How to Improve Presidential Elections...6 • Donald Trump is President • How could this have...
Transcript of How to Improve Presidential Elections...6 • Donald Trump is President • How could this have...
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How to Improve Presidential Elections
E. Maskin Harvard University
Roy Gardner Memorial LectureIndiana University
BloomingtonOctober 4, 2018
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• Donald Trump is President
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• Donald Trump is President• How could this have happened?
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• Donald Trump is President• How could this have happened?
– Trump got Republican nomination by winning in 36 states
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• Donald Trump is President• How could this have happened?
– Trump got Republican nomination by winning in 36 states– defeated Hillary Clinton in general election
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• Donald Trump is President• How could this have happened?
– Trump got Republican nomination by winning in 36 states– defeated Hillary Clinton in general election
• But in first 17 primaries he won, anti-Trump vote bigger than pro-Trump vote
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• Donald Trump is President• How could this have happened?
– Trump got Republican nomination by winning in 36 states– defeated Hillary Clinton in general election
• But in first 17 primaries he won, anti-Trump vote bigger than pro-Trump vote
• Same thing in general election
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• Donald Trump is President• How could this have happened?
– Trump got Republican nomination by winning in 36 states– defeated Hillary Clinton in general election
• But in first 17 primaries he won, anti-Trump vote bigger than pro-Trump vote
• Same thing in general election– even in Florida, Michigan, North Carolina, Pennsylvania,
and Wisconsin (all of which Trump won) anti-Trump vote exceeded pro-Trump vote
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no contradiction
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no contradiction• in primaries
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no contradiction• in primaries
– Trump got less than 50% vote in each first 17victories
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no contradiction• in primaries
– Trump got less than 50% vote in each first 17 victories– in Arkansas, got only 33%
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no contradiction• in primaries
– Trump got less than 50% vote in each first 17 victories– in Arkansas, got only 33%– but faced multiple opponents (Rubio, Cruz, Kasich,
…), so anti-Trump vote was split
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no contradiction• in primaries
– Trump got less than 50% vote in each first 17 victories– in Arkansas, got only 33%– but faced multiple opponents (Rubio, Cruz, Kasich,
…), so anti-Trump vote was split– given Trump’s extreme views, might well have been
defeated had there been just one mainstream rival
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no contradiction• in primaries
– Trump got less than 50% vote in each first 17 victories– in Arkansas, got only 33%– but faced multiple opponents (Rubio, Cruz, Kasich,
…), so anti-Trump vote was split– given Trump’s extreme views, might well have been
defeated had there been just one mainstream rival• in March 8 poll, both Cruz and Rubio would have easily beaten
Trump in two-candidate contest
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no contradiction• in primaries
– Trump got less than 50% vote in each first 17 victories– in Arkansas, got only 33%– but faced multiple opponents (Rubio, Cruz, Kasich,
…), so anti-Trump vote was split– given Trump’s extreme views, might well have been
defeated had there been just one mainstream rival• in March 8 poll, both Cruz and Rubio would have easily beaten
Trump in two-candidate contest
– voting-splitting among Rubio, Cruz, Kasich and others ensured Trump’s nomination
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• in general election
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• in general election– Trump got less than majority in all states
mentioned
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• in general election– Trump got less than majority in all states
mentioned– in Michigan, Pennsylvania, and Wisconsin
difference between Trump and Clinton smaller than number of Jill Stein voters
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• in general election– Trump got less than majority in all states
mentioned– in Michigan, Pennsylvania, and Wisconsin
difference between Trump and Clinton smaller than number of Jill Stein voters
– if Stein voters voted for Clinton, Clinton would have won those states - - and election
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• in general election– Trump got less than majority in all states
mentioned– in Michigan, Pennsylvania, and Wisconsin
difference between Trump and Clinton smaller than number of Jill Stein voters
– if Stein voters voted for Clinton, Clinton would have won those states - - and election
– so vote-splitting between Clinton and Stein allowed Trump to win.
