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第165章 悖论(1 / 2)

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“蒯得此人,曾立下小功,封地就在卫国边上,只隔着黄河,整天琢磨着一路征服卫都帝丘,一则获得河内的封地,二则觊觎下军将之职。他自然是主张兵车之会的,最好卫公不敢来会盟,这样就有借口,攻打卫国全境,对于戚城这么一个战略要地,他实在不愿意拱手相让。对于宋国,他一旦知晓宋卫在匡地交恶,自然愿意多一个宋国这样的盟友,将来打卫国多了一个帮手。这样的主张是为丁策。

如此我家太傅预计朝堂之上有四种主张。中军将不妨让大夫们一一在帛书上写下自己对四个策略的偏好排序,是为投票,最终结果少数服从多数。如此公平公开,中军将的决策自然就可以让众人皆服,推行下去了。”

赵盾道:“虽然投票能让人心服口服,但是最终结果不一定就是甲策啊?”

管理道:“投票形式上看似公平,其中颇有值得操纵之处。中军将且看。

我们不妨假设五十名大夫的偏好排序是这般:

甲甚于丙,甚于丁,甚于乙者十五人;

丁甚于丙,甚于乙,甚于甲者十四人;

乙甚于丁,甚于丙,甚于甲者十二人;

丙甚于乙,甚于甲,甚于丁者九人。”

赵盾道:“这么假设,自然是甲策胜。因为最偏好甲策的人最多。”

管理赞同道:“若事先分明说好按照‘最高票当选’,则甲胜必是无虞。但若事先说好按照‘排序复选法’投票则不然。”

赵盾:“‘排序复选法’规则如何?”

管理道:“中军将且看,丙策一开始为最低票数,理应废除,因此原先选择‘丙甚于乙,甚于甲,甚于丁者’只能退而求其次,选择第二偏好——乙策。

故而加其票于上,即可得到:

最偏好甲者十五人;

最偏好乙者十二加九等于二十一人;

最偏好丁者十四人。

如此一来,最偏好丁者最少,丁策废除,因此原先选择‘丁甚于丙,甚于乙,甚于甲者’十四人只能退而选择第二偏好——丙策,但丙策已然被剔除,只能再退选第三偏好乙策。

故而加十四票于上,得到:

最偏好甲者十五人;

最偏好乙者十四加二十一等于三十五人。

如此半数以上大夫觉得乙策比甲策更好,故而少数服从多数,乙策胜出。”

公子卬所述的‘排序复选法’听起来繁琐复杂,却被后世广泛应用于评选,除了电影届的奥斯卡奖、小说界的雨果奖,还有许多重大投票场合都参照此法。很多人认为‘最高票当选’的办法虽然原理简单,但是不能让超过半数的人信服,毕竟最偏好甲的只有十五人,不足五十的一半。而‘排序复选法’则能代表半数人的意愿。

赵盾听得瞠目结舌:“还能这么操纵投票结果的?那我要让丙策胜出,该如何拟定规则?”

管理道:“不妨给四个偏好赋分。每个人给最偏好的策略加四分,次偏好者三分,等而下之,两分,一分。

譬如说对于方才假设的结果,甲得到十五人的四分,十四人的一分,十二人的一分和九人的三分,如此甲总计有一百零四分。

类似的,乙一百一十八分,丙一百四十七分,丁一百三十一分。如此一来,丙策得分最多,胜出。”

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