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39 terms

single-choice ballot

A ballot where one only selects the top candidate

preference ballot

a ballot type where all the candidates are ranked from most favorite to least favorite

truncated preference ballot

a ballot where some of the candidates are ranked (for instance, top three)

winner only

an outcome where only the winner of the election is important

partial ranking

a ranking of the top candidates in an election (top two, top three, etc.)

(full) ranking

an election outcome where all the candidates are ranking from top to bottom

preference schedule

a table that shows the number of voters that voted in the same way on their preference ballots

plurality method

a voting method where the top vote getter wins

Condorcet candidate

a candidate preferred by a majority of the voters over every other candidate when compared head-to-head

plurality

the largest number of voted obtained in an election (if there are n candidates, then this must be strictly larger than 1/n)

majority

(strictly) more than 50% of votes cast

Borda count method

a voting method that assigns points to preferences with top points awarded to first place, less to second, less to third, etc. The standard is to award N points to 1st place if there are N candidates, and one less for each rank below first.

plurality-with-elimination//instant run-off voting

a voting method in which the lowest vote getters in an election are eliminated one-by-one (and preference schedules adjusted accordingly) until one candidate obtains a majority

pairwise comparison

a voting method where candidate preferences are compared head-to-head, and the winner is the candidate with the most head-to-head wins

Arrow's Impossibility Theorem

theorem says no election method can satisfy all fairness criteria

fairness criterion

a fairness standard that we would like to apply to all voting methods

majority criterion

a majority-winning candidate should be the victor in any voting method

Condorcet criterion

the winner of the election through pairwise comparisons should win in every voting method

monotonicity criterion

if candidate X wins, then X should still be the winner if X is ranked higher in the preference ballot (improvement in ranking should not hurt a candidate)

independence of irrelevant alternatives

a losing candidate dropping out of an election should not affect the outcome of the election

apportionment

dividing up elements fairly proportional to some measured standard, but where fractions of elements cannot be awarded

states

the parties in an apportionment problem among whom the "seats" are being divided

seats

the things being divvied up among the "states"

populations

a set of positive numbers used to determine how to portion the "seats"

apportionment method

a procedures that guarantees a division of of exactly M seats to N states

standard division

ratio of the population to the seats

standard quotas//fair quota

ratio of the state's population and the standard divisor

upper quota

the standard quota rounded up to the next whole number

lower quota

the standard quota rounded down to the next whole number

Hamilton's Method

Calculate the state's standard quote; round down; give out surplus seats one at a time to largest decimal portions until you award all seats

quota rule

no state should be awarded more seats than their upper quota, or fewer seats than their lower quota

Alabama Paradox

A state loses seats when more total seats are to be divided up

Jefferson's Method

begin with standard quota, round down; if all states not awarded, select a higher divisor and try again; repeat until exactly the right number of seats are awarded

Adam's Method

begin with standard quota, round up; if too many seats are awared, select a lower divisor and try again; repeat until exactly the right number of seats are awarded

Webster's Method

begin with standard quota, round normally; if all states not awarded (or too many), select a different divisor and try again; repeat until exactly the right number of seats are awarded

Huntington-Hill Method

begins like Hamilton's method, but uses the geometric mean to determine if state should be awarded an extra seat; if the correct number of seats are not awarded, modify the divisor and try again

population paradox

the rate of increase of a state is faster, but a slower growing state is awarded the extra seat

new-states paradox

a new state is added; despite attempting to add the correct number of seats for the new state, adding the state modifies the apportionment of old states

Balinksy-Young Impossibility Theorem

no apportionment method can satisfy both the quota rule in all cases and avoid all paradoxes