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Many other voting-splitting examples from U.S. presidential history
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Many other voting-splitting examples from U.S. presidential history• in election of 2000, contest between George W. Bush
and Al Gore came down to state of Florida
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Many other voting-splitting examples from U.S. presidential history• in election of 2000, contest between George W. Bush
and Al Gore came down to state of Florida– if Bush won Florida, he’d be president
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Many other voting-splitting examples from U.S. presidential history• in election of 2000, contest between George W. Bush
and Al Gore came down to state of Florida– if Bush won Florida, he’d be president– if Gore won Florida, he’d be president
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Many other voting-splitting examples from U.S. presidential history• in election of 2000, contest between George W. Bush
and Al Gore came down to state of Florida– if Bush won Florida, he’d be president– if Gore won Florida, he’d be president
• as it turned out, Bush defeated Gore (by fewer than 600 votes!)
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Many other voting-splitting examples from U.S. presidential history• in election of 2000, contest between George W. Bush
and Al Gore came down to state of Florida– if Bush won Florida, he’d be president– if Gore won Florida, he’d be president
• as it turned out, Bush defeated Gore (by fewer than 600 votes!)– but nearly 100,000 voters voted for Ralph Nader
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Many other voting-splitting examples from U.S. presidential history• in election of 2000, contest between George W. Bush
and Al Gore came down to state of Florida– if Bush won Florida, he’d be president– if Gore won Florida, he’d be president
• as it turned out, Bush defeated Gore (by fewer than 600 votes!)– but nearly 100,000 voters voted for Ralph Nader– probably overwhelming majority of Nader voters would
have voted for Gore had Nader not been on ballot
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Many other voting-splitting examples from U.S. presidential history• in election of 2000, contest between George W. Bush
and Al Gore came down to state of Florida– if Bush won Florida, he’d be president– if Gore won Florida, he’d be president
• as it turned out, Bush defeated Gore (by fewer than 600 votes!)– but nearly 100,000 voters voted for Ralph Nader– probably overwhelming majority of Nader voters would
have voted for Gore had Nader not been on ballot– voting-splitting between Gore and Nader handed election
to Bush
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Final example: 1992 U.S. Presidential election
(winner)Bill Clinton
George H.W. Bush
Ross Perot
42.9%
37.4%
18.9%
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Final example: 1992 U.S. Presidential election
(winner)Bill Clinton
George H.W. Bush
Ross Perot
42.9%
37.4%
18.9%
• Perot took votes primarily from Bush - -i.e., Bush and Perot split right-wing vote
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Final example: 1992 U.S. Presidential election
(winner)Bill Clinton
George H.W. Bush
Ross Perot
42.9%
37.4%
18.9%
• Perot took votes primarily from Bush - -i.e., Bush and Perot split right-wing vote
• Bush might well have won in absence ofPerot
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Final example: 1992 U.S. Presidential election
(winner)Bill Clinton
George H.W. Bush
Ross Perot
42.9%
37.4%
18.9%
• Perot took votes primarily from Bush - -i.e., Bush and Perot split right-wing vote
• Bush might well have won in absence ofPerot
• vote-splitting (between Bush and Perot)
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What do these examples show?
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What do these examples show?
• Republican primaries and general elections use plurality rule (first-past-the-post) as election method
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What do these examples show?
• Republican primaries and general elections use plurality rule (first-past-the-post) as election method– each voter votes for one candidate and winner is
candidate with most votes, even if doesn’t get majority
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What do these examples show?
• Republican primaries and general elections use plurality rule (first-past-the-post) as election method– each voter votes for one candidate and winner is
candidate with most votes, even if doesn’t get majority• plurality rule vulnerable to vote-splitting
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What do these examples show?
• Republican primaries and general elections use plurality rule (first-past-the-post) as election method– each voter votes for one candidate and winner is
candidate with most votes, even if doesn’t get majority• plurality rule vulnerable to vote-splitting
– two or more similar candidates split the vote, allowing a very different candidate to win
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Is there a better way to elect presidents?
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Is there a better way to elect presidents?
• Answer: yes
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Examples suggest that voting for just one candidate does not provide enough information about voters’ preferences
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Examples suggest that voting for just one candidate does not provide enough information about voters’ preferences• Rubio or Kasich might well have defeated Trump head-to-
head in early primaries, but this information not collected from voters
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Examples suggest that voting for just one candidate does not provide enough information about voters’ preferences• Rubio or Kasich might well have defeated Trump head-to-
head in early primaries, but this information not collected from voters
• possible that Clinton would have beaten Trump in Michigan, Pennsylvania, and Wisconsin in two-person race - - giving her the victory
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Examples suggest that voting for just one candidate does not provide enough information about voters’ preferences• Rubio or Kasich might well have defeated Trump head-to-
head in early primaries, but this information not collected from voters
• possible that Clinton would have beaten Trump in Michigan, Pennsylvania, and Wisconsin in two-person race - - giving her the victory
• Gore would probably have defeated Bush (Junior) in Florida head-to-head, but this not reflected in outcome
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Examples suggest that voting for just one candidate does not provide enough information about voters’ preferences• Rubio or Kasich might well have defeated Trump head-to-
head in early primaries, but this information not collected from voters
• possible that Clinton would have beaten Trump in Michigan, Pennsylvania, and Wisconsin in two-person race - - giving her the victory
• Gore would probably have defeated Bush (Junior) in Florida head-to-head, but this not reflected in outcome
• Bush (Senior) might have defeated Bill Clinton in two-way match-up, but we don’t know
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• Solution: should have voters providerankings of candidates
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• Solution: should have voters providerankings of candidates
e.g. Rubio Kasich Trump
Trumpor Kasich
Rubio
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• What should we do with these rankings?
• Solution: should have voters providerankings of candidates
e.g. Rubio Kasich Trump
Trumpor Kasich
Rubio
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“True” Majority Rule/Condorcet’s method(per Marquis de Condorcet)
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“True” Majority Rule/Condorcet’s method(per Marquis de Condorcet)
• voters submit rankings
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“True” Majority Rule/Condorcet’s method(per Marquis de Condorcet)
• voters submit rankings
• elect candidate who (according to rankings) would beat each of the others in head-to-head contest
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For example, suppose Republican electorate breaks down as follows
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For example, suppose Republican electorate breaks down as follows
40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
![Page 54: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/54.jpg)
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For example, suppose Republican electorate breaks down as follows
40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
• Kasich defeats Trump (35% + 25%= 60%)
![Page 55: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/55.jpg)
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For example, suppose Republican electorate breaks down as follows
40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
• Kasich defeats Trump (35% + 25%= 60%)• Kasich defeats Rubio (40% + 25%= 65%)
![Page 56: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/56.jpg)
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For example, suppose Republican electorate breaks down as follows
40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
• Kasich defeats Trump (35% + 25%= 60%)• Kasich defeats Rubio (40% + 25%= 65%)• so Kasich is true majority winner
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For example, suppose Republican electorate breaks down as follows
40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
• Kasich defeats Trump (35% + 25%= 60%)• Kasich defeats Rubio (40% + 25%= 65%)• so Kasich is true majority winner• contrast with plurality winner
![Page 58: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/58.jpg)
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For example, suppose Republican electorate breaks down as follows
40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
• Kasich defeats Trump (35% + 25%= 60%)• Kasich defeats Rubio (40% + 25%= 65%)• so Kasich is true majority winner• contrast with plurality winner
– Trump is plurality winner
![Page 59: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/59.jpg)
59
For example, suppose Republican electorate breaks down as follows
40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
• Kasich defeats Trump (35% + 25%= 60%)• Kasich defeats Rubio (40% + 25%= 65%)• so Kasich is true majority winner• contrast with plurality winner
– Trump is plurality winner– anti-Trump vote split between Rubio and Kasich
![Page 60: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/60.jpg)
For example, suppose Republican electorate breaks down as follows
40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
• Kasich defeats Trump (35% + 25%= 60%)• Kasich defeats Rubio (40% + 25%= 65%)• so Kasich is true majority winner• contrast with plurality winner
– Trump is plurality winner– anti-Trump vote split between Rubio and Kasich– if either of Rubio or Kasich drop out, other beats Trump 60
![Page 61: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/61.jpg)
61
48.7% 48.3% 3%Bush Gore NaderGore Bush GoreNader Nader Bush
![Page 62: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/62.jpg)
62
48.7% 48.3% 3%Bush Gore NaderGore Bush GoreNader Nader Bush
• Gore defeats Bush (48.3% + 3% = 51.3%)
![Page 63: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/63.jpg)
63
48.7% 48.3% 3%Bush Gore NaderGore Bush GoreNader Nader Bush
• Gore defeats Bush (48.3% + 3% = 51.3%)• Gore defeats Nader (48.7% + 48.3%= 97%)
![Page 64: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/64.jpg)
64
48.7% 48.3% 3%Bush Gore NaderGore Bush GoreNader Nader Bush
• Gore defeats Bush (48.3% + 3% = 51.3%)• Gore defeats Nader (48.7% + 48.3%= 97%)• Gore is true majority winner
![Page 65: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/65.jpg)
65
48.7% 48.3% 3%Bush Gore NaderGore Bush GoreNader Nader Bush
• Gore defeats Bush (48.3% + 3% = 51.3%)• Gore defeats Nader (48.7% + 48.3%= 97%)• Gore is true majority winner• but Bush is plurality winner
![Page 66: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/66.jpg)
66
48.7% 48.3% 3%Bush Gore NaderGore Bush GoreNader Nader Bush
• Gore defeats Bush (48.3% + 3% = 51.3%)• Gore defeats Nader (48.7% + 48.3%= 97%)• Gore is true majority winner• but Bush is plurality winner
– as he was in Florida
![Page 67: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/67.jpg)
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• Once voters submit rankings, many systems besides true majority rule become possible
![Page 68: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/68.jpg)
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• Once voters submit rankings, many systems besides true majority rule become possible
• Why limit ourselves to majority rule?
![Page 69: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/69.jpg)
69
For example, might use runoff voting (used in France, Brazil, Russia)
![Page 70: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/70.jpg)
70
For example, might use runoff voting (used in France, Brazil, Russia)• if some candidate gets majority of first-place
votes, elected
![Page 71: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/71.jpg)
71
For example, might use runoff voting (used in France, Brazil, Russia)• if some candidate gets majority of first-place
votes, elected• otherwise, look at 2 candidates getting most
first-place votes
![Page 72: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/72.jpg)
72
For example, might use runoff voting (used in France, Brazil, Russia)• if some candidate gets majority of first-place
votes, elected• otherwise, look at 2 candidates getting most
first-place votes• whichever candidate preferred by majority is
elected
![Page 73: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/73.jpg)
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40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
![Page 74: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/74.jpg)
74
40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
• no candidate gets majority of first-place votes
![Page 75: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/75.jpg)
75
40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
• no candidate gets majority of first-place votes• so Trump faces Rubio
![Page 76: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/76.jpg)
76
40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
• no candidate gets majority of first-place votes• so Trump faces Rubio
– majority prefer Rubio (35% + 25%)
![Page 77: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/77.jpg)
77
40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
• no candidate gets majority of first-place votes• so Trump faces Rubio
– majority prefer Rubio (35% + 25%)– so Rubio elected in runoff
![Page 78: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/78.jpg)
78
40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
• no candidate gets majority of first-place votes• so Trump faces Rubio
– majority prefer Rubio (35% + 25%)– so Rubio elected in runoff
• saw earlier that majority rule elects Kasich
![Page 79: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/79.jpg)
79
Which method – runoff voting or majority rule – is better?
![Page 80: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/80.jpg)
80
Which method – runoff voting or majority rule – is better?
• Way to answer question: which method does better job of satisfying basic requirements (principles) that any good voting rule should satisfy
![Page 81: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/81.jpg)
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Consensus principle/Pareto principle
![Page 82: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/82.jpg)
82
Consensus principle/Pareto principle
• if everyone agrees candidate A better than B, B won’t be elected
![Page 83: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/83.jpg)
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Consensus principle/Pareto principle
• if everyone agrees candidate A better than B, B won’t be elected
• satisfied by both true majority rule and runoff voting
![Page 84: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/84.jpg)
84
Equal-treatment principle/anonymity principle
![Page 85: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/85.jpg)
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Equal-treatment principle/anonymity principle
• all voters should count equally (doesn’t matter who you are)
![Page 86: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/86.jpg)
86
Equal-treatment principle/anonymity principle
• all voters should count equally (doesn’t matter who you are)
• violated by Electoral College method
![Page 87: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/87.jpg)
87
Equal-treatment principle/anonymity principle
• all voters should count equally (doesn’t matter who you are)
• violated by Electoral College method
• satisfied by true majority rule and runoff voting
![Page 88: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/88.jpg)
88
Neutrality
![Page 89: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/89.jpg)
89
Neutrality
− electoral rules should treat all candidates equally
![Page 90: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/90.jpg)
90
Neutrality
− electoral rules should treat all candidates equally
• Both true majority and runoff voting satisfy neutrality
![Page 91: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/91.jpg)
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“No vote splitting” Principle(Independence of Irrelevant Candidates)
![Page 92: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/92.jpg)
92
“No vote splitting” Principle(Independence of Irrelevant Candidates)
• which of candidates A and B winsshould not depend on whether candidate C is running or not
![Page 93: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/93.jpg)
93
“No vote splitting” Principle(Independence of Irrelevant Candidates)
• which of candidates A and B winsshould not depend on whether candidate C is running or not
• True majority rule satisfies IIC (if beats B and by a majority, then still beats)
![Page 94: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/94.jpg)
94
“No vote splitting” Principle(Independence of Irrelevant Candidates)
• which of candidates A and B winsshould not depend on whether candidate C is running or not
