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8/2/2019 Bully Algorithm
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Bully algorithm
From Wikipedia, the free encyclopedia
Jump to: navigation,search
The bully algorithm is a method indistributed computing for dynamically selecting a
coordinator by process ID number.
When a process P determines that the current coordinator is down because of messagetimeouts or failure of the coordinator to initiate a handshake, it performs the following
sequence of actions:
1. P broadcasts an election message (inquiry) to all other processes with higherprocess IDs.2. If P hears from no process with a higher process ID than it, it wins the election and
broadcasts victory.
3. If P hears from a process with a higher ID, P waits a certain amount of time for that
process to broadcast itself as the leader. If it does not receive this message in time,it re-broadcasts the election message.
4. If P gets an election message (inquiry) from another process with a lower ID it
sends an "I am alive" message back and starts new elections.
Note that if P receives a victory message from a process with a lower ID number, it
immediately initiates a new election. This is how the algorithm gets its name - a processwith a higher ID number will bully a lower ID process out of the coordinator position as
soon as it comes online.
Voting system
http://en.wikipedia.org/wiki/Voting_sys
tem
From Wikipedia, the free encyclopedia
Jump to: navigation,searchFor other uses, seeVoting system (disambiguation).
Part of thePolitics series
Electoral methods
http://en.wikipedia.org/wiki/Bully_algorithm#mw-head%23mw-headhttp://en.wikipedia.org/wiki/Bully_algorithm#p-search%23p-searchhttp://en.wikipedia.org/wiki/Bully_algorithm#p-search%23p-searchhttp://en.wikipedia.org/wiki/Distributed_computinghttp://en.wikipedia.org/wiki/Distributed_computinghttp://en.wikipedia.org/wiki/Voting_system#mw-head%23mw-headhttp://en.wikipedia.org/wiki/Voting_system#p-search%23p-searchhttp://en.wikipedia.org/wiki/Voting_system#p-search%23p-searchhttp://en.wikipedia.org/wiki/Voting_system_(disambiguation)http://en.wikipedia.org/wiki/Voting_system_(disambiguation)http://en.wikipedia.org/wiki/Category:Politicshttp://en.wikipedia.org/wiki/Category:Politicshttp://en.wikipedia.org/wiki/Bully_algorithm#mw-head%23mw-headhttp://en.wikipedia.org/wiki/Bully_algorithm#p-search%23p-searchhttp://en.wikipedia.org/wiki/Distributed_computinghttp://en.wikipedia.org/wiki/Voting_system#mw-head%23mw-headhttp://en.wikipedia.org/wiki/Voting_system#p-search%23p-searchhttp://en.wikipedia.org/wiki/Voting_system_(disambiguation)http://en.wikipedia.org/wiki/Category:Politics8/2/2019 Bully Algorithm
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Single-winner
Simple majoritarianism
Plurality
o First-past-the-post voting
o Multiple-round systems
Two round
Exhaustive ballot
Preferential systems
o Condorcet methods
Copeland's method
KemenyYoung method
Minimax
Nanson's method
Ranked pairs
Schulze method
o Bucklin voting
o Oklahoma primary electoral system
o Coombs' method
o Instant-runoff (alternative vote)
Contingent vote
o Borda count
Rated systems
o
Range votingo Approval voting
o Majority Judgment
Multiple-winner
Proportional representation
http://en.wikipedia.org/wiki/Single-winner_voting_systemhttp://en.wikipedia.org/wiki/Majority_rulehttp://en.wikipedia.org/wiki/Plurality_voting_systemhttp://en.wikipedia.org/wiki/First-past-the-post_votinghttp://en.wikipedia.org/wiki/Two-round_systemhttp://en.wikipedia.org/wiki/Exhaustive_ballothttp://en.wikipedia.org/wiki/Preferential_votinghttp://en.wikipedia.org/wiki/Condorcet_methodhttp://en.wikipedia.org/wiki/Copeland's_methodhttp://en.wikipedia.org/wiki/Kemeny%E2%80%93Young_methodhttp://en.wikipedia.org/wiki/Minimax_Condorcethttp://en.wikipedia.org/wiki/Nanson's_methodhttp://en.wikipedia.org/wiki/Ranked_pairshttp://en.wikipedia.org/wiki/Schulze_methodhttp://en.wikipedia.org/wiki/Bucklin_votinghttp://en.wikipedia.org/wiki/Oklahoma_primary_electoral_systemhttp://en.wikipedia.org/wiki/Coombs'_methodhttp://en.wikipedia.org/wiki/Instant-runoff_votinghttp://en.wikipedia.org/wiki/Contingent_votehttp://en.wikipedia.org/wiki/Borda_counthttp://en.wikipedia.org/wiki/Borda_counthttp://en.wikipedia.org/wiki/Range_votinghttp://en.wikipedia.org/wiki/Approval_votinghttp://en.wikipedia.org/wiki/Majority_Judgmenthttp://en.wikipedia.org/wiki/Voting_systems#Multiple-winner_methodshttp://en.wikipedia.org/wiki/Proportional_representationhttp://en.wikipedia.org/wiki/Single-winner_voting_systemhttp://en.wikipedia.org/wiki/Majority_rulehttp://en.wikipedia.org/wiki/Plurality_voting_systemhttp://en.wikipedia.org/wiki/First-past-the-post_votinghttp://en.wikipedia.org/wiki/Two-round_systemhttp://en.wikipedia.org/wiki/Exhaustive_ballothttp://en.wikipedia.org/wiki/Preferential_votinghttp://en.wikipedia.org/wiki/Condorcet_methodhttp://en.wikipedia.org/wiki/Copeland's_methodhttp://en.wikipedia.org/wiki/Kemeny%E2%80%93Young_methodhttp://en.wikipedia.org/wiki/Minimax_Condorcethttp://en.wikipedia.org/wiki/Nanson's_methodhttp://en.wikipedia.org/wiki/Ranked_pairshttp://en.wikipedia.org/wiki/Schulze_methodhttp://en.wikipedia.org/wiki/Bucklin_votinghttp://en.wikipedia.org/wiki/Oklahoma_primary_electoral_systemhttp://en.wikipedia.org/wiki/Coombs'_methodhttp://en.wikipedia.org/wiki/Instant-runoff_votinghttp://en.wikipedia.org/wiki/Contingent_votehttp://en.wikipedia.org/wiki/Borda_counthttp://en.wikipedia.org/wiki/Range_votinghttp://en.wikipedia.org/wiki/Approval_votinghttp://en.wikipedia.org/wiki/Majority_Judgmenthttp://en.wikipedia.org/wiki/Voting_systems#Multiple-winner_methodshttp://en.wikipedia.org/wiki/Proportional_representation8/2/2019 Bully Algorithm
