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 next-to-last place vote, etc.; candidate
with thelargest point total wins)
- Pairwise Comparisons (look at all
one-on-one matchups; 1 pt. for each one-on-one 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 1st Place overall; eliminate
winner, run a new election & find winner—gets 2nd 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 one-on-one 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(N-1)/2
possible one-on-one matchups.
Ex. With 4 candidates, there are
4(3)/2=12/2=6 possible one-on-one matchups.
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