Figure: Democracy Figure: Democracy Figure: Democracy Is Democracy Possible? Minhyong Kim WMI Masterclass June, 2020 Is Democracy Possible? Our approach today: Toy Models The hope is that they still cast light on the complicated phenomena of the world. I. Voting Methods Faculty Senate Election (elect one) Candidates: A,B,C,D,E 55 votes altogether. Rank Ballot Ballot Ballot Ballot Ballot Ballot 1 A B C D E E 2 D E B C B C 3 E D E E D D 4 C C D B C B 5 B A A A A A Votes 18 12 10 9 4 2 This is called a preferential ballot. Who should win? Plurality Method Election of candidate with most first place votes In our example, using the plurality method, A wins. Plurality Method Is the plurality method reasonable? Rank Ballot Ballot Ballot Ballot Ballot Ballot 1 A B C D E E 2 D E B C B C 3 E D E E D D 4 C C D B C B 5 B A A A A A Votes 18 12 10 9 4 2 Countries using Plurality Vote for Parliamentary Elections Antigua Azerbaijan Bahamas Bangladesh Barbados Belize Bermuda Bhutan Botswana Brazzaville Canada Comoros Cook Islands Cote d'Ivoire Dominica Eritrea Ethiopia Gabon Gambia Ghana Grenada India Iran Jamaica Kenya Kuwait Laos Liberia Malawi Malaysia Maldives Marshall Islands Micronesia Myanmar Nigeria Niue Oman Palau Saint Kitts and Nevis Saint Lucia Saint Vincent and the Grenadines Samoa Seychelles Sierra Leone Singapore Solomon Islands Swaziland Tanzania Tonga Trinidad and Tobago Tuvalu Uganda United Kingdom United States Yemen Zambia Two-Round System Count how many first place votes each candidate receives. If some candidate receives a majority, then that person wins. If no candidate receives a majority, eliminate all candidates except those two who have received the largest number of first place votes. Now, conduct a new election based on the preferences of the voters for these top two candidates. Two-Round System Rank Ballot Ballot Ballot Ballot Ballot Ballot 1 A B C D E E 2 D E B C B C 3 E D E E D D 4 C C D B C B 5 B A A A A A Votes 18 12 10 9 4 2 C, D, E are eliminated. Two-Round System Rank Ballot Ballot Ballot Ballot Ballot Ballot 1 A B 2 B B 3 4 B B 5 B A A A A A Votes 18 12 10 9 4 2 B wins by a large majority. Countries using Two-round System for Presidential Elections Afghanistan, Argentina, Austria, Benin, Brazil, Bulgaria, Burkina Faso, Cape Verde, Chile, Colombia, Costa Rica, Croatia, Czech Republic, Cyprus, Djibouti, Dominican Republic, East Timor, Ecuador, Egypt, El Salvador, Finland, France, Ghana, Guatemala, Haiti, India, Iran, Indonesia, Kyrgyzstan, Liberia, Malawi, North Macedonia, Peru, Poland, Portugal, Romania, Russia, Senegal, Serbia, Slovakia, Slovenia, Turkey, Ukraine, Uruguay and Zimbabwe. Exhaustive Ballot If no candidate gets a majority based on first place votes, eliminate the candidate with the fewest first place votes and hold a new election based on voting only for the smaller collection of candidates. Repeat the process until some candidate receives a majority of the first place votes. Exhaustive Ballot Rank Ballot Ballot Ballot Ballot Ballot Ballot 1 A B C D E E 2 D E B C B C 3 E D E E D D 4 C C D B C B 5 B A A A A A Votes 18 12 10 9 4 2 E is eliminated. Exhaustive Ballot Rank Ballot Ballot Ballot Ballot Ballot Ballot 1 A B C D 2 D B C B C 3 D D D 4 C C D B C B 5 B A A A A A Votes 18 12 10 9 4 2 D is eliminated. Exhaustive Ballot Rank Ballot Ballot Ballot Ballot Ballot Ballot 1 A B C 2 B C B C 3 4 C C B C B 5 B A A A A A Votes 18 12 10 9 4 2 B is eliminated. Exhaustive Ballot Rank Ballot Ballot Ballot Ballot Ballot Ballot 1 A C 2 C C 3 4 C C C 5 A A A A A Votes 18 12 10 9 4 2 C wins! Use of Exhaustive Ballot Scottish government, Host City of the Olympic Games, President of the European Parliament, Speaker of the British House of Commons, Speaker of the House of Commons of Canada, Leader of UK Conservative Party Borda Count Method Figure: Jean-Charles de Borda (1733-1799): French mathematician, physicist, political scientist, and sailor. Borda Count Method Assign points In an election with n candidates, a first place vote earns a candidate n − 1 