「我離港前到過一間精神科醫院。當時有位病人禮貌地問,一個以作為世上最悠久民主政體而自傲的國家,如何能夠將此地交給一個政治制度非常不同的國家,且既沒諮詢當地公民,又沒給予他們民主的前景,好讓他們捍衞自己的將來。一個隨行同事說,奇怪,香港提出最理智問題的人,竟在精神科醫院。」彭定康 金融時報

“During a visit to a mental hospital before I left Hong Kong, a patient politely asked me how a country that prided itself on being the oldest democracy in the world had come to be handing over his city to another country with a very different system of government, without either consulting the citizens or giving them the prospect of democracy to safeguard their future. Strange, said one of my aides, that the man with the sanest question in Hong Kong is in a mental hospital.”Chris Patten Financial Times

Non Chinese literate friends, please simply switch to English Version provided by LOUSY Google Translation

Please participate in the unregistered demography survey of visitors at the right hand side bar. You are: ?

敬請參與在右下方的不記名訪客分佈調查問卷,你是: ?

Thursday, March 20, 2008

博弈論 中的 囚徒困境

博弈論 中的 囚徒困境




之前幾次在網友處,提起 博弈論 中的 囚徒困境 論。


囚徒困境的主旨為:囚徒們雖然彼此合作,堅不吐實,可為全體帶來最佳利益(無罪開釋)。但在資訊不明的情況下,因為出賣同伙可為自己帶來利益(縮短刑期),也因為懷疑同伙可能把自己招出來,可為他帶來減刑利益,因此彼此互相出賣,雖違反最佳共同利益(無罪開釋),反而可能是自己謀求最大自身利益所在。


但實際上,執法機構不可能設立如此情境來誘使所有囚徒招供,因為囚徒們必須考慮刑期以外之因素(出賣同伙會在獄中及街頭受到報復等),而無法完全以執法者所設立之利益(刑期)作考量。


經典的囚徒困境如下:

警方逮捕甲、乙兩名嫌疑犯,但沒有足夠證據指控二人入罪。於是警方分開囚禁嫌疑犯,分別和二人見面,並向雙方提供以下相同的選擇:

若一人認罪並作證检控對方(相關術語稱「背叛」對方),而對方保持沉默,此人將即時獲釋,沉默者將判監10年。

若二人都保持沉默(相關術語稱互相「合作」),則二人同樣判監半年。

若二人都互相檢舉(互相「背叛」),則二人同樣判監2年。


用表格概述如下:


××××××××××××××甲沉默(合作)××××××××甲認罪(背叛)
乙沉默(合作)××二人同服刑半年××××××××甲即時獲釋;乙服刑10年
乙認罪(背叛)××甲服刑10年;乙即時獲釋××二人同服刑2年


「博弈論」看來像是很高深的學問,而其中的 「囚徒困境」論好像是犯罪心理學。不過其實是把人性加以深入研究罷了。


小學時代,記得是在小二,老師轉頭寫黑板時,聽到同學談話,遂要同學自己站出來,認罪否則全班一起罰企,老師把『保甲連坐』古為今用。初時沒有同學出聲,但不竟只得七八歲小孩,不多久就有二五仔,篤先前談話的同學出來,而那兩位談話的同學,亦不想見所有同學一同罰企,認了罪救了全班,之後做二五仔的那位同學,被全班杯葛整個月,而兩位敢於認罪的同學做了英雄。


又另有一次,已經是中一, 大家都有十二三歲, 那年當老師背著寫黑板時(其實是用Marker筆寫在百版上),全班大部份同學,互射碼子,有一隻碼子誤中老師,大乜鑊! 老師又是出『連坐』這一招,一係自首,否則全班要留堂。 大家已經十二三歲,懂得做男生要有『雷氣』,無人肯做二五仔,其實無人知道邊個射中老師,好了,老師下不了臺, 老羞成怒,放學後真的整班學生四十幾人,全班排隊去教員室罰企。


校車,保母車,白牌車,私家車司機們入來了解,發生了甚麼事,繼而通知家長,不久有部分家長們抵達,成百人塞在教員室裡面,連校長修士都驚動了,由修士樓上宿舍,落來睇下發生乜嘢事,真係慘,又要顧存老師面子,又要注重紀律,又要平釋事件,最後先放學生回家。 記得好像在期考這一科每人降一個 GRADE,但不用記過,真的還是假的無人知,亦無人續個去問,如果是真,無份射碼子的同學都幾冤枉。


博弈論(Game Theory),有時也稱為對策論,或者賽局理論,電影
A Beautiful Mind (film), 根據 A Beautiful Mind (book) 』本書拍成,就是講 博弈宗師,一九九四年 Nobel Memorial Prize in Economic Sciences Winner 諾貝爾獎 得獎者,John Nash 的經歷,阿尊一九二八年生,尚還在世。


人生本來就是一場博弈,選擇和被選擇,互相交替,成與敗,得或失,就像玩遊戲 Game 一場, 尚未釘蓋,都未能有最後定論!


本文已經寫好很久,儲起來等候機會登出。剛巧有網友講起『二五仔女』,『誅連』、『連坐』的古代執法,剩機出籠。




後記:


微豆兄 提出 Plea Bargaining 這個 Topic 與 囚徒困境 的博弈類同,但因為有了減刑的誘因,可以胡亂說謊把無辜的人拉入案件,增加自己的減刑機會。


【維基百科】Plea bargaining in the United States is very common; the vast majority of criminal cases in the United States are settled by plea bargain rather than by a jury trial.

They have also been increasing in frequency—they rose from 84% of federal cases in 1984 to 94% by 2001. Plea bargains are subject to the approval of the court, and different States and jurisdictions have different rules. Game theory has been used to analyze the plea bargaining decision.

The constitutionality of plea bargaining was established by Brady v. United States in 1970, although the Supreme Court warned that plea incentives which were sufficiently large or coercive as to over-rule defendants' abilities to act freely, or used in a manner giving rise to a significant number of innocent people pleading guilty, might be prohibited or lead to concerns over constitutionality. Santobello v. New York added that when plea bargains are broken, legal remedies exist.

Several features of the American justice system tend to promote plea bargaining. The adversarial nature of the system puts judges in a passive role, in which they are completely dependent upon the parties to develop the factual record and cannot independently discover information with which to assess the strength of the case against the defendant.

The parties thus can control the outcome of the case by exercising their rights or bargaining them away. The lack of compulsory prosecution also gives prosecutors greater discretion. And the inability of crime victims to mount a private prosecution and their limited ability to influence plea agreements also tends to encourage plea bargaining. Prosecutors have been described as monopsonists.

The shadow-of-trial argument states that plea agreements merely reflect the outcome that would have transpired had the case gone to trial. For example, if the accused faces 10 years and has a 50% chance of losing in court, then an agreement will result in a five-year sentence, less some amount deducted for saving the government the cost of trial.

Theoretically, the shadow-of-trial should work even better in criminal cases than in civil cases, because civil judgments are discretionary, while criminal judgments are often regulated by mandatory minima and sentencing guidelines, making sentences more predictable.

A counter-argument is that criminal sentencing laws are "lumpy", in that the sentencing ranges are not as precise as the dollars-and-cents calibration that can be achieved in civil case settlements. Furthermore, because some defendants facing small amounts of prison time are jailed pending trial, they may find it in their interests to plead guilty so as to be sentenced to time served, or in any event to end up serving less time than they would serve waiting for trial.

Outcomes in criminal cases are also made less predictable by the fact that, while a plaintiff in a civil case has a financial incentive to seek the largest judgment possible, a prosecutor does not necessarily have an incentive to pursue the most severe sentence possible.

The United States Supreme Court has recognized plea bargaining as both an essential and desirable part of the criminal justice system. The benefits of plea-bargaining are said to be obvious: the relief of court congestion, alleviation of the risks and uncertainties of trial, and its information gathering value.

However, in 1975 the Attorney-General of Alaska, Avrum Gross, ordered an end to all plea-bargaining; subsequent attorneys-general continued the practice. Similar consequences were observed in New Orleans, Ventura County, California, and in Oakland County, Michigan, where plea bargaining has been terminated.

Some legal scholars argue that plea bargaining is unconstitutional because it takes away a person's right to a trial by jury. In fact, Justice Hugo Black once noted that, in America, the defendant “has an absolute, unqualified right to compel the State to investigate its own case, find its own witnesses, prove its own facts, and convince the jury through its own resources. Throughout the process, the defendant has a fundamental right to remain silent, in effect challenging the State at every point to ‘Prove it!’” By limiting the powers of the police and prosecutors, the Bill of Rights safeguards freedom.

Plea bargaining is also criticized, particularly outside the United States, on the grounds that its close relationship with rewards, threats and coercion potentially endangers the correct legal outcome.

The theoretical work based on the prisoner's dilemma is one reason why, in many countries, plea bargaining is forbidden. Often, precisely the prisoner's dilemma scenario applies: it is in the interest of both suspects to confess and testify against the other suspect, irrespective of the innocence of the accused. Arguably, the worst case is when only one party is guilty—here, the innocent one is unlikely to confess, while the guilty one is likely to confess and testify against the innocent.

It has been argued that plea bargaining benefits society by ensuring that the guilty are not acquitted.

Another argument against plea bargaining is that it may not actually reduce the costs of administering justice. For example, if a prosecutor has only a 25% chance of winning his case and sending the defendant away to prison for 10 years, he may make a plea agreement for a one-year sentence; but if plea bargaining is unavailable, he may drop the case completely.