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o Party-list (openclosedmixedlocal)
Highest averages
D'Hondt method
Sainte-Lagu method
Largest remainder
Hare quota
Droop quota
Imperiali quota
o Single transferable vote
CPO-STV
Schulze STV
Wright system
Semi-proportional representation
o Cumulative voting
o Limited voting
Single non-transferable vote
o Additional member system
o Parallel voting
Majoritarian representation
o Plurality-at-large
o Preferential block voting
o General ticket
Proxy voting
Delegable proxy
Delegated proxy
Random selection
Demarchy
Sortition
Random ballot
http://en.wikipedia.org/wiki/Proportional_representationhttp://en.wikipedia.org/wiki/Party-list_proportional_representationhttp://en.wikipedia.org/wiki/Open_listhttp://en.wikipedia.org/wiki/Closed_listhttp://en.wikipedia.org/wiki/Closed_listhttp://en.wikipedia.org/wiki/Mixed_member_proportional_representationhttp://en.wikipedia.org/wiki/Mixed_member_proportional_representationhttp://en.wikipedia.org/wiki/Mixed_member_proportional_representationhttp://en.wikipedia.org/wiki/Localized_listhttp://en.wikipedia.org/wiki/Highest_averages_methodhttp://en.wikipedia.org/wiki/D'Hondt_methodhttp://en.wikipedia.org/wiki/Sainte-Lagu%C3%AB_methodhttp://en.wikipedia.org/wiki/Largest_remainder_methodhttp://en.wikipedia.org/wiki/Hare_quotahttp://en.wikipedia.org/wiki/Droop_quotahttp://en.wikipedia.org/wiki/Imperiali_quotahttp://en.wikipedia.org/wiki/Single_transferable_votehttp://en.wikipedia.org/wiki/CPO-STVhttp://en.wikipedia.org/wiki/Schulze_STVhttp://en.wikipedia.org/wiki/Wright_systemhttp://en.wikipedia.org/wiki/Semi-proportional_representationhttp://en.wikipedia.org/wiki/Cumulative_votinghttp://en.wikipedia.org/wiki/Limited_votinghttp://en.wikipedia.org/wiki/Single_non-transferable_votehttp://en.wikipedia.org/wiki/Additional_Member_Systemhttp://en.wikipedia.org/wiki/Parallel_votinghttp://en.wikipedia.org/wiki/Majoritarian_representationhttp://en.wikipedia.org/wiki/Plurality-at-large_votinghttp://en.wikipedia.org/wiki/Preferential_block_votinghttp://en.wikipedia.org/wiki/General_tickethttp://en.wikipedia.org/wiki/Proxy_votinghttp://en.wikipedia.org/wiki/Delegable_proxyhttp://en.wikipedia.org/wiki/Delegated_votinghttp://en.wikipedia.org/wiki/Demarchyhttp://en.wikipedia.org/wiki/Sortitionhttp://en.wikipedia.org/wiki/Random_ballothttp://en.wikipedia.org/wiki/Party-list_proportional_representationhttp://en.wikipedia.org/wiki/Open_listhttp://en.wikipedia.org/wiki/Closed_listhttp://en.wikipedia.org/wiki/Mixed_member_proportional_representationhttp://en.wikipedia.org/wiki/Localized_listhttp://en.wikipedia.org/wiki/Highest_averages_methodhttp://en.wikipedia.org/wiki/D'Hondt_methodhttp://en.wikipedia.org/wiki/Sainte-Lagu%C3%AB_methodhttp://en.wikipedia.org/wiki/Largest_remainder_methodhttp://en.wikipedia.org/wiki/Hare_quotahttp://en.wikipedia.org/wiki/Droop_quotahttp://en.wikipedia.org/wiki/Imperiali_quotahttp://en.wikipedia.org/wiki/Single_transferable_votehttp://en.wikipedia.org/wiki/CPO-STVhttp://en.wikipedia.org/wiki/Schulze_STVhttp://en.wikipedia.org/wiki/Wright_systemhttp://en.wikipedia.org/wiki/Semi-proportional_representationhttp://en.wikipedia.org/wiki/Cumulative_votinghttp://en.wikipedia.org/wiki/Limited_votinghttp://en.wikipedia.org/wiki/Single_non-transferable_votehttp://en.wikipedia.org/wiki/Additional_Member_Systemhttp://en.wikipedia.org/wiki/Parallel_votinghttp://en.wikipedia.org/wiki/Majoritarian_representationhttp://en.wikipedia.org/wiki/Plurality-at-large_votinghttp://en.wikipedia.org/wiki/Preferential_block_votinghttp://en.wikipedia.org/wiki/General_tickethttp://en.wikipedia.org/wiki/Proxy_votinghttp://en.wikipedia.org/wiki/Delegable_proxyhttp://en.wikipedia.org/wiki/Delegated_votinghttp://en.wikipedia.org/wiki/Demarchyhttp://en.wikipedia.org/wiki/Sortitionhttp://en.wikipedia.org/wiki/Random_ballot8/2/2019 Bully Algorithm
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Social choice theory
Arrow's theorem
GibbardSatterthwaite theorem
Voting system criteria
Politics portal
vde
A voting system orelectoral system is a method by which voters make a choice between
options, often in an election or on a policy referendum.
A voting system contains rules for valid voting, and how votes are counted and aggregatedto yield a final result. Since voting involves counting, it isalgorithmic in nature, and, since
it involves polling the sentiments of a person, this represents affective data. Together, withthe exception ofproxy voting, this corresponds to in-degree centrality in graph theory and
social network analysis, with votes as directed edges, and voters and candidates as nodes. [1]
Common voting systems are majority rule,proportional representation orplurality voting
with a number of variations and methods such as first-past-the-post orpreferential voting.
The study of formally defined voting systems is called voting theory, a subfield ofpoliticalscience,economics, ormathematics.
With majority rule, those who are unfamiliar with voting theory are often surprised that
another voting system exists, or that disagreements may exist over the definition of what it
means to be supported by a majority. Depending on the meaning chosen, the common"majority rule" systems can produce results that the majority does not support. If every
election had only two choices, the winner would be determined using majority rule alone.
However, when there are three or more options, there may not be a single option that ismost liked or most disliked by a majority. A simple choice does not allow voters to express
the ordering or the intensity of their feeling. Different voting systems may give very
different results, particularly in cases where there is no clear majority preference.
