property
Letter from Simon Fallowfield to Mary Foster November 29th, 1866.
My Dear Miss,

I now take up my pen to write to you hoping these few lines will find you well as it leaves me at present Thank God for it. You will perhaps be surprised that I should make so bold as to write to you who is such a lady and I hope you will not be vex at me for it. I hardly dare say what I want, I am so timid about ladies, and my heart trimmels like a hespin. But I once seed in a book that faint heart never won fair lady, so here goes.

I am a farmer in a small way and my age is rather more than forty years and my mother lives with me and keeps my house, and she has been very poorly lately and cannot stir about much and I think I should be more comfortabler with a wife.

I have had my eye on you a long time and I think you are a very nice young woman and one that would make me happy if only you think so. We keep a servant girl to milk three kye and do the work in the house, and she goes on a bit in the summer to gadder wickens and she snags a few turnips in the back kend. I do a piece of work on the farm myself and attends Pately Market, and I sometimes show a few sheep and I feeds between 3 & 4 pigs agen Christmas, and the same is very useful in the house to make pies and cakes and so forth, and I sells the hams to help pay for the barley meal.

I have about 73 pund in Naisbro Bank and we have a nice little parlour downstairs with a blue carpet, and an oven on the side of the fireplace and the old woman on the other side smoking. The Golden Rules claimed up on the walls above the long settle, and you could sit all day in the easy chair and knit and mend my kytles and leggums, and you could make the tea ready agin I come in, and you could make butter for Pately Market, and I would drive you to church every Sunday in the spring cart, and I would do all that bees in my power to make you happy. So I hope to hear from you. I am in desprit and Yurnest, and will marry you at May Day, or if my mother dies afore I shall want you afore. If only you will accept of me, my dear, we could be very happy together.

I hope you will let me know your mind by return of post, and if you are favourable I will come up to scratch. So no more at present from your well wisher and true love.

Simon Fallowfield

P.S. I hope you will say nothing about this. If you will not accept of me I have another very nice woman in my eye, and I think I shall marry her if you do not accept of me, but I thought you would suit me mother better, she being very crusty at times. So I tell you now before you come, she will be Maister.
Re: Desirable property
Это из обычного сборника писем и стихов о любви. Она его предложение отвергла, кстати. Сейчас не могу найти его. Называeтся Love. Мне кажется, вам должна очень понравиться книга Parallel Mariages by Phyllis Rose.

Edited at 2017-09-07 09:49 am (UTC)
Не учитываются тройные, четверные и так далее обмены. :-).