• True majority rule satisfies IIC (if beats B and by a majority, then still beats)– ifA is winner when A, B, and C running, must beat each of B
and C by majority
![Page 95: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/95.jpg)
95
“No vote splitting” Principle(Independence of Irrelevant Candidates)
• which of candidates A and B winsshould not depend on whether candidate C is running or not
• True majority rule satisfies IIC (if beats B and by a majority, then still beats)– ifA is winner when A, B, and C running, must beat each of B
and C by majority– but still beats B majority if C not running
![Page 96: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/96.jpg)
96
“No vote splitting” Principle(Independence of Irrelevant Candidates)
• which of candidates A and B winsshould not depend on whether candidate C is running or not
• True majority rule satisfies IIC (if beats B and by a majority, then still beats)– ifA is winner when A, B, and C running, must beat each of B
and C by majority– but still beats B majority if C not running
• But runoff voting violates IIC
![Page 97: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/97.jpg)
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40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
![Page 98: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/98.jpg)
98
40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
• saw that in 3-way race, Rubio wins
![Page 99: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/99.jpg)
99
40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
• saw that in 3-way race, Rubio wins• but notice that if Trump doesn’t run, Kasich wins
![Page 100: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/100.jpg)
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40% 35% 25%Trump Rubio KasichKasich Kasich RubioRubio Trump Trump
• saw that in 3-way race, Rubio wins• but notice that if Trump doesn’t run, Kasich wins• so runoff voting violates “no vote splitting” principle
(IIC)
![Page 101: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/101.jpg)
101
So far, true majority rule fares better than runoff voting
![Page 102: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/102.jpg)
102
So far, true majority rule fares better than runoff voting
• both satisfy consensus, anonymity, and neutrality
![Page 103: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/103.jpg)
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So far, true majority rule fares better than runoff voting
• both satisfy consensus, anonymity, and neutrality• but only majority rule satisfies IIC
![Page 104: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/104.jpg)
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But majority rule has a flaw:
![Page 105: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/105.jpg)
105
But majority rule has a flaw:
• there may not always be a candidate that beats all the others
![Page 106: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/106.jpg)
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35% 33% 32%Trump Rubio KasichRubio Kasich TrumpKasich Trump Rubio
![Page 107: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/107.jpg)
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35% 33% 32%Trump Rubio KasichRubio Kasich TrumpKasich Trump Rubio
Rubio beats Kasich (68% to 32%)
![Page 108: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/108.jpg)
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35% 33% 32%Trump Rubio KasichRubio Kasich TrumpKasich Trump Rubio
Rubio beats Kasich (68% to 32%)Trump beats Rubio (67% to 33%)
![Page 109: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/109.jpg)
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35% 33% 32%Trump Rubio KasichRubio Kasich TrumpKasich Trump Rubio
Rubio beats Kasich (68% to 32%)Trump beats Rubio (67% to 33%)But Kasich beats Trump! (65% to 35%)
![Page 110: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/110.jpg)
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35% 33% 32%Trump Rubio KasichRubio Kasich TrumpKasich Trump Rubio
Rubio beats Kasich (68% to 32%)Trump beats Rubio (67% to 33%)But Kasich beats Trump! (65% to 35%)
• this is called a Condorcet cycle
![Page 111: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/111.jpg)
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35% 33% 32%Trump Rubio KasichRubio Kasich TrumpKasich Trump Rubio
Rubio beats Kasich (68% to 32%)Trump beats Rubio (67% to 33%)But Kasich beats Trump! (65% to 35%)
• this is called a Condorcet cycle• majority rule violates decisiveness principle, which
requires that a winner always exists
![Page 112: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/112.jpg)
112
35% 33% 32%Trump Rubio KasichRubio Kasich TrumpKasich Trump Rubio
Rubio beats Kasich (68% to 32%)Trump beats Rubio (67% to 33%)But Kasich beats Trump! (65% to 35%)
• this is called a Condorcet cycle• majority rule violates decisiveness principle, which
requires that a winner always exists• runoff voting satisfies decisiveness
![Page 113: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/113.jpg)
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• So true majority rule satisfiesconsensus anonymity neutrality IIC
![Page 114: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/114.jpg)
114
• So true majority rule satisfiesconsensus anonymity neutrality IIC
• Runoff voting satisfiesconsensus anonymity neutrality decisiveness
![Page 115: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/115.jpg)
115
Does any voting method satisfy all five principles?