http://en.wikipedia.org/wiki/Social_choice_theoryhttp://en.wikipedia.org/wiki/Arrow's_theoremhttp://en.wikipedia.org/wiki/Gibbard%E2%80%93Satterthwaite_theoremhttp://en.wikipedia.org/wiki/Voting_system#Criteria_in_evaluating_single_winner_voting_systemshttp://en.wikipedia.org/wiki/Portal:Politicshttp://en.wikipedia.org/wiki/Template:Electoral_systemshttp://en.wikipedia.org/wiki/Template_talk:Electoral_systemshttp://en.wikipedia.org/w/index.php?title=Template:Electoral_systems&action=edithttp://en.wikipedia.org/wiki/Votinghttp://en.wikipedia.org/wiki/Referendumhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Proxy_votinghttp://en.wikipedia.org/wiki/Degree_centralityhttp://en.wikipedia.org/wiki/Graph_theoryhttp://en.wikipedia.org/wiki/Social_network_analysishttp://en.wikipedia.org/wiki/Voting_system#cite_note-0%23cite_note-0http://en.wikipedia.org/wiki/Majority_rulehttp://en.wikipedia.org/wiki/Majority_rulehttp://en.wikipedia.org/wiki/Proportional_representationhttp://en.wikipedia.org/wiki/Plurality_votinghttp://en.wikipedia.org/wiki/Plurality_votinghttp://en.wikipedia.org/wiki/First-past-the-posthttp://en.wikipedia.org/wiki/Preferential_votinghttp://en.wikipedia.org/wiki/Political_sciencehttp://en.wikipedia.org/wiki/Political_sciencehttp://en.wikipedia.org/wiki/Political_sciencehttp://en.wikipedia.org/wiki/Economicshttp://en.wikipedia.org/wiki/Economicshttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Social_choice_theoryhttp://en.wikipedia.org/wiki/Arrow's_theoremhttp://en.wikipedia.org/wiki/Gibbard%E2%80%93Satterthwaite_theoremhttp://en.wikipedia.org/wiki/Voting_system#Criteria_in_evaluating_single_winner_voting_systemshttp://en.wikipedia.org/wiki/Portal:Politicshttp://en.wikipedia.org/wiki/Template:Electoral_systemshttp://en.wikipedia.org/wiki/Template_talk:Electoral_systemshttp://en.wikipedia.org/w/index.php?title=Template:Electoral_systems&action=edithttp://en.wikipedia.org/wiki/Votinghttp://en.wikipedia.org/wiki/Referendumhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Proxy_votinghttp://en.wikipedia.org/wiki/Degree_centralityhttp://en.wikipedia.org/wiki/Graph_theoryhttp://en.wikipedia.org/wiki/Social_network_analysishttp://en.wikipedia.org/wiki/Voting_system#cite_note-0%23cite_note-0http://en.wikipedia.org/wiki/Majority_rulehttp://en.wikipedia.org/wiki/Proportional_representationhttp://en.wikipedia.org/wiki/Plurality_votinghttp://en.wikipedia.org/wiki/First-past-the-posthttp://en.wikipedia.org/wiki/Preferential_votinghttp://en.wikipedia.org/wiki/Political_sciencehttp://en.wikipedia.org/wiki/Political_sciencehttp://en.wikipedia.org/wiki/Economicshttp://en.wikipedia.org/wiki/Mathematics8/2/2019 Bully Algorithm
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Contents
[hide]
1 Aspects of voting systems
o 1.1 The balloto 1.2 Candidates
o 1.3 Weight of votes
o 1.4 Status quo
o 1.5 Constituencies
2 Multiple-winner methods
o 2.1 Proportional methods
o 2.2 Semiproportional methods
o 2.3 Nonproportional and semiproportional methods
3 Single-winner methods
o 3.1 Single or sequential vote methods
o 3.2 Ranked voting methodso 3.3 Rated voting methods
o 3.4 Evaluating voting systems using criteria
3.4.1 Mathematical criteria
3.4.1.1 Compliance of selected systems (table) 3.4.2 Experimental criteria
3.4.3 "Soft" criteria
4 History
o 4.1 Early democracy
o 4.2 Foundations of voting theory
o 4.3 The single-winner revival
o 4.4 Influence of game theoryo 4.5 Post-1980 developments
5 See also
6 References
o 6.1 Notes on systems comparison table
o 6.2 General references
o 6.3 References
7 External links
[edit] Aspects of voting systems
A voting system specifies the form of the ballot, the set of allowable votes, and the tallying
method, analgorithmfor determining the outcome. This outcome may be a single winner,
or may involve multiple winners such as in the election of a legislative body. The votingsystem may also specify how voting power is distributed among the voters, and how voters
are divided into subgroups (constituencies) whose votes are counted independently.
http://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Voting_system#Aspects_of_voting_systems%23Aspects_of_voting_systemshttp://en.wikipedia.org/wiki/Voting_system#The_ballot%23The_ballothttp://en.wikipedia.org/wiki/Voting_system#Candidates%23Candidateshttp://en.wikipedia.org/wiki/Voting_system#Weight_of_votes%23Weight_of_voteshttp://en.wikipedia.org/wiki/Voting_system#Status_quo%23Status_quohttp://en.wikipedia.org/wiki/Voting_system#Constituencies%23Constituencieshttp://en.wikipedia.org/wiki/Voting_system#Multiple-winner_methods%23Multiple-winner_methodshttp://en.wikipedia.org/wiki/Voting_system#Proportional_methods%23Proportional_methodshttp://en.wikipedia.org/wiki/Voting_system#Semiproportional_methods%23Semiproportional_methodshttp://en.wikipedia.org/wiki/Voting_system#Nonproportional_and_semiproportional_methods%23Nonproportional_and_semiproportional_methodshttp://en.wikipedia.org/wiki/Voting_system#Single-winner_methods%23Single-winner_methodshttp://en.wikipedia.org/wiki/Voting_system#Single_or_sequential_vote_methods%23Single_or_sequential_vote_methodshttp://en.wikipedia.org/wiki/Voting_system#Ranked_voting_methods%23Ranked_voting_methodshttp://en.wikipedia.org/wiki/Voting_system#Rated_voting_methods%23Rated_voting_methodshttp://en.wikipedia.org/wiki/Voting_system#Evaluating_voting_systems_using_criteria%23Evaluating_voting_systems_using_criteriahttp://en.wikipedia.org/wiki/Voting_system#Mathematical_criteria%23Mathematical_criteriahttp://en.wikipedia.org/wiki/Voting_system#Compliance_of_selected_systems_.28table.29%23Compliance_of_selected_systems_.28table.29http://en.wikipedia.org/wiki/Voting_system#Experimental_criteria%23Experimental_criteriahttp://en.wikipedia.org/wiki/Voting_system#.22Soft.22_criteria%23.22Soft.22_criteriahttp://en.wikipedia.org/wiki/Voting_system#History%23Historyhttp://en.wikipedia.org/wiki/Voting_system#Early_democracy%23Early_democracyhttp://en.wikipedia.org/wiki/Voting_system#Foundations_of_voting_theory%23Foundations_of_voting_theoryhttp://en.wikipedia.org/wiki/Voting_system#The_single-winner_revival%23The_single-winner_revivalhttp://en.wikipedia.org/wiki/Voting_system#Influence_of_game_theory%23Influence_of_game_theoryhttp://en.wikipedia.org/wiki/Voting_system#Post-1980_developments%23Post-1980_developmentshttp://en.wikipedia.org/wiki/Voting_system#See_also%23See_alsohttp://en.wikipedia.org/wiki/Voting_system#References%23Referenceshttp://en.wikipedia.org/wiki/Voting_system#Notes_on_systems_comparison_table%23Notes_on_systems_comparison_tablehttp://en.wikipedia.org/wiki/Voting_system#General_references%23General_referenceshttp://en.wikipedia.org/wiki/Voting_system#References_2%23References_2http://en.wikipedia.org/wiki/Voting_system#External_links%23External_linkshttp://en.wikipedia.org/w/index.php?title=Voting_system&action=edit§ion=1http://en.wikipedia.org/wiki/Ballothttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Legislative_bodyhttp://en.wikipedia.org/wiki/Constituencyhttp://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Voting_system#Aspects_of_voting_systems%23Aspects_of_voting_systemshttp://en.wikipedia.org/wiki/Voting_system#The_ballot%23The_ballothttp://en.wikipedia.org/wiki/Voting_system#Candidates%23Candidateshttp://en.wikipedia.org/wiki/Voting_system#Weight_of_votes%23Weight_of_voteshttp://en.wikipedia.org/wiki/Voting_system#Status_quo%23Status