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Det er kun7tre reelle alternativ som ligger nцr nok arbeidsplassen-1. Den billige, men akk sх dјlle Kantinen (K)/2. Den supergode, men akk sх dyre Tagatelle (T)03. Den hippe, men akk sх rјykfylte Hr. Haven (H)KAlle sender e-post til deg der man har rangert stedene. Du sitter igjen med+fјlgende resultater (inkl. ditt eget svar):KDa er mitt spјrsmхl. Hvilket sted bјr du velge hvis du јnsker х oppfјre degmest mulig demokratisk?Kantinen Tagatelle Hr. HavenOppsett: RESULTAT:G* 6 (40%) foretrekker Kantinen fremfor Tagatelle fremfor Hr.Haven (KTH)G* 5 (33%) foretrekker Hr.Haven fremfor Tagatelle fremfor Kantinen (HTK)G* 4 (27%) foretrekker Tagatelle fremfor Hr.Haven fremfor Kantinen (THK)6* Ergo sх kan man fortsatt ikke si hvem som bјr velges>* Men symmetrisk demokrati (kalles Borda count) tar hјyde for Salle јnsker, ogsх andre og tredjevalg etc. Dermed er dette det riktigste resultatetPublished: March 18, 2000 $ Source: Taiwan Headlines f Opposition candidate Chen Shui-bian and his running mate Annette Lu emerged this evening as> the winners of the 2000 ROC presidential election. [ At 7:20 p.m. March 18, ROC Central Election Commission chairman Huang Shih-chengp announced the preliminary results of ballot counting for the election of the tenth president and vicei president of the Republic of China, indicating that Chen and Lu, of the Democratic Progressive6 Party (DPP), had gathered 4,977,737 votes. ` Independent James Soong and running mate Chang Chau-hsiung placed a close second withe 4,664,922 votes, while Lien Chan and Vincent Siew, candidates for the current ruling partyP Kuomintang (KMT), lagged behind in third place with 2,925,513 votes. _ Independents Hsu Hsin-liang and Chu Hui-liang garnered 79,429 votes, while New Party> candidates Li Ao and Fung Hu-hsiang gained 16,782. l Huang Shih-cheng noted that a total of 12,786,671 voters cast ballots in this year's presidentiala election. Of these, 12,665,393 ballots were valid. The voter turn-out rate was 82.69%,e approximately six percentage points higher than the presidential election four years ago. m Chen Shui-bian, 49, will be the youngest president of the Republic of China, and as vice presidentR Annette Lu will be the highest-ranking woman in ROC political history. i At his national campaign headquarters, Chen expressed gratitude for his victory, and announcedg his intention to create a "multi-partisan working group," including representatives from theb Kuomintang, the New Party and independents, to work together for a democratic Taiwanese society. k Chen also quickly weighed in on the question of cross-strait relations, saying he was willing tom handle the issue with the highest measure of good will, and that in the future he hoped to open upj communication, trade and transport ties with mainland China, and to build a bilateral mechanism0 of mutual trust in military affairs. l Chen also reiterated his willingness to travel with his running mate Annette Lu to mainland Chinan for a visit of "reconciliation and communication." At the same time, he invited PRC president Jiange Zemin, premier Zhu Rongji and Wang Daohan, director of the PRC's Association for Relations7 Across the Taiwan Straits, to visit Taiwan. j Chen affirmed that, based on the precedents set by other democratic national governments duringh transitions of power, he hopes to build a channel of communication with current president Leem Teng-hui in the interim period before he takes office, and after assuming the presidency, he hopesl to rely upon President Lee's experience in cross-strait relations and Taiwan's system of military preparedness. g According to convention, Lee Teng-hui usually appears in the capacity of KMT chairman at hism party's central headquarters to view the vote count during a major election, but the president was$ absent on this occasion. l In a press conference at his presidential campaign headquarters, Lien Chan admitted his defeat ina the election, and in a very dignified manner announced that he had already offered hisl congratulations to Chen Shui-bian. Lien added he eagerly anticipates that Chen will appropriatelyM manage the nation's affairs, and lead the country into a new era. f James Soong came in second place with around 4.6 million votes, but was still more than 1.5h million votes ahead of the KMT's Lien Chan. The Soong camp is thus already poised to become a# major opposition force. i With this in mind, some of Soong's campaign advisors stated after the election results came inj that they should take this opportunity to form a party as a means to solidify their power. Theyk suggested further that the Soong camp should now set its sights on gaining seats in the National Assembly. e The Soong camp always maintained that if elected Soong would not oppose the KMT, nor woulde he seek to form a separate party. This, the Soong campaign argued, was in keeping with theh "cross-party" spirit that they were championing. However, when it became clear by what a slimT margin Soong had lost, his supporters expressed regret at this strategy. l Following the orderly completion of the election at 4:00 p.m., Chief of the General Staff Generale Tang Yiao-ming, issued a statement concerning the stance and mission of the national armedd forces, according to an announcement from the ROC Ministry of National Defense's Military0 Spokesman Office and Liaison Office. l General Tang stated that as the military corps of the nation, the armed forces of the Republic ofr China will fully act "with the constitution as its foundation and the will of the people as its guide."e The armed forces will obey the chief of state and carry out their mission according to the constitution. j General Tang also represented the entire armed forces in expressing their resolute assurance tok the new commander-in-chief of the three branches of the armed forces that they will fully devotes their will and loyalty, and make a sacrificial contribution, in order to safeguard the national security% of the Republic of China. n Since Chen Shui-bian's victory has the potential to increase tensions across the Strait, figures inj the financial community are bracing for another expected blast to the economy. Some expect thatX the increased tensions will lead first to a reduction in cross-Strait trade. h In addition, efforts to open up direct communication, trade and transportation links with thej mainland, as well as planned adjustments to the current administration's "no haste, be patient"g economic policy toward the PRC, are both expected to encounter delays due to tensions caused by Chen's victory. ` Analysts also expect the stock market to take another blow following the DPP victory.l Nonetheless, stock analysts argue that Taiwan's economic fundamentals are solid. Therefore, it is\ unlikely that Taiwan's benchmark index, the TAIEX, will fall below 8,000 points. g Meanwhile, members of the securities industry predict a similar scenario. They do expect t< hek market to encounter some jitters in the short run. However, they believe that in the longer termN Taiwan's fundamentals will still reflect positively on the market. i As for how the PRC's reaction will affect markets, one analyst argued that the mainland should_ observe the new president's policies and statements before determining any actions. #http://th.gio.gov.tw/p2000/main.cfm: The mathematics of voting - Democratic symmetry INDEX TERMS X Science|voting, mathematics of different systems;Mathematics|voting, differingT systems' benefits and drawbacks;Elections|voting, mathematics of different systems; DATE 4-Mar-00 WORDS $ The mathematics of voting Y FIFTEEN mathematicians went out to buy drink for a party. They decided to buy aZ single beverage in bulk to save money, but they wanted to choose which one in asb logical and fair a way as possible. So each listed the three drinks on offer (beer, wine_ and milk) in order of preference. Six preferred milk, followed by wine and then beer;] five liked beer the most, followed by wine and then milk; and four were wine-lovers: whose second choice was beer, followed by milk. [ The question was how to decide the outcome from these preferences. One milk-lover] proposed a plurality vote, in which each person casts a single vote for their firsta choice. This would give milk six votes, beer five, and wine four, ensuring that his own\ favourite would prevail. Not so fast, said a beer-drinker. Given that wine was the^ least popular first choice, why not stage a run-off between milk and beer? Since the\ four whose first choice was wine said that they preferred beer to milk, this would: mean that beer would win, by nine votes to six. U Humbug, said a wine buff. She suggested a more elaborate approach: pairwise\ comparison. Taking all stated preferences into account, it was clear that, given a[ choice between wine and beer, a majority (ten of the 15) would choose wine; givenY the choice between wine and milk, a majority (nine of the 15) would also choose^ wine. Although it had the smallest number of first choices, in other words, wine had the broadest appeal. a This sorry tale has a serious point: that the outcome of an election is a reflection ofZ voting procedure as much as voters wishes. In 70% of three-candidate elections,X changing the procedure changes the final ranking. So the results of real-world? elections can seem paradoxical, or downright unfair. S In a paper just published in the journal Economic Theory, Donald Saari, a_ mathematician at Northwestern University in Evanston, Illinois, claims to have got to] the root of the problem. It is, he says, all to do with symmetry (technically, with^ something called the wreath product of symmetry groups). Essentially, says Dr Saari,a voting paradoxes arise when the system fails to respect natural cancellations of votes.\ In a two-candidate contest, for example, nobody would deny that the candidate withb the most first-preference votes should win. One way to explain this is that votes of the_ form AB (ie, candidate A is preferred to candidate B ) should cancel out votes of theB form BA . If this leaves a surplus of AB , then A wins. Q These cancellations are a form of reflectional symmetry. But votes in aY three-candidate election should cancel out, too. Consider three votes in such a] contest: ABC , BCA and CAB . Each candidate is placed first, second and third once,_ so it is clear that these three votes should cancel each other out. This is a form ofL rotational symmetry, since the three votes form a rotating cycle. ` Taking these two symmetries into account, it is possible to characterise all paradoxes` for a three-candidate election under any voting procedure. Dr Saari s results can also^ be generalised for elections with more than three candidates using more complicated,e but closely related symmetries. It is thus possible to evaluate the  fairness of different voting systems. W Plurality voting, one of the most common democratic systems, fails to respect` reflectional symmetry. Since it is only each voter s first choice that counts, a voter] with preference ABC fails to cancel out an equal-and-opposite voter with preference` CBA ; instead, the result is one vote for A , and one for C . As a result, paradoxical^ results are possible under plurality voting. Similarly, pairwise comparison does notH respect rotational symmetry, so it can lead to paradoxes too. [ The fairest voting system, says Dr Saari, would respect both symmetries. The only\ system that fits the bill is the Borda count, proposed by Jean-Charles de Borda inZ 1770 to elect members to the Academy of Sciences in Paris. In an election with X_ candidates, each voter awards X points to his first choice, X-1 to his second choice,[ and so on. The results are added up and the candidate with the most points wins. ` Admittedly, this is more complex than plurality voting and cannot be used with current\ American voting machines (though it is used in Australia). Also, if voters are not_ familiar with all candidates, and do not rank them all, the unassigned points must beY divided up evenly between the unranked candidates. But for small elections, the_ system is ideal. And our thirsty mathematicians? Having read Dr Saari s results, they/ should now be merrily quaffing wine. 9http://www.economist.com/displaystory.cfm?story_id=288778/(From The Economist print edition) Mar 4th 2000 Candidate Independent Two first One Electionwins withe one elektionwins with two elektionSource for numbersSymmetrical democracy Two electionsU* I.e. all the three main candidates could win, depending on what election upset usedr* Symmetrical democracy (also known as Borda count) include all preferences, including second, third, etc, wishes D* Symmetrical democracy may be regarded as the most correct results.qthe Borda count, proposed by Jean-Charles de Borda in 1770 to elect members to the Academy of Sciences in Paris. wIn an election with X candidates, each voter