除了犯人可以用利用 Plea Bargaining 換取較短刑期,有時也會無辜被冤枉的可以被帶上法庭,牽涉入內的人要經過經年的法律程序,又要延聘律師付出金錢時間心力,家庭事業受到不必要的影響,最終才可以打甩罪名。



近日 嗜悲 追看一套 朝日電視的日劇:天使與惡魔 日文:天使 と 惡魔


故事:天使 と 惡魔


天使 と 惡魔 司法取引 預告片 TV Asahi





伸延閱覽:
唔做二五仔! 新鮮人


我的舊文:
問書







17 comments:

新鮮人 said...

我記得你以往多次談理過這題目喎,
你好似好喜歡討論這個topic!

古代的"誅連"就唔同囉,
皇帝唔係要人供出真兇,
而係有殺錯無放過,
又或者係要殺草除根,
就算你無做過都好,
九族同誅,物人都死光啦,
邊度仲會有相關人翻案吖?
厲害唔厲害呢?
諗出黎嗰個人就真係要畀個"諾貝爾"殺人獎佢囉! =p

微豆 Haricot said...

很好的一篇討論文章和參考資料(包括新鮮人的【唔做二五仔!】),我覺得当权者「統治」管理的手段,其目的不只是調查真相,而是有企图鞏固控制权力的硬度。連坐丶誅九族丶背叛分化等都是手段,是和賽局理論的利益有關,但对尋求事實和担負責任的原本目的有幫助嗎?? 正如plea bargaining 一樣:

1. Does the end justify the means?
2. What are the implications to the values and perceptions of justice?
3. Will it set a precedence and become an acceptable practice in the name of seeking truth and justice?

新鮮人 said...

其實法律同正義不是對等的,
都是當權者和有錢佬的玩意!

Hyacinthus said...

好熱鬧哦, 我又來 ~

Game Theory係經濟學中的熱門話題,凡唸過ECON的或多或少都知道點,當年的數學理論,今日放諸四海皆宜也,說穿了,有點像人性心理學,深奧的等式其實是利益關係的角力!前幾年,某導演將此題材搬上了大影幕, A Beautiful Mind既寫實也火扇情,學人生涯,並非外人眼內的象牙塔,那內省跟自我要求,逼得緊時真的會走火!

記得電影落幕後的某年,Prof John Nash應HKU校長之邀,在中山階前排下了擂台陣,與莘莘學子相較量,上至深奧的學術理論,下至簡單的生活點滴,連電影裡的橋段也可是一話題,相談甚歡!其實,理論又怎能與生活脫離,問題是怎去好好應運 ~

新鮮人 said...

風子果然係學富五車!

the inner space said...

嘩,多謝嗮啲回應先!

在未回答各位前,讓我也加入討論。 其實以下觀點,本是文中的一部份,為避免太長,讓人看得入睡,所以刪掉的,依家攞埋出來。

中國自古以來,歷代均採用近乎『愚民政策』,認為這樣易于統治。 不同朝代,都有『鎖國排外』的政策。 當然中原文化博大,在古代確是在地區上,獨領風騷。

當歐洲進入『文藝復興』,在文藝,藝術,思想,主義,理論,甚至科學各個范疇,開始萌芽,發酵,大部份中國人,還是處于民智未開。

中國人對于法治觀念薄弱,傾向人治,認為有個好皇帝,有個好官,是人民最緊要的,曰:『父母官』! 溫總就是其中之一想做到的。。。(一笑!)。

顧有『包青天』,『包黑炭』,凡事倚靠,為人民作主,去撥亂反正。 連帶文藝戲曲,都大力提倡。 無線 麗的 當年爭拍『包青天』爭收視,大受歡迎,可見『人治』根植于中國人的『脫氧核糖核酸』DNA。

但試問世間上,有幾多個『包青天』呢?

啲父母官、清官,單靠一己之力,有時不能兼顧,遂變了質,成為酷吏,一己之見,屈打成招。 皇帝就更加唔得閒,點理得咁微細,咁Detail, 又要鞏固統治權力,漸漸凝聚成為『高壓統治』。 『誅九族』,『保甲連坐』,用來嚇怕人民!

好了! 到此為止, 太長氣了!

順帶一提, 個人覺得英文的 Justice 一個字,
就包括了 中文的 『公平』fairness、『公正』impartial、『公義』righteous,可能還有更多,可知中國人對這方面,還有不及!

歡迎加入討論!

新鮮人 said...

表面上看法治一定好過人治,
實際是又不全是,
中國人對法治思想自春秋戰國時的法家思想,
相信絶不是你講的民智未開吧,
只是法治後來淪為統治者的工具,
人民才不見其利,只受其害啫!

現代西方人的所謂法治亦有利有弊,
大家都見到現今法律是為有權有勢的人去服務的,
而且還會為一些不公平的事情合理化,
對於我們平民百姓來說,
去到法律層面往往受制多於受助,
就好似早前電訊中途加合約收費,
因為有法律團做後盾,
我們小市民又可以做什麼呢?

Justice這個字可以有高尚的解釋,
但事實是怎樣呢?
大家不要自欺欺人吧,
法治精神只是高高在中的美麗名詞,
法律則還不是有錢人玩意,
人根本就是自私自利的動物,
就算再好的東西到了人手上都只是自求利益的工具而已!

The Inner Space said...

新鮮兄:

韓非子 《有度》

峻法,所以禁過外私也;
嚴刑,所以遂令懲下也。


嚴刑峻法,有阻嚇作用。

至于『誅九族』已經在你處講過,不贅!

可惜『諾貝爾』獎委員會,沒有設置此獎項,
不過你可去信『邵逸夫』獎委員會,提議加設。

:o

The Inner Space said...

微豆兄:

多謝到訪及留言!

『囚徒困境』祇是『博弈論/對策論』其中的一個單元,舉出的例子。


有關 管治、管理、管人,的研究理論,多如恒河沙數,有放任的、有懷柔的、有高壓的、有恐怖的,繁此種種,有排講唔完。 只要有人,就有『博弈』、『對策』方面的理論!

plea bargaining 又是一大項目,我不是讀法律的,祇知道有限,你有暇請在你處,多寫一些,讓我學學嘢!

orz

The Inner Space said...

新鮮兄:

其實法律同正義不是對等的,
都是當權者和有錢佬的玩意!


但係窮得不名一文,也可申請『法援』,
最悲哀是『高不成低不就』的中產階級!

The Inner Space said...

風子:

歡迎加入,多啲討論更熱鬧!

『博弈/對策』論,在各方面范疇都可引用,
就如我文中所說:

『人生本來就是一場博弈,選擇和被選擇,互相交替,成與敗,得或失,就像玩遊戲 Game 一場, 尚未釘蓋,都未能有最後定論!』

你有幸參加『納殊教授』的討論答問大會,
好似是要抽簽才得到『入場劵』參與其會,
港大網頁有冇就答問的文字記錄呢?

The Inner Space said...

新鮮兄:


筍子的門生 『韓非』是法家的代表人物,他是戰國時代的人。 至於儒家的孔孟,也是春秋戰國的人。

之後『儒家』被捧為正統,科舉進士,都靠熟讀『儒學』,但都只是一小闕人,普通百姓,都是『民智未開』,或者被帝皇,統治者推行的的『愚民政策』,方便管理,易於管治。

至于『法治』好, 還是『人治』優,不斷有人評論,討論、議論。

法國思想家 伏爾泰 Voltaire 就有名句:
"The best government is a benevolent tyranny tempered by an occasional assassination."

另外『法治』雖然尚未能盡善,就跟『民主』政制一樣,雖然不是最 Efficient 的政制模式,但是在眾多之中,暫時較可行的模式,去尋求 justice !

新鮮兄 不要失望,五代不成,十代不完,只要精神不滅,薪火相傳,那怕廿代卅代後,終有一日,可以達到一個理想的國度。

:P

新鮮人 said...

韓非雖是戰國人,
但就是荀子亦都是承集前人思想而滙出法家學說,
所以說法家源自戰國就不對了!

儒表法裏根本就是中國幾千年皇帝統治的手法啦!
至於你講的十代百代問題,
我就不抱樂觀態度了,
問題不在於時間而是在於人性,
人好易會有私心,
有私心就會用盡任何方法去取得自己的利益,
而法律就是當權者和有錢佬的工具囉,
就好易以前啲皇帝嘅儒表法裏囉!

the inner space said...

新鮮兄:

一定是我表達能力差,令你誤會我說『法家思想』,始于『戰國時代』!

the inner space said...



新鮮兄:

我不是樂觀的人,簡直是極度悲觀添!相信有生之年我看不見,更佳的制度。

我只是想話,有人類就會不斷的去改變,現今被認為『法治』同『民主』是較可取,他朝可能被踢埋一面,只要人類不滅,終有一日,可以達到一個理想的國度。

又是我的文字表達能力差,至令你誤會了!

orz

新鮮人 said...

人性易自私,
好難會做到一個較美的制度出來,
因為人人著眼點都在保護自己的利益.
我意思係每個人都有自己的立場,
根本唔會發展到一個人人公平的制度,
就算有都會實行不了!

the inner space said...

可能真係畀 法國思想家 伏爾泰 Voltaire 講中咗,

"The best government is a benevolent tyranny tempered by an occasional assassination."