_quohttp://en.wikipedia.org/wiki/Voting_system#Constituencies%23Constituencieshttp://en.wikipedia.org/wiki/Voting_system#Multiple-winner_methods%23Multiple-winner_methodshttp://en.wikipedia.org/wiki/Voting_system#Proportional_methods%23Proportional_methodshttp://en.wikipedia.org/wiki/Voting_system#Semiproportional_methods%23Semiproportional_methodshttp://en.wikipedia.org/wiki/Voting_system#Nonproportional_and_semiproportional_methods%23Nonproportional_and_semiproportional_methodshttp://en.wikipedia.org/wiki/Voting_system#Single-winner_methods%23Single-winner_methodshttp://en.wikipedia.org/wiki/Voting_system#Single_or_sequential_vote_methods%23Single_or_sequential_vote_methodshttp://en.wikipedia.org/wiki/Voting_system#Ranked_voting_methods%23Ranked_voting_methodshttp://en.wikipedia.org/wiki/Voting_system#Rated_voting_methods%23Rated_voting_methodshttp://en.wikipedia.org/wiki/Voting_system#Evaluating_voting_systems_using_criteria%23Evaluating_voting_systems_using_criteriahttp://en.wikipedia.org/wiki/Voting_system#Mathematical_criteria%23Mathematical_criteriahttp://en.wikipedia.org/wiki/Voting_system#Compliance_of_selected_systems_.28table.29%23Compliance_of_selected_systems_.28table.29http://en.wikipedia.org/wiki/Voting_system#Experimental_criteria%23Experimental_criteriahttp://en.wikipedia.org/wiki/Voting_system#.22Soft.22_criteria%23.22Soft.22_criteriahttp://en.wikipedia.org/wiki/Voting_system#History%23Historyhttp://en.wikipedia.org/wiki/Voting_system#Early_democracy%23Early_democracyhttp://en.wikipedia.org/wiki/Voting_system#Foundations_of_voting_theory%23Foundations_of_voting_theoryhttp://en.wikipedia.org/wiki/Voting_system#The_single-winner_revival%23The_single-winner_revivalhttp://en.wikipedia.org/wiki/Voting_system#Influence_of_game_theory%23Influence_of_game_theoryhttp://en.wikipedia.org/wiki/Voting_system#Post-1980_developments%23Post-1980_developmentshttp://en.wikipedia.org/wiki/Voting_system#See_also%23See_alsohttp://en.wikipedia.org/wiki/Voting_system#References%23Referenceshttp://en.wikipedia.org/wiki/Voting_system#Notes_on_systems_comparison_table%23Notes_on_systems_comparison_tablehttp://en.wikipedia.org/wiki/Voting_system#General_references%23General_referenceshttp://en.wikipedia.org/wiki/Voting_system#References_2%23References_2http://en.wikipedia.org/wiki/Voting_system#External_links%23External_linkshttp://en.wikipedia.org/w/index.php?title=Voting_system&action=edit§ion=1http://en.wikipedia.org/wiki/Ballothttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Legislative_bodyhttp://en.wikipedia.org/wiki/Constituency8/2/2019 Bully Algorithm
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The real-world implementation of an election is generally notconsidered part of the voting
system. For example, though a voting system specifies the ballot abstractly, it does not
specify whether the actual physical ballot takes the form of a piece of paper, a punch card,or a computer display. A voting system also does not specify whether or how votes are kept
secret, how to verify that votes are counted accurately, or who is allowed to vote. These are
aspects of the broader topic of elections and election systems.
[edit] The ballot
In a simpleplurality ballot, the voter is expected to mark only one selection.
Different voting systems have different forms for allowing the individual to express his or
her vote. In ranked ballot or "preference" voting systems, such as Instant-runoff voting, theBorda count, or aCondorcet method, voters order the list of options from most to least
preferred. In range voting, voters rate each option separately on a scale. Inplurality voting
(also known as "first-past-the-post"), voters select only one option, while in approval
voting, they can select as many as they want. In voting systems that allow "plumping", likecumulative voting, voters may vote for the same candidate multiple times.
Some voting systems include additional choices on the ballot, such aswrite-in candidates, a
none of the above option, or a no confidence in that candidate option.
[edit] Candidates
Some methods call for aprimary election first to determine which candidates will be on the
ballot.
[edit] Weight of votes
Main article: Weighted voting
http://en.wikipedia.org/wiki/Electronic_votinghttp://en.wikipedia.org/wiki/Electronic_votinghttp://en.wikipedia.org/wiki/Enfranchisementhttp://en.wikipedia.org/wiki/Enfranchisementhttp://en.wikipedia.org/wiki/Election_systemhttp://en.wikipedia.org/w/index.php?title=Voting_system&action=edit§ion=2http://en.wikipedia.org/wiki/Plurality_voting_systemhttp://en.wikipedia.org/wiki/Ranked_ballothttp://en.wikipedia.org/wiki/Instant-runoff_votinghttp://en.wikipedia.org/wiki/Borda_counthttp://en.wikipedia.org/wiki/Condorcet_methodhttp://en.wikipedia.org/wiki/Condorcet_methodhttp://en.wikipedia.org/wiki/Range_votinghttp://en.wikipedia.org/wiki/Plurality_voting_systemhttp://en.wikipedia.org/wiki/Approval_votinghttp://en.wikipedia.org/wiki/Approval_votinghttp://en.wikipedia.org/wiki/Cumulative_votinghttp://en.wikipedia.org/wiki/Cumulative_votinghttp://en.wikipedia.org/wiki/Write-in_candidatehttp://en.wikipedia.org/wiki/Write-in_candidatehttp://en.wikipedia.org/wiki/None_of_the_abovehttp://en.wikipedia.org/w/index.php?title=Voting_system&action=edit§ion=3http://en.wikipedia.org/wiki/Primary_electionhttp://en.wikipedia.org/w/index.php?title=Voting_system&action=edit§ion=4http://en.wikipedia.org/wiki/Weighted_votinghttp://en.wikipedia.org/wiki/File:Plurality_ballot.svghttp://en.wikipedia.org/wiki/File:Plurality_ballot.svghttp://en.wikipedia.org/wiki/Electronic_votinghttp://en.wikipedia.org/wiki/Enfranchisementhttp://en.wikipedia.org/wiki/Election_systemhttp://en.wikipedia.org/w/index.php?title=Voting_system&action=edit§ion=2http://en.wikipedia.org/wiki/Plurality_voting_systemhttp://en.wikipedia.org/wiki/Ranked_ballothttp://en.wikipedia.org/wiki/Instant-runoff_votinghttp://en.wikipedia.org/wiki/Borda_counthttp://en.wikipedia.org/wiki/Condorcet_methodhttp://en.wikipedia.org/wiki/Range_votinghttp://en.wikipedia.org/wiki/Plurality_voting_systemhttp://en.wikipedia.org/wiki/Approval_votinghttp://en.wikipedia.org/wiki/Approval_votinghttp://en.wikipedia.org/wiki/Cumulative_votinghttp://en.wikipedia.org/wiki/Write-in_candidatehttp://en.wikipedia.org/wiki/None_of_the_abovehttp://en.wikipedia.org/w/index.php?title=Voting_system&action=edit§ion=3http://en.wikipedia.org/wiki/Primary_electionhttp://en.wikipedia.org/w/index.php?title=Voting_system&action=edit§ion=4http://en.wikipedia.org/wiki/Weighted_voting8/2/2019 Bully Algorithm
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Many elections are held to the ideal of "one person, one vote," meaning that every voter's
votes should be counted with equal weight. This is not true of all elections, however.
Corporate elections, for instance, usually weight votes according to the amount of stockeach voter holds in the company, changing the mechanism to "one share, one vote". Votes
can also be weighted unequally for other reasons, such as increasing the voting weight of
higher-ranked members of an organization.
Voting weight is not the same thing as voting power. In situations where certain groups ofvoters will all cast the same vote (for example,political parties in a parliament), voting
power measures the ability of a group to change the outcome of a vote. Groups may form
coalitions to maximize voting power.