points, second place vote n − 2 points, third place vote n − 3 points, and so on. Borda Count Method Rank Ballot Ballot Ballot Ballot Ballot Ballot 1 A B C D E E 2 D E B C B C 3 E D E E D D 4 C C D B C B 5 B A A A A A Votes 18 12 10 9 4 2 A: 18 × 4+0+0+0+0=72 points B: 12 × 4 + 14 × 3 + 11 × 1 =48+42+11=101 points C: 10 × 4 + 11 × 3 + 34 × 1=40+33+34=107 points D: 9 × 4 + 18 × 3 + 18 × 2 + 10 × 1=36+54+ 36+10=136 points E: 6 × 4 + 12 × 3 + 37 × 2=24+36+ 74=134 points In our example, using the Borda count method, D wins. Summary Method Winner Plurality A Two-Round System B Exhaustive Ballot C Borda Count D Condorcet Criterion Figure: Nicola de Condorcet (1743-1794): French philosopher, mathematician, and political scientist His ideas, including support for a liberal economy, free and equal public instruction, constitutional government, and equal rights for women and people of all races, have been said to embody the ideals of the Age of Enlightenment and Enlightenment rationalism. He died in prison after a period of flight from French Revolutionary authorities. (Entry from Wikipedia) Condorcet Criterion Pairwise Comparison Condorcet Criterion Rank Ballot Ballot Ballot Ballot Ballot Ballot 1 A B C D E E 2 D E B C B C 3 E D E E D D 4 C C D B C B 5 B A A A A A Votes 18 12 10 9 4 2 A versus B 18 vs. 37 B wins. Condorcet Criterion Rank Ballot Ballot Ballot Ballot Ballot Ballot 1 A B C D E E 2 D E B C B C 3 E D E E D D 4 C C D B C B 5 B A A A A A Votes 18 12 10 9 4 2 B versus C 16 vs. 39 C wins. Condorcet Criterion Rank Ballot Ballot Ballot Ballot Ballot Ballot 1 A B C D E E 2 D E B C B C 3 E D E E D D 4 C C D B C B 5 B A A A A A Votes 18 12 10 9 4 2 C versus D 12 vs. 43 D wins. Condorcet Criterion Rank Ballot Ballot Ballot Ballot Ballot Ballot 1 A B C D E E 2 D E B C B C 3 E D E E D D 4 C C D B C B 5 B A A A A A Votes 18 12 10 9 4 2 D versus E 27 vs. 28 E wins. Condorcet Criterion Rank Ballot Ballot Ballot Ballot Ballot Ballot 1 A B C D E E 2 D E B C B C 3 E D E E D D 4 C C D B C B 5 B A A A A A Votes 18 12 10 9 4 2 E versus A, 37:18 E versus B, 33:22 E versus C, 36:19 Condorcet Criterion E is the Condorcet candidate, i.e., preferred by the voters to all other candidates in pairwise comparison. Condorcet candidate should win, right? Condorcet Method Method Winner Plurality A Two-Round B Exhaustive Ballot C Borda Count D Condorcet Criterion E What should we do? II. Social Choice Theory Social Choice Theory Stanford Encyclopaedia of Philosophy: Social choice theory is the study of collective decision processes and procedures. It is not a single theory, but a cluster of models and results concerning the aggregation of individual inputs into collective outputs. Social Choice Theory (Complicated) collection of individual preferences Method ? Social Preference Election, legislation, constitution, ... Modern social choice theory has its roots in the enlightenment and its emphasis on reason. Social Choice Theory Continued from the Stanford Encyclopaedia Pioneered in the 18th century by Nicolas de Condorcet and Jean-Charles de Borda and in the 19th century by Charles Dodgson (also known as Lewis Carroll), social choice theory took off in the 20th century with the works of Kenneth Arrow, Amartya Sen, and Duncan Black. Its influence extends across economics, political science, philosophy, mathematics, and recently computer science and biology. Apart from contributing to our understanding of collective decision procedures, social choice theory has applications in the areas of institutional design, welfare economics, and social epistemology. Social Choice Theory Figure: Immanuel Kant (1724{1804) Social Choice Theory "Of the three forms of the state, that of democracy is, properly speaking, necessarily a despotism, because it establishes an executive power in which "all" decide for or even against one who does not agree; that is, "all," who are not quite all, decide, and this is a contradiction of the general will with itself and with freedom.." from 'Perpetual Peace: A Philosophical Sketch (1795)'.