![Page 116: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/116.jpg)
116
Does any voting method satisfy all five principles?
consensus anonymity neutrality IICdecisiveness
![Page 117: How to Improve Presidential Elections...6 • Donald Trump is President • How could this have happened? – Trump got Republican nomination by winning in 36 states – defeated Hillary](https://reader035.fdocuments.us/reader035/viewer/2022070712/5ecea47922f5392b8030f5e2/html5/thumbnails/117.jpg)
117
Does any voting method satisfy all five principles?
consensus anonymity neutrality IICdecisiveness
Answer: No
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Does any voting method satisfy all five principles?
consensus anonymity neutrality IICdecisiveness
Answer: No• Implied by Arrow’s Impossibility Theorem
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But Arrow’s theorem too negative
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But Arrow’s theorem too negative
• insists electoral method must work for anyrankings by voters
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But Arrow’s theorem too negative
• insists electoral method must work for anyrankings by voters
• but some rankings may be quite unlikely
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For example, most Republicans either love Trump or hate him
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For example, most Republicans either love Trump or hate him• among supporters, Trump is better than any other Republican
candidate
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For example, most Republicans either love Trump or hate him• among supporters, Trump is better than any other Republican
candidate• among other Republicans, almost any other Republican
candidate is better than Trump
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For example, most Republicans either love Trump or hate him• among supporters, Trump is better than any other Republican
candidate• among other Republicans, almost any other Republican
candidate is better than Trump• so might have rankings
Trump Trump Rubio KasichKasich or Rubio or Kasich or RubioRubio Kasich Trump Trump
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For example, most Republicans either love Trump or hate him• among supporters, Trump is better than any other Republican
candidate• among other Republicans, almost any other Republican
candidate is better than Trump• so might have rankings
– but not
Trump Trump Rubio KasichKasich or Rubio or Kasich or RubioRubio Kasich Trump Trump
Rubio KasichTrump or TrumpKasich Rubio
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• this sort of polarization may be bad for Republican party
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• this sort of polarization may be bad for Republican party
• but very good for majority rule
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• this sort of polarization may be bad for Republican party
• but very good for majority rule• if most voters polarized, then the majority rule
is decisive (no Condorcet cycles)
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• Define a voting method to work well for restricted class of rankings if it satisfies consensus, anonymity, neutrality, IIC, and decisiveness when voters’ rankings drawn from that class
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• Define a voting method to work well for restricted class of rankings if it satisfies consensus, anonymity, neutrality, IIC, and decisiveness when voters’ rankings drawn from that class
(e.g. true majority rule works well for the class of polarized rankings)
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Dasgupta-Maskin Majority Domination Theorem:
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Dasgupta-Maskin Majority Domination Theorem:
• if a voting method works well for some particular class of rankings, then true majority rule also works well for that class
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Dasgupta-Maskin Majority Domination Theorem:
• if a voting method works well for some particular class of rankings, then true majority rule also works well for that class
• furthermore, there exists some class of rankings for which true majority rule works well but other voting method does not
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Dasgupta-Maskin Majority Domination Theorem:
• if a voting method works well for some particular class of rankings, then true majority rule also works well for that class
• furthermore, there exists some class of rankings for which true majority rule works well but other voting method does not
• thus, true majority rule works well more often than any other method
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• Thus there is precise sense in which true majority rule is best
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• Thus there is precise sense in which true majority rule is best
• true majority rule not always decisive
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• Thus there is precise sense in which true majority rule is best
• true majority rule not always decisive– then need tie breaker
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Majority Rule could help in another way
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Majority Rule could help in another way• In general election, many voters reviled Trump
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Majority Rule could help in another way• In general election, many voters reviled Trump
– but couldn’t bring themselves to vote for Hillary Clinton
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Majority Rule could help in another way• In general election, many voters reviled Trump
– but couldn’t bring themselves to vote for Hillary Clinton– so either didn’t vote or voted for third-party candidates
with no chance of winning
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Majority Rule could help in another way• In general election, many voters reviled Trump
– but couldn’t bring themselves to vote for Hillary Clinton– so either didn’t vote or voted for third-party candidates
with no chance of winning
• many of them might have voted for Michael Bloomberg (moderates or conservatives) or Bernie Sanders (millennials) had they been on ballot
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Majority Rule could help in another way• In general election, many voters reviled Trump
– but couldn’t bring themselves to vote for Hillary Clinton– so either didn’t vote or voted for third-party candidates
with no chance of winning
• many of them might have voted for Michael Bloomberg (moderates or conservatives) or Bernie Sanders (millennials) had they been on ballot– but Bloomberg and Sanders choose not to run
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Majority Rule could help in another way• In general election, many voters reviled Trump
– but couldn’t bring themselves to vote for Hillary Clinton– so either didn’t vote or voted for third-party candidates
with no chance of winning
• many of them might have voted for Michael Bloomberg (moderates or conservatives) or Bernie Sanders (millennials) had they been on ballot– but Bloomberg and Sanders choose not to run– afraid of taking votes away from Clinton and handing
election to Trump - - vote splitting again
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Majority Rule could help in another way• In general election, many voters reviled Trump
– but couldn’t bring themselves to vote for Hillary Clinton– so either didn’t vote or voted for third-party candidates
with no chance of winning
• many of them might have voted for Michael Bloomberg (moderates or conservatives) or Bernie Sanders (millennials) had they been on ballot– but Bloomberg and Sanders choose not to run– afraid of taking votes away from Clinton and handing
election to Trump - - vote splitting again– public left with 2 deeply disliked candidates
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42% 40% 18%Trump Clinton Bloomberg
Bloomberg Bloomberg Clinton-TrumpClinton Trump
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• Bloomberg beats Trump (60% to 40%)
42% 40% 18%Trump Clinton Bloomberg
Bloomberg Bloomberg Clinton-TrumpClinton Trump
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• Bloomberg beats Trump (60% to 40%)• Bloomberg beats Clinton (58% to 42%)
42% 40% 18%Trump Clinton Bloomberg
Bloomberg Bloomberg Clinton-TrumpClinton Trump
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• Bloomberg beats Trump (60% to 40%)• Bloomberg beats Clinton (58% to 42%)• Bloomberg is majority winner
42% 40% 18%Trump Clinton Bloomberg
Bloomberg Bloomberg Clinton-TrumpClinton Trump
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• Bloomberg beats Trump (60% to 40%)• Bloomberg beats Clinton (58% to 42%)• Bloomberg is majority winner• Trump is plurality winner
42% 40% 18%Trump Clinton Bloomberg
Bloomberg Bloomberg Clinton-TrumpClinton Trump
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Will we see true majority rule adopted for presidential elections?
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Will we see true majority rule adopted for presidential elections?• up to individual states - - no Constitutional change
needed
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Will we see true majority rule adopted for presidential elections?• up to individual states - - no Constitutional change
needed• something quite close to majority rule (ranked
choice) already used in several American cities, e.g. San Francisco and Minneapolis
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Will we see true majority rule adopted for presidential elections?• up to individual states - - no Constitutional change
needed• something quite close to majority rule (ranked
choice) already used in several American cities, e.g. San Francisco and Minneapolis
• State of Maine has adopted ranked choice for governor, U.S. Senate, and U.S. House of Representatives
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Will we see true majority rule adopted for presidential elections?• up to individual states - - no Constitutional change
needed• something quite close to majority rule (ranked
choice) already used in several American cities, e.g. San Francisco and Minneapolis
• State of Maine has adopted ranked choice for governor, U.S. Senate, and U.S. House of Representatives
• so there’s reason for optimism that presidential elections will improve