5 VOTING METHODS (4 Preferential*, 1
Nonpreferential)
(*Preferential Voting Methods are those which require the use of a
Preference Schedule...a list of candidates in order of preference).
PREFERENTIAL VOTING METHODS
 Plurality (candidate with the most
first place votes wins)
 Plurality with Elimination (winner
is selected through a series of Plurality elections in which the
candidate with the fewest votes is eliminated in each round)
 Borda Count (1 pt. for each last
place vote, 2 pts. for each nexttolast place vote, etc.; candidate
with thelargest point total wins)
 Pairwise Comparisons (look at all
oneonone matchups; 1 pt. for each oneonone win (½ pt. for a tie);
candidate with the largest point total wins)
A NONPREFERENTIAL VOTING METHOD
(Arrow's Impossibility Theorem does not apply to nonpreferential voting
methods.)
 Approval Voting (voters ‘approve’
as many of the candidates as they wish; candidate with the most approval
votes wins)
2 RANKING PROCEDURES*
(*Ranking Methods provide a complete ranking from first place to last place)
 Extended Rankings (run the
election; rank candidates based on how they did relative to the other
candidates)
 Recursive Rankings (run the
election & find winner—gets 1^{st} Place overall; eliminate
winner, run a new election & find winner—gets 2^{nd} Place
overall; continue until all candidates are ranked)
Note: Each of these Ranking Methods can
be applied to each of the Voting Methods.
Note: For Approval Voting, Extended and Recursive Ranking Methods always
produce the same results.
4 FAIRNESS CRITERIA*
(*Fairness Criteria represent some ‘common sense’ ideas on which one
might judge the ‘fairness’ of various Voting Methods)
 Majority Criterion (Any candidate
receiving a majority of first place votes should be the winner.)
 Condorcet Criterion (Any candidate
who wins all oneonone matchups with the remaining candidates should be
the winner.)
 Monotonicity Criterion (An
election is run and produces a winner. This original winner should
remain the winner in any revote in which all ballot changes are in favor
of the original winner.)
 Irrelevant Alternatives Criterion
(An election is run and produces a winner. If any of the losing
candidates are dropped & election results recalculated, the winner
should be the same.)
Note: Arrow’s Impossibility Theorem
tells us that no preferential voting method can satisfy all of these
Fairness Criteria.
MISCELLANEOUS TIDBITS
 The total number of points in a Borda
Count election (with 1 pt. for the last place candidate, etc.) is given
by:
(SUM OF THE POINT VALUE FOR EACH PLACE)(NUMBER OF VOTERS).
Ex. With 5 candidates & 100 voters,
there are a total of (1+2+3+4+5)(100)=(15)(100)=1500 points in a Borda
Count election.
 With N candidates, there are
N(N1)/2
possible oneonone matchups.
Ex. With 4 candidates, there are
4(3)/2=12/2=6 possible oneonone matchups.