In some German states, most notablyPrussia and Sachsen, there was before 1918 a
weighted vote system known as the Prussian three-class franchise, where the electorate
would be divided into three categories based on the amount ofincome tax paid. Each
category would have equal voting power in choosing the electors. [2] they are known as
candidates
[edit] Status quo
Some voting systems are weighted in themselves, for example if a supermajority is
required to change the status quo. An extreme case of this is unanimous consent, wherechanging the status quo requires the support of every voting member. If the decision is
whether to accept a new member into an organization, failure of this procedure to admit the
new member is calledblackballing.
A different mechanism that favors the status quo is the requirement for aquorum, which
ensures that the status quo remains if not enough voters participate in the vote. Quorumrequirements often depend only on the total number of votes rather than the number of
actual votes cast for the winning option; however, this can sometimes encourage dissentingvoters to refrain from voting entirely to prevent a quorum.
[edit] Constituencies
Main article: Constituency
Often the purpose of an election is to choose a legislative body made of multiple winners.This can be done by running a single election and choosing the winners from the same pool
of votes, or by dividing up the voters into constituencies that have different options and
elect different winners.
Some countries, likeIsrael, fill their entire parliament using a single multiple-winnerdistrict (constituency), while others, like the Republic of Ireland orBelgium, break up their
national elections into smaller multiple-winner districts, and yet others, like the United
States or the United Kingdom, hold only single-winner elections. The AustralianbicameralParliament has single-member electorates for the legislative body (lower house) and multi-
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member electorates for itsSenate (upper house). Some systems, like theAdditional
member system, embed smaller districts (constituencies) within larger ones.
The way constituencies are created and assigned seats can dramatically affect the results.Apportionment is the process by which states, regions, or larger districts are awarded seats,
usually according to population changes as a result of a census.Redistrictingis the processby which the borders of constituencies are redrawn once apportioned. Both procedures can
become highly politically contentious due to the possibility of both malapportionment,where there are unequal representative to population ratios across districts, and
gerrymandering, where electoral districts are manipulated for political gain. An example of
this were the UKRotten and pocket boroughs, parliamentary constituencies that had a verysmall electorate - e.g. an abandoned town - and could thus be used by a patron to gain
undue and unrepresentative influence within parliament. This was a feature of the
unreformed House of Commons before the Great Reform Act of 1832.
[edit] Multiple-winner methods
Seats won by each party in the 2005 German federal election, an example of a proportional
voting system.
Most Western democracies use some form of multiple-winner voting system, with the
United States and the United Kingdom being notable exceptions.
A vote with multiple winners, such as the election of a legislature, has different practicaleffects than a single-winner vote. Often, participants in a multiple winner election are more
concerned with the overall composition of the legislature than exactly which candidates get
elected. For this reason, many multiple-winner systems aim for proportional representation,which means that if a given party (or any other political grouping) gets X% of the vote, it
should also get approximately X% of the seats in the legislature. Not all multiple-winner
voting systems are proportional.
[edit] Proportional methods
Main article: Proportional representation
Truly proportional methods make some guarantee of proportionality by making each
winning option represent approximately the same number of voters. This number is called a
quota. For example, if the quota is 1000 voters, then each elected candidate reflects the
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opinions of 1000 voters, within a margin of error. This can be measured using the
Gallagher Index.
Most proportional systems in use are based onparty-list proportional representation, inwhich voters vote for parties instead of for individual candidates.[3] For each quota of votes
a party receives, one of their candidates wins a seat on the legislature. The methods differin how the quota is determined or, equivalently, how the proportions of votes are rounded
off to match the number of seats.
The methods of seat allocation can be grouped overall into highest averages methods and
largest remainder methods. Largest remainder methods set a particular quota based on the
number of voters, while highest averages methods, such as theSainte-Lagu method andthe d'Hondt method, determine the quota indirectly by dividing the number of votes the
parties receive by a sequence of numbers.
Independently of the method used to assign seats, party-list systems can be open listor
closed list. In an open listsystem, voters decide which candidates within a party win theseats. In a closed list system, the seats are assigned to candidates in a fixed order that the
party chooses. TheMixed Member Proportional system is a mixed method that only uses a
party list for a subset of the winners, filling other seats with the winners of regional
elections, thus having features of open list and closed list systems.
In contrast to party-list systems, the Single Transferable Vote is a proportional
representation system in which voters rank individual candidates in order of preference.
Unlike party-list systems, STV does not depend on the candidates being grouped intopolitical parties. Votes are transferred between candidates in a manner similar to instant
runoff voting, but in addition to transferring votes from candidates who are eliminated,
excess votes are also transferred from candidates who already have a quota.
[edit] Semiproportional methods
An alternative method called Cumulative voting (CV) is a semiproportional voting system
in which each voter has n votes, where n is the number of seats to be elected (or, in some
potential variants, a different number, e.g. 6 votes for each voter where there are 3 seats).
Voters can distribute portions of their vote between a set of candidates, fully upon onecandidate, or a mixture. It is considered aproportionalsystem in allowing a united
coalition representing a m/(n+1) fraction of the voters to be guaranteed to elect m seats of
an n-seat election. For example in a 3-seat election, 3/4 of the voters (if united on 3
candidates) can guarantee control over all three seats. (In contrast,plurality at large, whichallows a united coalition (majority) (50%+1) to control all the seats.)
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This ballot design, used in cumulative voting, allows a voter to split his vote amongmultiple candidates.
Cumulative voting is a common way of holding elections in which the voters have unequalvoting power, such as in corporate governance under the "one share, one vote" rule.
Cumulative voting is also used as a multiple-winner method, such as in elections for a
corporate board.
Cumulative voting is not fully proportional because it suffers from the samespoiler effectof theplurality voting system without a run-off process. A group of like-minded voters
divided among "too many" candidates may fail to elect any winners, or elect fewer than
they deserve by their size. The level of proportionality depends on how well-coordinatedthe voters are.
Limited votingis a multi-winner system that gives voters fewer votes than the number of
seats to be decided. The simplest and most common form of limited voting is Single Non-
Transferable Vote(SNTV). It can be considered a special variation of cumulative votingwhere a full vote cannot be divided among more than one candidate. It depends on a
statistical distributions of voters to smooth out preferences that CV can do by individual
voters.
For example, in a 4-seat election a candidate needs 20% to guarantee election. A coalition
of 40% can guarantee 2-seats in CV by perfectly splitting their votes as individualsbetween 2 candidates. In comparison, SNTV tends towards collectively dividing 20%
between each candidate by assuming every coalition voter flipped a coin to decide whichcandidate to support with their single vote. This limitation simplifies voting and counting,
at the cost of more uncertainty of results.
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[edit] Nonproportional and semiproportional methods
Main article: Election by list
Many multiple-winner voting methods are simple extensions of single-winner methods,without an explicit goal of producing a proportional result. Bloc voting, orplurality-at-
large, has each voter vote forNoptions and selects the topNas the winners. Because of itspropensity forlandslide victorieswon by a single winning slate of candidates, bloc votingis nonproportional. Two similar plurality-based methods with multiple winners are the
Single Non-Transferable Vote or SNTV method, where the voter votes for only one option,
and cumulative voting, described above. Unlike bloc voting, elections using the Single
Nontransferable Vote or cumulative voting may achieve proportionality if voters usetactical voting orstrategic nomination.
Because they encourage proportional results without guaranteeing them, the Single
Nontransferable Vote and cumulative voting methods are classified assemiproportional.
Other methods that can be seen as semiproportional are mixed methods, which combine the
results of a plurality election and a party-list election (described below).Parallel voting isan example of a mixed method because it is only proportional for a subset of the winners.
[edit] Single-winner methods
Main article: Single-winner voting systems
Single-winner systems can be classified based on their ballot type. In one vote systems, a
voter picks one choice at a time. In ranked voting systems, each voter ranks the candidates
in order of preference. In rated voting systems, voters give a score to each candidate.
[edit] Single or sequential vote methods
An example ofrunoff voting. Runoff voting involves two rounds of voting. Only two
candidates continue to the second round.
The most prevalent single-winner voting method, by far, is plurality (also called "first-past-the-post", "relative majority", or "winner-take-all"), where each voter votes for one choice,
and the choice that receives the most votes wins, even if it receives less than a majority of
votes.
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Runoff methods hold multiple rounds of plurality voting to ensure that the winner is elected
by a majority.Top-two runoffvoting, the second most common method used in elections,
holds a runoff election between the two highest polling options if there is no absolutemajority (50% plus one). In elimination runoffelections, the weakest candidate(s) are
eliminated until there is a majority.
A primary election process is also used as a two round runoff voting system. The two
candidates or choices with the most votes in the open primary ballot progress to the generalelection. The difference between a runoff and an open primary is that a winner is never
chosen in the primary, while the first round of a runoff can result in a winner if one
candidate has over 50% of the vote.
In the Random ballot method, each voter votes for one option and a single ballot is selected
at random to determine the winner. This is mostly used as a tiebreaker for other methods.
[edit] Ranked voting methodsMain article: Preferential voting
In a typical ranked ballot, a voter is instructed to place the candidates in order of
preference.
Also known aspreferential voting methods, these methods allow each voter to rank the
candidates in order of preference. Often it is not necessary to rank all the candidates:unranked candidates are usually considered to be tied for last place. Some ranked ballot
methods also allow voters to give multiple candidates the same ranking.
The most common ranked voting method is instant-runoff voting (IRV), also known as the"alternative vote" or simply preferential voting, which uses voters' preferences to simulate
an elimination runoff election without multiple voting events. As the votes are tallied, the
option with the fewest first-choice votes is eliminated. In successive rounds of counting,
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the next preferred choice still available from each eliminated ballot is transferred to
candidates not yet eliminated. The least preferred option is eliminated in each round of
counting until there is a majority winner, with all ballots being considered in every roundof counting.
The Borda count is a simple ranked voting method in which the options receive pointsbased on their position on each ballot. A class of similar methods is calledpositional voting
systems.
Other ranked methods include Coombs' method,Supplementary voting,Bucklin voting,
and Condorcet method.
Condorcet methods, orpairwise methods, are a class of ranked voting methods that meet
the Condorcet criterion. These methods compare every option pairwise with every otheroption, one at a time, and an option that defeats every other option is the winner. An option
defeats another option if a majority of voters rank it higher on their ballot than the other
option.
These methods are often referred to collectively as Condorcet methods because theCondorcet criterion ensures that they all give the same result in most elections, where there
exists a Condorcet winner. The differences between Condorcet methods occur in situations
where no option is undefeated, implying that there exists a cycle of options that defeat oneanother, called a Condorcet paradox orSmith set. Considering a generic Condorcet method
to be an abstract method that does not resolve these cycles, specific versions of Condorcet
that select winners even when no Condorcet winner exists are called Condorcet completionmethods.
A simple version of Condorcet is Minimax: if no option is undefeated, the option that isdefeated by the fewest votes in its worst defeat wins. Another simple method is Copeland's
method, in which the winner is the option that wins the most pairwise contests, as in manyround-robin tournaments. The Schulze method (also known as "Schwartz sequential
dropping", "cloneproof Schwartz sequential dropping" or the "beatpath method") and
Ranked pairs are two recently designed Condorcet methods that satisfy a large number of
voting system criteria.
The Kemeny-Young method, theSchulze method, and the ranked pairs method are
Condorcet methods that fully rank all the candidates from most popular to least popular.
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[edit] Rated voting methods
On a rated ballot, the voter may rate each choice independently.
Rated ballots allow even more flexibility than ranked ballots, but few methods are designed
to use them. Each voter gives a score to each option; the allowable scores could be numeric
(for example, from 0 to 100) or could be "grades" like A/B/C/D/F.
An approval voting ballot does not require ranking or exclusivity.
Rated ballots can be used for ranked voting methods, as long as the ranked method allowstied rankings. Some ranked methods assume that all the rankings on a ballot are distinct,
but many voters would be likely to give multiple candidates the same rating on a rated
ballot.
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In range voting, voters give numeric ratings to each option, and the option with the highest
total or average score wins. In majority judgment, similar ballots are used, but the winner is
the candidate with the highestmedian score.
Approval voting, where voters may vote for as many candidates as they like, can be seen as
an instance of range voting (or majority judgment) where the allowable ratings are 0 and 1.It has recently been studied by, among others Brams 2003 who notes that 'The chief reason
for its nonadoption in public elections, and by some societies, seems to be a lack of key"insider" support.'
There are variants within cumulative voting. In the points form, each voter has as many
votes as there are choices, and can distribute those votes as desired: all on one choice orspread in any other pattern. Cumulative voting is used in a number of communities as well
as corporate boards. It was examined and developed perhaps most thoroughly by Lani
Guinier(1994).
[edit] Evaluating voting systems using criteria
In the real world, attitudes toward voting systems are highly influenced by the systems'
impact on groups that one supports or opposes. This can make the objective comparison of
voting systems difficult.
There are several ways to address this problem. Criteria can be defined mathematically,such that any voting system either passes or fails. This gives perfectly objective results, but
their practical relevance is still arguable. Another approach is to define ideal criteria that no
voting system passes perfectly, and then see how often or how close to passing varioussystems are over a large sample of simulated elections. This gives results which are
practically relevant, but the method of generating the sample of simulated elections can stillbe arguably biased. A final approach is to create imprecisely-defined criteria, and then
assign a neutral body to evaluate each system according to these criteria. This approach canlook at aspects of voting systems which the other two approaches miss, but both the
definitions of these criteria and the evaluations of the methods are still inevitably
subjective.
[edit] Mathematical criteria
To compare systems fairly and independently of political ideologies, voting theorists use
voting system criteria, which define potentially desirable properties of voting systems
mathematically.
It is impossible for one voting system to pass all criteria in common use. EconomistKenneth Arrow proved Arrow's impossibility theorem, which demonstrates that several
desirable features of voting systems are mutually contradictory. For this reason, someone
implementing a voting system has to decide which criteria are important for the election.
