1. VOTING THEORY: DECISION-MAKING In th following profile, 12 voters – Messrs. i to u cast their prefereences on five different options, A.B, C, D and E. So which option - A, B, C, D or E - best represents the collective will of the twelve voters?

2. 2 5 OPTIO NS 12 voters and their preferences ijklmnpqrstu A 1111-5553544 B 24-311435332 C 33-42214222- D 452233211453 E523--4324111 VOTING THEORY － A VOTERS ’ PROFILE

3. 5 OPTIO NS 12 voters and their preferences RESU LTS ijklmnpqrstu A 1111-55535444 B 24-3114353322 C33-42214222-1 D4522332114532 E523--43241113 MAJORITY/PLURALITY VOTING

4. 5 OPTIO NS 12 voters and their preferences RESU LTS ijklmnpqrstu A 1111-55535445 B 24-311435332 － C33-42214222- － D452233211453 － E523--43241116 TWO-ROUND SYSTEM (TRS)

5. 5 OPTIO NS 12 voters and their preferences RESU LTS ijklmnpqrstu A 1111-55535444 B 24-3114353322 C33-42204222-0 D452233 2 (1) 114533 E523--43241113 A KNOCK-OUT (stage ii)

6. 5 OPTIO NS 12 voters and their preferences RESU LTS ijklmnpqrstu A 1111-55535444 B 24-3004353320 C33-42204222-0 D4522 3 (1) 3 (1) 2 (1) 114535 E523--43241113 A KNOCK-OUT (stage iii)

7. 5 OPTIO NS 12 voters and their preferences RESU LTS ijklmnpqrstu A 1111-55535 4 (1) 45 B 24-3004353320 C33-42204222-0 D4522 3 (1) 3 (1) 2 (1) 11 4 (1) 5 3 (1) 7 E523--43240000 A KNOCK-OUT (stage iv)

8. 5 OPTIO NS 12 voters and their preferences RESU LTS ijklmnpqrstu A 1515 1515 1515 1515 －－－－ 5151 5151 5151 3333 5151 4242 424231 B 2424 4242－ 3333 1515 1515 4242 3333 5151 3333 3333 242435 C 3333 3333 －－－－ 4242 2424 2424 1515 4242 2424 2424 2424－ D 4242 5151 2424 2424 3333 3333 2424 1515 1515 4242 5151 333337 E5151 2424 3333 －－－－ －－－－ 4242 3333 2424 4242 1515 1515 151534 POINTS BORDA COUNT, BC

9. 5 OPTIO NS 12 voters and their preferences RESU LTS ijklmnpqrstu A 1515 1515 1313 1414 -－-－ 5151 5151 5151 3333 5151 4242 414127 B 2424 4242 -－-－ 3232 1313 1515 4242 3333 5151 3333 3333 232331 C 3333 3333 -－-－ 4141 2222 2424 1515 4242 2424 2424 2424 -－-－ 32 D 4242 5151 2222 2323 3131 3333 2424 1515 1515 4242 5151 323231 E5151 2424 3131 -－-－ -－-－ 4242 3333 2424 4242 1515 1515 1414 POINTS MODIFIED BORDA COUNT, MBC

10. 10 5 OPTIO NS 12 voters and their preferences ResultsWins ijklmnpqrstu A 1111-55535445 B 24-31143533271 C33-42214222- D452233211453 E523--4324111 LEAGUE - A:B

11. 11 5 OPTIO NS 12 voters and their preferences ResultsWins ijklmnpqrstu A 1111-5553544 B 24-3114353321 C33-42214222-60.5 D452233211453 E523--43241116 LEAGUE - A:B, C:E

12. 12 5 OPTIO NS 12 voters and their preferences ResultsWins ijklmnpqrstu A 1111-5553544 B 24-31143533272 C33-42214222-0.5 D4522332114535 E523--4324111 LEAGUE - A:B, C:E, B:D

13. 13 5 OPTIO NS 12 voters and their preferences ResultsWins ijklmnpqrstu A 1111-5553544- B 24-3114353323 C33-42214222-2.5 D45223321145382 E523--43241114 LEAGUE - A:B, A:C, A:D, A:E B:C, B:D, B:E C:D, C:E D:E

14. Methodology Social RankingExamples of use in: 1 st 2 nd 3 rd 4 th 5 th Decision-makingElections Majority/Plurali ty vote A EB/D-C Finland (referendums) UK Kenya Two-round System E A--- New Zealand Norway (parliament) France Ivory Coast Knock-out Alternative vote D A---Australia BC D B/C -EADublin Nauru Slovenia MBC C B/D/E--A-- League Condorcet B C/E-DA-- DIFFERENT ‘DEMOCRATIC’ RESULTS

15. CLOSED QUESTIONS SEMI-OPEN QUESTIONS OPEN QUESTIONS ↑ All Prefs DECISION-MAKING Borda BC / MBC C BC = Borda Count MBC = modified Borda count NI = Northern Ireland UK = United Kingdom UN = United Nations Condorcet (League) O Some 1. Approval Vote 2. Alternative Vote (knock-out) U prefsSerial voting Sweden* N 1 st prefs only Weighted majority UN Consociational NI, Belgium 2-round voting Norway** T Simple majority Ireland, UK, Taiwan Twin Majority Switzerland Plurality New Zealand * a series of majority votes ** a first- round plurality and then a majority vote 1 of 2 options 1 of some options 1 or some of some options 1or some or all of all options 1 st preference onlyPreferential BINARYMULTI-OPTIONAL VOTERS ’ CHOICE → →

16. Peter Emerson 爱默生 彼得 Питер Эмерсон The de Borda Institute 德博达 研究所 Инситут им. де Борда Promoting inclusive voting procedures 推广具有包容性的投票系统 www.deborda.org