congress approved a bill for a 120 member House and Hamilton's method to apportion seats among the states. Hamilton's method won out over jefferson's method. Hamilton's method was supported by the federalist while jefferson's method was supported by the republicans
President Washington vetos the above bill (first veto in the U.S. history
the house, unable to override the veto, passed a new bill for a 105 member house and jefferson's method to apportion seats among the states. this method was used until 1840.
the house size was chosen to be 283 so that hamilton and webster methods would again agree. after much political infighting, 9 more seats were added and the final apportionment did not agree with either method
Rutherford b hayes became president based on the botched apportionment of 1872, the electoral college vote was 185 for hayes and 184 for tilden. tilden would have won if the correct apportionment as required by law had been used
no reapportionment was done after the 1920 census in direct violation of the constitution
the huntington-hill method was adopted with a house size of 435 and is currently what we use today
people vote for their local representative in their geographical district
people vote nationally for the party of their choice and the percentage of the votes a party receives determines the percentage of the seats that party receives
balinsky and youngs impossibility theorem
there cannot exist and never will an apportionment method which never violates quota or exhibits paradoxes. in other words any apportionment method which never violates quota can sometimes exhibit paradoxes. any apportionment method which never exhibits paradoxes can sometimes violate quota
jefferson's method is biased towards larger populations and adams method is biased towards smaller populations
the fundamental mathematical issue of apportionment is rounding
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