http://en.wikipedia.org/wiki/Range_votinghttp://en.wikipedia.org/wiki/Majority_judgmenthttp://en.wikipedia.org/wiki/Medianhttp://en.wikipedia.org/wiki/Medianhttp://www.nyu.edu/gsas/dept/politics/faculty/brams/theory_to_practice.pdfhttp://en.wikipedia.org/wiki/Cumulative_votinghttp://books.google.com/books?id=aRF7XdcCLq0C&q=inauthor:%22Lani+Guinier%22&dq=inauthor:%22Lani+Guinier%22&hl=en&ei=9i4FTbTjOISisAOZ_tWBDQ&sa=X&oi=book_result&ct=result&resnum=2&ved=0CC4Q6AEwAQhttp://books.google.com/books?id=aRF7XdcCLq0C&q=inauthor:%22Lani+Guinier%22&dq=inauthor:%22Lani+Guinier%22&hl=en&ei=9i4FTbTjOISisAOZ_tWBDQ&sa=X&oi=book_result&ct=result&resnum=2&ved=0CC4Q6AEwAQhttp://en.wikipedia.org/w/index.php?title=Voting_system&action=edit§ion=15http://en.wikipedia.org/w/index.php?title=Voting_system&action=edit§ion=16http://en.wikipedia.org/wiki/Kenneth_Arrowhttp://en.wikipedia.org/wiki/Arrow's_impossibility_theoremhttp://en.wikipedia.org/wiki/Arrow's_impossibility_theoremhttp://en.wikipedia.org/wiki/Range_votinghttp://en.wikipedia.org/wiki/Majority_judgmenthttp://en.wikipedia.org/wiki/Medianhttp://www.nyu.edu/gsas/dept/politics/faculty/brams/theory_to_practice.pdfhttp://en.wikipedia.org/wiki/Cumulative_votinghttp://books.google.com/books?id=aRF7XdcCLq0C&q=inauthor:%22Lani+Guinier%22&dq=inauthor:%22Lani+Guinier%22&hl=en&ei=9i4FTbTjOISisAOZ_tWBDQ&sa=X&oi=book_result&ct=result&resnum=2&ved=0CC4Q6AEwAQhttp://books.google.com/books?id=aRF7XdcCLq0C&q=inauthor:%22Lani+Guinier%22&dq=inauthor:%22Lani+Guinier%22&hl=en&ei=9i4FTbTjOISisAOZ_tWBDQ&sa=X&oi=book_result&ct=result&resnum=2&ved=0CC4Q6AEwAQhttp://en.wikipedia.org/w/index.php?title=Voting_system&action=edit§ion=15http://en.wikipedia.org/w/index.php?title=Voting_system&action=edit§ion=16http://en.wikipedia.org/wiki/Kenneth_Arrowhttp://en.wikipedia.org/wiki/Arrow's_impossibility_theorem8/2/2019 Bully Algorithm
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Using criteria to compare systems does not make the comparison completely objective. For
example, it is relatively easy to devise a criterion that is met by one's preferred voting
method, and by very few other methods. Doing this, one can then construct a biasedargument for the criterion, instead of arguing directly for the method. There is no ultimate
authority on which criteria should be considered, but the following are some criteria that
are accepted and considered to be desirable by many voting theorists:
Majority criterionIf there exists a majority that ranks (or rates) a single candidateat the top, higher than all other candidates, does that candidate always win?
Mutual majority criterion (MMC)If there exists a majority that ranks (or rates) a
group of candidates higher than all others, does one of those candidates always win?This also implies the Majority loser criterionif a majority of voters prefers every
other candidate over a given candidate, then does that candidate not win? Therefore, of
the systems listed, all pass neither or both criteria, except for Borda, which passesMajority Loser while failing Mutual Majority.
Monotonicity criterion (Monotone)Is it impossible to cause a winning candidate
to lose by ranking him higher, or to cause a losing candidate to win by ranking himlower?
Consistency criterionIf the electorate is divided in two and a choice wins in both
parts, does it always win overall?
Participation criterionIs voting honestly always better than not voting at all?(This is grouped with the distinct but similar Consistency Criterion in the table below.[4])
Condorcet criterionIf a candidate beats every other candidate in pairwisecomparison, does that candidate always win? (This implies the majority criterion,
above)
Condorcet loser criterion (Cond. loser)If a candidate loses to every other
candidate in pairwise comparison, does that candidate always lose? Independence of irrelevant alternatives (IIA)If a candidate is added or removed,
do the relative rankings of the remaining candidates stay the same?
Independence of clones criterion (Cloneproof)Is the outcome the same ifcandidates identical to existing candidates are added?
Reversal symmetryIf individual preferences of each voter are inverted, does the
original winner never win?
Polynomial time (Polytime)Can the winner be calculated in a runtime that is
polynomial in the number of candidates and the number of voters?
Summability (Summable)How much information must be transmitted from eachpolling station to a central location in order to determine the winner? This is expressed
as an order function of the number of candidates N. Slower-growing functions such as
O(N) or O(N2) make for easier counting, while faster-growing functions such as O(N!)might make it harder to catch fraud by election administrators.
Allows equal rankingsCan a voter choose whether to rank any two candidates
equally at any position on the ballot? This can reduce the prevalence of spoiled ballots
due to overvotes, and can give a less-dishonest alternative to some tactical votingstrategies.
http://en.wikipedia.org/wiki/Majority_criterionhttp://en.wikipedia.org/wiki/Mutual_majority_criterionhttp://en.wikipedia.org/wiki/Majority_loser_criterionhttp://en.wikipedia.org/wiki/Monotonicity_criterionhttp://en.wikipedia.org/wiki/Consistency_criterionhttp://en.wikipedia.org/wiki/Participation_criterionhttp://en.wikipedia.org/wiki/Voting_system#cite_note-3%23cite_note-3http://en.wikipedia.org/wiki/Condorcet_criterionhttp://en.wikipedia.org/wiki/Condorcet_loser_criterionhttp://en.wikipedia.org/wiki/Independence_of_irrelevant_alternativeshttp://en.wikipedia.org/wiki/Independence_of_clones_criterionhttp://en.wikipedia.org/wiki/Reversal_symmetryhttp://en.wikipedia.org/wiki/Polynomial_timehttp://en.wikipedia.org/wiki/Voting_machine#Vote-tabulation_Technologieshttp://en.wikipedia.org/wiki/Big_O_notationhttp://en.wikipedia.org/wiki/Overvotehttp://en.wikipedia.org/wiki/Tactical_votinghttp://en.wikipedia.org/wiki/Majority_criterionhttp://en.wikipedia.org/wiki/Mutual_majority_criterionhttp://en.wikipedia.org/wiki/Majority_loser_criterionhttp://en.wikipedia.org/wiki/Monotonicity_criterionhttp://en.wikipedia.org/wiki/Consistency_criterionhttp://en.wikipedia.org/wiki/Participation_criterionhttp://en.wikipedia.org/wiki/Voting_system#cite_note-3%23cite_note-3http://en.wikipedia.org/wiki/Condorcet_criterionhttp://en.wikipedia.org/wiki/Condorcet_loser_criterionhttp://en.wikipedia.org/wiki/Independence_of_irrelevant_alternativeshttp://en.wikipedia.org/wiki/Independence_of_clones_criterionhttp://en.wikipedia.org/wiki/Reversal_symmetryhttp://en.wikipedia.org/wiki/Polynomial_timehttp://en.wikipedia.org/wiki/Voting_machine#Vote-tabulation_Technologieshttp://en.wikipedia.org/wiki/Big_O_notationhttp://en.wikipedia.org/wiki/Overvotehttp://en.wikipedia.org/wiki/Tactical_voting8/2/2019 Bully Algorithm
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Allows later preferences (later prefs)Can a voter indicate different levels of
support through ranking or rating candidates?
Later-no-harm criterion and Later-no-help criterionCan adding a later preferenceto a ballot harm/help any candidate already listed? Note that these criteria are not
applicable to methods which do not allow later preferences; although such methods
technically pass, they can be said to fail from a voter's perspective.[5]
Note on terminology: A criterion is said to be "weaker" than another when it is passed bymore voting systems. Frequently, this means that the conditions for the criterion to apply
are stronger. For instance, the majority criterion (MC) is weaker than the multiple majority
criterion (MMC), because it requires that a single candidate, rather than a group of anysize, should win. That is, any system which passes the MMC also passes the MC, but not
vice versa; while any required winner under the MC must win under the MMC, but not
vice versa.
