孟曉娟，周軒偉

(溫州大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院，浙江溫州，325035)

k?較多規(guī)則的理性條件

孟曉娟，周軒偉?

(溫州大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院，浙江溫州，325035)

對于群體決策問題，證明了k?較多規(guī)則滿足有關(guān)文獻(xiàn)提出的關(guān)于序數(shù)型的匿名性、中立性、局部非獨裁性及pareto原則等的理性條件，并給出了該規(guī)則的幾個性質(zhì)．

群體決策；k?較多規(guī)則；理性條件

群體決策是決策科學(xué)的重要分支，它在現(xiàn)代政治、管理、軍事和科技等重大決策問題中起著越來越重要的作用．1951年，Arrow在文獻(xiàn)[1]中提出著名的“不可能性定理”，為群體決策的序數(shù)理論奠定了基礎(chǔ)．此后，許多學(xué)者尤其是經(jīng)濟學(xué)家們?yōu)橥晟坪桶l(fā)展集體選擇和群體偏愛理論進(jìn)行了不斷的努力，給出了許多研究成果[2-7]，例如文獻(xiàn)[7]根據(jù)k?較多序理論提出了群體決策的一種新的社會福利函數(shù)——k?較多規(guī)則．本文在文獻(xiàn)[7]的基礎(chǔ)上，進(jìn)一步給出了與文獻(xiàn)[2]和[6]提出的關(guān)于序數(shù)型的匿名性、中立性、局部非獨裁性及pareto原則相對應(yīng)的基數(shù)型理性條件，并證明了k?較多規(guī)則滿足上述所有性質(zhì)．

1 群體決策的k?較多規(guī)則

2 k?較多規(guī)則的理性性質(zhì)

[1] Arrow K J. Social choice and individual value [M]. New York: John Wiley and Sons, 1951: 26-124.

[2] Sen A K. Collective choice and social welfare [M]. San Francisco: HolderDay, 1970: 15-79.

[3] Kelly J S. Arrow impossibility t heorems [M]. New York: Academic Press, 1978: 18-109.

[4] Greenberg J. Consisitent majority rules over compact s of alternatives [J]. Econometria, 1979, 47(3): 627-636.

[5] Suzumura K. Rational choice, collective decisions and social Welfare [M]. Cambridge: Cambridge University Press, 1983: 30-170.

[6] May K O. A set of independent, necessary and sufficient conditions for simple majority decision [J]. Econometria, 1952, 20: 680-684.

[7] 王曉敏. 群體決策的k?較多規(guī)則[J]. 上海交通大學(xué)學(xué)報, 1995, 29(3): 168-170.

Study on Rational Conditions ofk?Major Rule

MENG Xiaojuan, ZHOU Xuanwei
(College of Mathematic and Information Science, Wenzhou University, Wenzhou, China 325035)

As for group decision making issue, thek?Major rule was proved to satisfy some rational conditions about ordinal anonymity, neutrality, local nondictatorship, and pareto rule that proposed in some papers. Then, some properties of the rule were also achieved.

Group Decision Making;k?Major Rule; Rational Condition

(編輯：王一芳)

O22

A

1674-3563(2011)06-0009-04

10.3875/j.issn.1674-3563.2011.06.002 本文的PDF文件可以從xuebao.wzu.edu.cn獲得

2010-10-14

孟曉娟(1987- )，女，山西晉中人，碩士研究生，研究方向：群體決策與多目標(biāo)優(yōu)化．? 通訊作者，zhouxuanwei@mail.wzptt.zj.cn