女人能向男人求婚吗？

女人能向男人求婚吗？
 
 
作者：英国《金融时报》专栏作家提姆•哈福德(Tim Harford)
2006年11月7日 星期二

 
 
亲爱的经济学家：

传统上，女人必须等待男人求婚，实际上，就连约会也是如此。这难道不是一种过时而又不公平的做法吗？

菲奥娜•奥卡拉汉(Fiona O'Callaghan)，都柏林

 

 

亲爱的菲奥娜：

自1962年起，这就已经过时了。当时，戴维•盖尔(David Gale)和劳埃德•夏普利(Lloyd Shapley)发表了一篇关于谁和谁结婚的论文，研究是否有一种让有情男女彼此结合，从而消除潜在通奸者的方式。或许还是会有一些没有爱情的单身人士，但只要没有人愿意跟他们结婚，这种状况就可以被称为“稳定分配”(stable assignment)。

盖尔和夏普利提出了一种程序，可以确保实现稳定分配。每个男人都向自己的首选伴侣求婚；然后，每个女人都拒绝掉所有吸引力较小的求婚者，留下一个家伙，以备出现更好的人选。接着，遭到拒绝的人向次爱的人求婚，每个女人再次只留下迄今最佳的人选。这个有损尊严的过程将持续下去。

最终，这种程序会产生稳定分配的结果，即没有人会抛弃自己已有的伴侣，去选择一个有意的对象。这一程序还会让无数人心碎；也许这种分配之所以“稳定”，就是因为没有人希望再经历整个过程。

如果是女人求婚、男人拒绝，这个程序同样也会起作用。从直观上看，说不清你应该更喜欢哪种选择方式，但是数学是没有歧义的：在现有的各种稳定分配结果中，男人求婚的模式对女人最糟糕，对男人最美妙。这个研究结果公诸于世已近50年，可能早就应该改变传统了。

如有问题，请致信[e-mail]

译者/徐柳

 

 

DEAR ECONOMIST --- DATING
 
 
 
Tuesday, November 07, 2006
 
 
Dear Economist,

Traditionally, women have to wait for men to propose marriage - or, indeed, a date. Isn't this out of date and unfair, too?

Fiona O'Callaghan, Dublin

 

Dear Fiona,

It has been out of date since 1962, when David Gale and Lloyd Shapley published a paper on the problem of who marries whom, to work out whether there is a way of pairing up men and women so that no potential adulterers would rather marry each other. There may be loveless singletons around, but as long as nobody wants to marry them, the situation is said to be a "stable assignment".

Gale and Shapley suggested an algorithm guaranteed to produce a stable assignment. Each man proposed to his preferred partner; each woman then rejected all the less attractive offers and kept the remaining fellow on tenterhooks in case someone better came along. The rejects would then propose marriage to someone closer to their league, each woman would reject all but the best so far, and the humiliating process would continue.

The algorithm eventually produces a stable assignment, where nobody prefers a willing partner to the one they have. It also produces a billion broken hearts; presumably the assignment is stable because nobody wants to go through the whole thing again.

The algorithm works equally well if the women do the proposing and the men do the rejecting. Intuitively it's not clear which you should prefer, but the mathematics are unambiguous: out of all the stable assignments that exist, the one where men propose is the very worst for women and the very best for men. Nearly five decades after this revelation, a change in tradition is probably overdue.

Questions to: [e-mail]