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December 14, 2008

仿照反摩尔定律,写一个反六度分隔理论。

关于“反摩尔定律”,这里抄谷歌黑板报上,吴军研究员给的定义

Google(谷歌)的 CEO 埃里克•施密特在一次采访中指出,如果你反过来看摩尔定理,一个 IT 公司如果今天和十八个月前卖掉同样多的、同样的产品,它的营业额就要降一半。IT 界把它称为反摩尔定理。

也就是说,作为IT硬件产业驱动力的摩尔定律,也有其残酷的一面。

六度分隔(Six degrees of separation)理论说,只需要很少的人(比如,6个),就可以联系起世界上的任何两个陌生人。

这个理论让社交网络的从业者们兴奋异常,但是,这个理论是否也有其阴暗的一面呢?

我们反过来看这个理论,假定一个人对自己的信任度为1,对陌生人的信任度接近0,那么我们可以拟合出一条曲线:随着分隔度数D的增长,信任T降低。我们知道两个数据点:在分隔度数为0的时候,也就是自己对自己的信任为1;在度数D是6的时候,信任度T接近0.

通俗的说:我们都信任自己,但是对于朋友的朋友的朋友的朋友的朋友的朋友,他谁啊他?

最简单的拟合方法,在知道两个数据点的时候,做一条直线,就象这样:

这张图说明什么呢?对于有的人来说,多隔一层关系,就少一份信任。

不过对于有的人来说,朋友的朋友的朋友的朋友的朋友的朋友其实跟朋友的朋友的朋友的朋友的朋友差不多,都是陌生人,那么对于他们,下面这种指数递减的曲线更合适:

对于接近这种曲线的人来说,朋友的朋友,就离陌生人不远了。

我相信这个指数递减的曲线更符合信任的传递关系。这里我们需要先定义一下信任度。我对信任度的定义是:我们对朋友的话,选择相信还是不信的概率。通俗的说:我们对自己的话是100%相信的;如果我们对朋友信任度是80%,那么朋友的100句话,我们只相信80句。

那么假设人对朋友的信任度平均值是μ,一个人A有朋友B,B有朋友C。C说100句话,B只信任μ * 100句,假设B把这些话转述给A,那么A只相信100 * μ²句。如果你相信我的这个说法的话,那么社交网络的信任度,就是随着分隔度数的增加,而指数递减的。

μ很难确定,不同的人对朋友的信任度不同,一个人对不同的朋友的信任度也不同。这里我们取一个平均值:½。就可以得到上面这张图。

看看这张图吧,我们对于朋友的朋友的说法,只相信¼,而对于朋友的朋友的朋友的话,10句里面只相信一句而已。

假如某个社交网站希望用朋友之间的关系来推广商品的话,那么很不幸,朋友的朋友说的话,未必有社会上广泛承认的专家说的话更有效果。

信任,就是如此的脆弱。

15 Comments »

  1. 社交网站往往会出现,两个或者三个朋友都在说同一件事情!那么这个事情的可信度就一下上去了!

    Comment by 陈茂龙 — December 15, 2008 @ 5:08 am

  2. 收藏至20ju.com

    Comment by 草根网 — December 15, 2008 @ 6:00 am

  3. [...] 我之前认为的SNS基础社会化逻辑都是基于真实关系的,这跟六度理论的逻辑完全是totally的两码子事。拿我深度使用的facebook、校内为例,我一直以来都拒绝加陌生人为好友。虽然我很烦陈一舟,但我还是不断地给陈一舟贡献着IP和PV。因为在校内,我有近150个见不着面同学朋友在那扎推,他们大部分遍布中国各大城市以及海外。所以我坐在班车上,都wap一下校内,看看巴黎的C、北京的D、上海的F童鞋的近况。我的思维里,SNS的基本逻辑是真实(ps 魏OO说真实 ≠ 使命哟)。所以我从来不认为六度逻辑是SNS,我是个彻底的反六度理论主义。 [...]

    Pingback by 再侃SNS逻辑 « 我叫光耀 — December 15, 2008 @ 9:11 am

  4. 若真的要在朋友的朋友上做文章,肯定不单是那么简单,还需要考虑:
    1 共同的朋友数
    2 是否同ip
    3 其它资料(学校、公司)的匹配度
    ……

    加上这些因素的话,朋友的朋友中自然有更靠谱的关系涌现在前面,这些关系可以好好利用

    Comment by 灰力普 — December 15, 2008 @ 7:24 pm

  5. 我觉得六度理论用在网络社区中比现实中更理像,在现实中闪度理论,我觉得不是那么可信,比如我和王菲,六度能联系上吗?十六度也联不上吧,呵呵,或许我的理解有误,很愿意和大家一起讨论。MSN:happybirdfly_5@hotmail.com

    Comment by sunny — December 16, 2008 @ 2:29 am

  6. for hyperlink between webpages, μ=0.85.

    to sunny
    我很确定你和王菲6度能联系上。 最近的paper说, MSN messenger network的平均最短路径是6.5, median是6

    Comment by NickCave — December 17, 2008 @ 4:19 pm

  7. @NickCave,

    μ在webpage link里 > ½是比较好理解的,毕竟如果人们愿意去建立一个link,就说明了人们还是相信这个link的目标内容的。

    Page rank把每个link当做一次投票,如果μ在webpage link里也是½的话,page rank也就没什么用处了。

    Comment by 美人她爹 — December 21, 2008 @ 1:19 am

  8. = = 是用信任来衡量的么,人与人的关系是多元的。只能说可能与朋友的朋友志趣不相投。都不认识,谈什么信任,朋友的朋友是默认生人?首先一个陌生人,信任度就只有20%,不需要量化成表了
    而且,把两个陌生人联系起来,和信任一毛钱关系没有。只是认识而已,需要一定发生什么吗?

    Comment by 咚咚 — December 24, 2008 @ 8:48 pm

  9. @咚咚:

    信任了才有商机啊

    Comment by 美人她爹 — December 27, 2008 @ 1:36 am

  10. 这个社会,缺少商机!

    Comment by chris — January 6, 2010 @ 1:09 am

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  12. 都不认识,谈什么信任,朋友的朋友是默认生人?

    Comment by buy dvd online — May 15, 2013 @ 1:41 am

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