awards X points to his first choice, X-1 to his second choice, and so on. t" ...The fairest voting system, says Dr Saari, would respect both symmetries. The only system that fits the bill is LThe results are added up and the candidate with the most points wins.... ". (The full text is available here (login) [1]8What candidate do you prefer as the second candidate [2]“[1] Actual numbers from the election: DPP have a bit higher numbers since all other candidates except Independent and Koumingtang is included here Two ElectionsDemocratic symmetry QIf no candidate get 50 %, a second election is held between these two candidates. One electionLthe second candidate X-1 points etc. The candidate with most point wins ... !wins under symmetrical democracy [2] The numbers are hypotethicalLExample - Results in the Election held in Taiwan (Republic of China) 2000-</034Plurality voting - The candidate with most votes win†Borda count - All voters give votes to all candidates. Lets say there are X candidates. Each voter gives her first candidate X point, (http://en.wikipedia.org/wiki/Borda_count Tre systemDemokratisk symmetriTo valgomganger2Flertallsvalg. Kandidaten med flest stemmer vinneroHvis ingen kandidater fхr 50 %, gjennomfјres en annen valgomgang mellom de to fјrste kandidatene fra omgang en.Borda count - Alle stemmer pх alle kandidatene med forskjellige poeng. La oss si at det er X kandidater. Hver stemmeberettiget _gir den fјrste kandidaten X poeng, den neste X-1 poeng etc. Kandidaten med flest poeng vinner. [1] Reelle valgtall: DPP har litt for hјyt tall, disse inneholder alle stemmene som ikke gikk til de to andre hovedutfordrereneA[2] Tallene som sier noe om foretrukket 2.kandidat er hypotetiske Three systemsHEksempel - Resulta fra valget holdt i Taiwan (Republic of China) 2000-03Š* I.e. sх kan alle tre kandidatene vinne, avhengig av type system som brukes (foutsetning at de hypotetiske tallene er nogenlunde riktige)~* Symmetrisk demokrati (kjent som Borda count) inkluderer alle preferansene, inkludert annet-, tredje-, fjerde-, etc. valghet.p* Symmetrisk demokrati kan betraktes som det mest korrekte siden dette systemet tar hensyn til alle preferanser.KilderResultat(http://no.wikipedia.org/wiki/Borda_countKilde for tallResultsSourcesNorwegian versionEnglish versionsymmetrical_democracy.xls* Excel sheet with calculationsZ* From The Economist 2000-03-02 article "The mathematics of voting - Democratic symmetry " * Borda count[* FraThe Economist 2000-03-02-artikkelen ЋThe mathematics of voting - Democratic symmetry Л4* Excel-ark med kalkulasjoner samt et annet eksempelџњЬ NŽdЄФ?РЭ zК y!ЙO$E'…4*t-Q*0j32Н4й>6Z9;Џ;Ы р>ќ ПAл;EW‡HЃКKж{L—YNuЋPЧLRDkTcqWiћWѓ u'ЭЩ€ !…alpl  dќЉёвMbP?_*+‚€%џСКЗ&R&6&"Arial,Normal"C:\Documents and Settings\Nikolai\Skrivebord\&F - &A (&P/&N)&L&6&"Arial,Normal"Created by nsaa@pvv.org on 2000-03-19 16:44 Last Saved by Nikolai on 2005-11-19 14:00ƒ„MЪCanon i560мьп š 4d§џA4ьBJDM €€Rt,T`Oфp,T`OфpRt,T`Oфp,T`OфpXXKLADDEksempel 1' d Rt Rt“H/џџџџ џџRtчџCanon i560мьп š 4d§џA4;-ГЁ" dXXр?р?U } m } m } л} m ! џџџџџџџ џ џ џ џџ џ џ џ џ џ џ џ џ џ џ џ џ§  § § § § § § § § § § § § 1О § О" § § 4?дџџџDР KantinenH?дџџџDР Tagatelle\?дџџџDР Hr. Haven§ § §  #§  '%š™™™™™й?џ§ &~ '№?(џ DРR)№?џ<%Ett valg%A+DР  Bf*š™™™™™й?џPDР ;DРDРDРDРDРDРDРBcЮЬЬЬЬЬќ?џMDРDРDРDРDРDРDРDРDР #p?дџџџDР Kantinen§  '%б?џ~ '§ &(№?ў DРR)џ<%Ett valg%A+DР  Bf*3„?дџџџPDР ;DРDРDРDРDРDРDРBc+""""""@џMDРDРDРDРDРDРDРDРDР #ˆ?дџџ џDР Tagatelle§ !%,UUUUUUе?џDРDР~ 2-№?џ DР§ .R/№?џ<%Ett valg%A+DР  Bf0333333у? џPDР ;DРDРDРDРDРDРDРBcююююююў?џMDРDРDРDРDРDРDРDРDР $œ?дџџ џDР Hr. Haven§ 15А?дџџИ?е§%РРB%џџ@ @Bf Kantinen§  5Ф?дџџџ%РРB%џџ@ @Bf Hr. Haven§  5и?дџџџ%РРB%џџ@ @Bf Tagatelle§  § § з49 Ь2мЭЮЬVWW џ§  з"Т   џьЮ№Ю№№Ж№( № №№~Ђ № Ѓ №<€ вˆ…П XPƒPП?П№дK  №]4@ вˆАGG kСЯН4@Ћ’|$н€Џь №Ж0<1Fra The Economist 2000-03-07 "The mathematics of voting - Democratic symmetry " "...The fairest voting system, says Dr Saari, would respect both symmetries. The only system that fits the bill is the Borda count, proposed by Jean-Charles de Borda in 1770 to elect members to the Academy of Sciences in Paris. In an election with X candidates, each voter awards X points to his first choice, X-1 to his second choice, and so on. The results are added up and the candidate with the most points wins...". 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