VMA_toPrint_changed.DVI Mathematical Problems of Computer Science 23, 2004, 102{118. Application of Voting M ethods to Str ategies Analysis and Assessment E m m a H . D a n ie lya n Institute for Informatics and Automation Problems of NAS of RA e-mail emma danielyan@yahoo.com Abstract Classi¯cation of known voting methods in the frame of the Management Optimal Strategy Provision and Skill Assessment problems is given. Methods applicable to these problems are presented with pseudo code and their complexities are calculated. The applicability of voting methods is shown on the scheme with methods separation on two basic classes - Condorcet consistent and Scoring methods. The Kendall-Wei tournament participants ranking method is analyzed for mentioned problems. Refer ences [1 ] T. Co r m e n , Ch . L e is e r s o n , R . R ive s t Introduction to Algorithms, ( in R u s s ia n ) , Mo s c o w, 2 0 0 1 . [2 ] E . D a n ie lya n , E . P o g o s s ia n " A p p lic a t io n o f V o t in g Me t h o d s t o S t r a t e g y A s s e s s m e n t " , P roceedings of the Conference on Computer Science and Information Technologies (CSIT'99), pp. 165 - 169, Yerevan, Armenia, 1999, [3 ] Ma r k D u n lo p " Te a c h in g A lg o r it h m s &Co m p le xit y: B ig Oh R o u g h Gu id e " http://www.cs.strath.ac.uk/~mdd/teaching/alg&comp/big oh.html [4 ] J. W . Mo o n Topics on Tournaments, N Y , H o lt , R in e h e va r t & W in s t o n , 1 9 6 8 . [5 ] H . Mo u lin Axioms of Cooperative D ecision M aking, IS B N -0 -5 2 1 -3 6 0 5 5 -2 , V ir g in ia P o ly- t e c h n ic & S t a t e U n ive r s it y, 1 9 8 8 . [6 ] E . M. P o g o s s ia n \ D e ve lo p m e n t o f Ma n a g e m e n t S kill A s s e s s m e n t " , P roceedings of the AB SE L -98, M aui, Honolulu, 1998. [7 ] E . M. P o g o s s ia n \ Ma n a g e m e n t S t r a t e g y S e a r c h a n d A s s e s s m e n t P r o g r a m m in g " , P roceedings of the Conference on Computer Science and Information Technologies (CSIT'99), pp. 46 - 66, Yerevan, Armenia, 1999. [8 ] E . M. P o g o s s ia n \ Fo c u s in g Ma n a g e m e n t S t r a t e g y P r o vis io n S im u la t io n " P roceedings of the Third International Conference in Computer Sciences and Information Technolo- gies(CSIT'01), pp. 243 - 247,Yerevan, Armenia, 2001. [9 ] L . E . S a d o vs ki, A . L . S a d o vs ki M athematics and Sport, ( in R u s s ia n ) , Mo s c o w, Fiz -Ma t L it e r a t u r e , 1 9 8 5 . 1 0 2 E. H. Danielyan 1 0 3 [1 0 ] S t e ve n S . S kie n a The Algorithm D esign M anual, S p r in g e r -V e r la g N e w-Y o r k, In c . 1 9 9 8 . [1 1 ] H e r b e r t S . W ilf \ S e a r c h in g t h e we b wit h e ig e n ve c t o r s " a p r il 1 3 , 2 0 0 1 , http://www.math.scar.utoronto.ca/b24/K endallW ei.pdf. êïñ³ï»·Ç³Ý»ñÇ ·Ý³Ñ³ïáõÙ ¨ ³Ý³Éǽ ùí»³ñÏáõÃÛ³Ý Ù»Ãá¹Ý»ñÇ ÏÇñ³éٳٵ ¾. Ð. ¸³ÝÇ»ÉÛ³Ý ²Ù÷á÷áõÙ Ðá¹í³ÍáõÙ ¹Çï³ñÏíáõÙ ¿ ÙÇ ß³ñù ѳÛïÝÇ ùí»³ñÏáõÃÛ³Ý Ù»Ãá¹Ý»ñÇ ¿ýý»ÏïÇí ÏÇñ³éáõÃÛáõÝÁ ٻݻçÙ»ÝïÇ ûåïÇÙ³É ëïñ³ï»·Ç³ÛÇ ¨ ٻݻç»ñÝ»ñÇ ·Çï»ÉÇùÝ»ñÇ ·Ý³Ñ³ïÙ³Ý ËݹÇñÝ»ñáõÙ: ¶ñ³ýÇÏáñ»Ý óáõÛó ¿ ïñí³Í Ù»Ãá¹Ý»ñÇ µ³Å³ÝáõÙÁ »ñÏáõ ÑÇÙÝ³Ï³Ý ¹³ë»ñǪ ·Ý³Ñ³ï³Ï³ÝÝ»ñÇ Ñ³ßí³éÙ³Ý ¨ ѳٳӳÛÝ»óí³Í Îáݹáñë»ïáí, Ýñ³Ýó ÏÇñ³é»ÉÇáõÃÛ³Ý Ýϳñ³·ñáõÃÛ³Ùµ: ²ß˳ï³ÝùáõÙ Ù³Ýñ³Ù³ëÝáñ»Ý ¹Çï³ñÏíáõÙ ¿ ݳ¨ λݹ³É-ì»ÛÇ Ù»Ãá¹Á, áñÁ ÃáõÛÉ ¿ ï³ÉÇë ¹³ë³Ï³ñ·»É ÙñóáõÛÃÇ Ù³ëݳÏÇóÝ»ñÇݪ û·ï³·áñÍ»Éáí áõųÛÇÝ í»ÏïáñÇ Ñ³ëϳóáÕáõÃÛáõÝÁ: ²Ûë Ù»Ãá¹Á ÝáõÛÝå»ë ³é³ç³ñÏíáõÙ ¿ í»ñáÑÇßÛ³É ËݹÇñÝ»ñÇ Ñ³Ù³ñ: øí»³ñÏáõÃÛ³Ý ³ÛÝ Ù»Ãá¹Ý»ñÁ, áñáÝù ÏÇñ³é»ÉÇ »Ý ٻݻçÙ»ÝïÇ ûåïÇÙ³É ëïñ³ï»·Ç³Ç ¨ ٻݻç»ñÝ»ñÇ ·Çï»ÉÇùÝ»ñÇ ·Ý³Ñ³ïÙ³Ý ËݹÇñÝ»ñáõÙ Ý»ñϳ۳óíáõÙ »Ý å먹áÏá¹áí: гßí³ñÏíáõÙ ¿ ³Û¹ Ù»Ãá¹Ý»ñÇ µ³ñ¹áõÃáõÝÁ: ²é³ÝÓÇÝ ³ÕÛáõë³Ïáí óáõÛó ¿ ïñíáõÙ ùí»³ñÏáõÃÛ³Ý Ù»Ãá¹Ý»ñÇ Ñ³Ù³å³ï³ë- ˳ÝáõÃáõÝÁ ùí»³ñÏáõÃÛ³Ý ï»ëáõÃÛ³Ý ÑÇÙÝ³Ï³Ý ³ùëÇáÙÝ»ñÇݪ ÇÙ³ëï³íáñí³Í ëïñ³ï»·Ç³Ý»ñÇ ·Ý³Ñ³ïÙ³Ý ËݹÇñÝ»ñÇ Ñ³Ù³ñ: