US Prime Ministers, 1789-2020

No, the title isn't a typo. The POD is that instead of choosing (or arguably creating) the modern presidential system, the Constitutional Convention instead decides that the British system is the most efficient, with a few changes (no rotten boroughs, an independent judiciary, written constitution, elected figurehead head of state, etc.).

The rules:

1. Elections must be held at least every 4 years.
2. One election per post
3. Wait at least two turns before going again.
4. Go in order.

1789: George Washington (crossbencher)
 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)

1802: Charles Cotesworth Pinckney (Federalization Party)
 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
1802: Charles Cotesworth Pinckney (Federalization Party)
1804: Charles Cotesworth Pinckney (Rederalization Party)
 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
1802: Charles Cotesworth Pinckney (Federalization Party)
1804: Charles Cotesworth Pinckney (Federalization Party)
1808: James Madison (American Whig)
 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
1802: Charles Cotesworth Pinckney (Federalization Party)
1804: Charles Cotesworth Pinckney (Federalization Party)
1808: James Madison (American Whig)
1812: James Madison (American Whig)
 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
1802: Charles Cotesworth Pinckney (Federalization Party)
1804: Charles Cotesworth Pinckney (Federalization Party)
1808: James Madison (American Whig)
1812: James Madison (American Whig)

1814: Daniel D. Tompkins(American Party)
 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
1802: Charles Cotesworth Pinckney (Federalization Party)
1804: Charles Cotesworth Pinckney (Federalization Party)
1808: James Madison (American Whig)
1812: James Madison (American Whig)
1814: Daniel D. Tompkins(American Party) (Madison killed by British troops)
1816: James Monroe (Whig)
 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
1802: Charles Cotesworth Pinckney (Federalization Party)
1804: Charles Cotesworth Pinckney (Federalization Party)
1808: James Madison (American Whig)
1812: James Madison (American Whig)
1814: Daniel D. Tompkins(American Party) (Madison killed by British troops)
1816: James Monroe (Whig)

1820: James Monroe (American Whig)
 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
1802: Charles Cotesworth Pinckney (Federalization Party)
1804: Charles Cotesworth Pinckney (Federalization Party)
1808: James Madison (American Whig)
1812: James Madison (American Whig)
1814: Daniel D. Tompkins(American Party) (Madison killed by British troops)
1816: James Monroe (Whig)

1820: James Monroe (American Whig)
1822: Andrew Jackson (American-Glory)
 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
1802: Charles Cotesworth Pinckney (Federalization Party)
1804: Charles Cotesworth Pinckney (Federalization Party)
1808: James Madison (American Whig)
1812: James Madison (American Whig)
1814: Daniel D. Tompkins(American Party) (Madison killed by British troops)
1816: James Monroe (American Whig)
1820: James Monroe (American Whig)
1822: Andrew Jackson (American-Glory)
1826: Andrew Jackson (American Glory)
 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
1802: Charles Cotesworth Pinckney (Federalization Party)
1804: Charles Cotesworth Pinckney (Federalization Party)
1808: James Madison (American Whig)
1812: James Madison (American Whig)
1814: Daniel D. Tompkins(American Party) (Madison killed by British troops)
1816: James Monroe (American Whig)
1820: James Monroe (American Whig)
1822: Andrew Jackson (American Glory)
1826: Andrew Jackson (American Glory)
1830: Andrew Jackson (American Glory)
 
Hmm... I would expect this list would more resemble that of Speakers of the House rather than Presidents...

1789: George Washington (Crossbencher)

1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
1802: Charles Cotesworth Pinckney (Federalization Party)
1804: Charles Cotesworth Pinckney (Federalization Party)
1808: James Madison (American Whig)
1812: James Madison (American Whig)
1814: Daniel D. Tompkins(American Party) (Madison killed by British troops)
1816: James Monroe (American Whig)
1820: James Monroe (American Whig)
1822: Andrew Jackson (American Glory)
1826: Andrew Jackson (American Glory)
1830: Andrew Jackson (American Glory)
1835: John Bell (American Whig)
 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
1802: Charles Cotesworth Pinckney (Federalization Party)
1804: Charles Cotesworth Pinckney (Federalization Party)
1808: James Madison (American Whig)
1812: James Madison (American Whig)
1814: Daniel D. Tompkins(American Party) (Madison killed by British troops)
1816: James Monroe (American Whig)
1820: James Monroe (American Whig)
1822: Andrew Jackson (American Glory)
1826: Andrew Jackson (American Glory)
1830: Andrew Jackson (American Glory)
1835: John Bell (American Whig)
1839: Martin Van Buren (American Gory)
 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
1802: Charles Cotesworth Pinckney (Federalization Party)
1804: Charles Cotesworth Pinckney (Federalization Party)
1808: James Madison (American Whig)
1812: James Madison (American Whig)
1814: Daniel D. Tompkins(American Party) (Madison killed by British troops)
1816: James Monroe (American Whig)
1820: James Monroe (American Whig)
1822: Andrew Jackson (American Glory)
1826: Andrew Jackson (American Glory)
1830: Andrew Jackson (American Glory)
1835: John Bell (American Whig)
1839: Martin Van Buren (American Gory)

1843: James K. Polk (Manifest Destiny Party)
 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
1802: Charles Cotesworth Pinckney (Federalization Party)
1804: Charles Cotesworth Pinckney (Federalization Party)
1808: James Madison (American Whig)
1812: James Madison (American Whig)
1814: Daniel D. Tompkins(American Party) (Madison killed by British troops)
1816: James Monroe (American Whig)
1820: James Monroe (American Whig)
1822: Andrew Jackson (American Glory)
1826: Andrew Jackson (American Glory)
1830: Andrew Jackson (American Glory)
1835: John Bell (American Whig)
1839: Martin Van Buren (American Glory)
1843:
James K. Polk (Manifest Destiny Party)
1846: James K. Polk (Coalition)*


*Manifest Destiny, American Glory, and several smaller Southern parties.

 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
1802: Charles Cotesworth Pinckney (Federalization Party)
1804: Charles Cotesworth Pinckney (Federalization Party)
1808: James Madison (American Whig)
1812: James Madison (American Whig)
1814: Daniel D. Tompkins(American Party) (Madison killed by British troops)
1816: James Monroe (American Whig)
1820: James Monroe (American Whig)
1822: Andrew Jackson (American Glory)
1826: Andrew Jackson (American Glory)
1830: Andrew Jackson (American Glory)
1835: John Bell (American Whig)
1839: Martin Van Buren (American Glory)
1843:
James K. Polk (Manifest Destiny Party)
1846: James K. Polk (Coalition)
1849: Charles Francis Adams, Sr.(Free Nation)
 
1789: George Washington (Crossbencher)
1792: George Washington (Federalization Party)
1796: Thomas Jefferson (American Whig)
1800: Thomas Jefferson (American Whig)
1802: Charles Cotesworth Pinckney (Federalization Party)
1804: Charles Cotesworth Pinckney (Federalization Party)
1808: James Madison (American Whig)
1812: James Madison (American Whig)
1814: Daniel D. Tompkins(American Party) (Madison killed by British troops)
1816: James Monroe (American Whig)
1820: James Monroe (American Whig)
1822: Andrew Jackson (American Glory)
1826: Andrew Jackson (American Glory)
1830: Andrew Jackson (American Glory)
1835: John Bell (American Whig)
1839: Martin Van Buren (American Glory)
1843:
James K. Polk (Manifest Destiny Party)
1846: James K. Polk (Coalition)*
1849: Charles Francis Adams, Sr.(Free Nation)
1853: Zachary Taylor (AW)
 
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