[edit] Compliance of selected systems (table)
The following table shows which of the above criteria are met by several single-winner
systems.
Majo
r ity/
MM
C
Mon
o -
tone
Consis
t ency/
Partic
ip -
ation
Condor
cet
Con
d.
lose
r
IIAClonepr
oof
Revers
al
symme
try
Pol
y -
tim
e
Sum
m -
able
Equal
ranki
ngs
can
exist
Lat
er
pref
s
Later
-no-
help/
Later
-no-
harm
Approva
l[nb 1]
Ambi
g uousYes
Yes[nb2] No
[nb 2] NoAmbi
guous
Ambig.-[nb 3] Yes Yes O(N) Yes No
[nb 4]
Borda
countNo Yes Yes No Yes No
No
(teamin
g)
Yes Yes O(N) No Yes No
IRV
(AV)Yes No No No Yes No Yes No Yes
O(N!
)[nb 5]No Yes Yes
Kemeny
-YoungYes Yes No Yes Yes
No(but
ISDA)
No(teamin
g)
Yes NoO(N2
)[nb 6]Yes Yes No
Majorit
y Judg -
ment[nb 7]
Yes[nb8] Yes No
[nb 9] No[nb 2]No[n
b 10] Yes Yes No[nb 11] Yes
O(N
)[nb 12] Yes Yes
Yes/
No
Minima
x
Yes/
NoYes No
Yes[nb13] No No
No
(spoilers)
No YesO(N2
)
Some
variants
YesNo[nb
13]
PluralityYes/
NoYes Yes No No No
No
(spoiler
s)
No Yes O(N) No No[nb 4]
http://en.wikipedia.org/wiki/Preferential_votinghttp://en.wikipedia.org/wiki/Later-no-harm_criterionhttp://en.wikipedia.org/wiki/Voting_system#cite_note-4%23cite_note-4http://en.wikipedia.org/w/index.php?title=Voting_system&action=edit§ion=17http://en.wikipedia.org/wiki/Majority_criterionhttp://en.wikipedia.org/wiki/Majority_criterionhttp://en.wikipedia.org/wiki/Mutual_majority_criterionhttp://en.wikipedia.org/wiki/Mutual_majority_criterionhttp://en.wikipedia.org/wiki/Monotonicity_criterionhttp://en.wikipedia.org/wiki/Monotonicity_criterionhttp://en.wikipedia.org/wiki/Monotonicity_criterionhttp://en.wikipedia.org/wiki/Consistency_criterionhttp://en.wikipedia.org/wiki/Consistency_criterionhttp://en.wikipedia.org/wiki/Participation_criterionhttp://en.wikipedia.org/wiki/Participation_criterionhttp://en.wikipedia.org/wiki/Participation_criterionhttp://en.wikipedia.org/wiki/Condorcet_criterionhttp://en.wikipedia.org/wiki/Condorcet_criterionhttp://en.wikipedia.org/wiki/Condorcet_loser_criterionhttp://en.wikipedia.org/wiki/Condorcet_loser_criterionhttp://en.wikipedia.org/wiki/Condorcet_loser_criterionhttp://en.wikipedia.org/wiki/Condorcet_loser_criterionhttp://en.wikipedia.org/wiki/Independence_of_irrelevant_alternativeshttp://en.wikipedia.org/wiki/Clone_independencehttp://en.wikipedia.org/wiki/Clone_independencehttp://en.wikipedia.org/wiki/Reversal_symmetryhttp://en.wikipedia.org/wiki/Reversal_symmetryhttp://en.wikipedia.org/wiki/Reversal_symmetryhttp://en.wikipedia.org/wiki/Reversal_symmetryhttp://en.wikipedia.org/wiki/Polynomial_timehttp://en.wikipedia.org/wiki/Polynomial_timehttp://en.wikipedia.org/wiki/Polynomial_timehttp://en.wikipedia.org/wiki/Polynomial_timehttp://en.wikipedia.org/wiki/Voting_machine#Vote-tabulation_Technologieshttp://en.wikipedia.org/wiki/Voting_machine#Vote-tabulation_Technologieshttp://en.wikipedia.org/wiki/Voting_machine#Vote-tabulation_Technologieshttp://en.wikipedia.org/wiki/Later-no-harmhttp://en.wikipedia.org/wiki/Later-no-harmhttp://en.wikipedia.org/wiki/Later-no-harmhttp://en.wikipedia.org/wiki/Approval_votinghttp://en.wikipedia.org/wiki/Approval_votinghttp://en.wikipedia.org/wiki/Approval_votinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-approvalrangecriteria-5%23cite_note-approvalrangecriteria-5http://en.wikipedia.org/wiki/Approval_votinghttp://en.wikipedia.org/wiki/Majority_criterion#Approval_votinghttp://en.wikipedia.org/wiki/Majority_criterion#Approval_votinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-approvalnash-6%23cite_note-approvalnash-6http://en.wikipedia.org/wiki/Voting_system#cite_note-approvalnash-6%23cite_note-approvalnash-6http://en.wikipedia.org/wiki/Condorcet_criterion#Approval_votinghttp://en.wikipedia.org/wiki/Condorcet_criterion#Approval_votinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-approvalnash-6%23cite_note-approvalnash-6http://en.wikipedia.org/wiki/Condorcet_criterion#Approval_votinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-ambiguous-7%23cite_note-ambiguous-7http://en.wikipedia.org/wiki/Voting_system#cite_note-approvalLNH-8%23cite_note-approvalLNH-8http://en.wikipedia.org/wiki/Borda_counthttp://en.wikipedia.org/wiki/Borda_counthttp://en.wikipedia.org/wiki/Majority_criterion#Borda_counthttp://en.wikipedia.org/wiki/Condorcet_criterion#Borda_counthttp://en.wikipedia.org/wiki/Strategic_nominationhttp://en.wikipedia.org/wiki/Strategic_nominationhttp://en.wikipedia.org/wiki/Later-no-harm_criterion#Noncomplying_methodshttp://en.wikipedia.org/wiki/Instant-runoff_votinghttp://en.wikipedia.org/wiki/Majority_criterion#Instant-runoff_votinghttp://en.wikipedia.org/wiki/Monotonicity_criterion#Instant-runoff_votinghttp://en.wikipedia.org/wiki/Condorcet_criterion#Instant-runoff_votinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-9%23cite_note-9http://en.wikipedia.org/wiki/Later-no-harm_criterion#Complying_methodshttp://en.wikipedia.org/wiki/Kemeny-Young_methodhttp://en.wikipedia.org/wiki/Kemeny-Young_methodhttp://en.wikipedia.org/wiki/Majority_criterion#Kemeny-Young_methodhttp://en.wikipedia.org/wiki/Condorcet_criterion#Kemeny-Young_methodhttp://en.wikipedia.org/wiki/Independence_of_Smith-dominated_alternativeshttp://en.wikipedia.org/wiki/Strategic_nominationhttp://en.wikipedia.org/wiki/Strategic_nominationhttp://en.wikipedia.org/wiki/Voting_system#cite_note-10%23cite_note-10http://en.wikipedia.org/wiki/Kemeny-Young_method#Failed_criteria_for_all_Condorcet_methodshttp://en.wikipedia.org/wiki/Majority_Judgmenthttp://en.wikipedia.org/wiki/Majority_Judgmenthttp://en.wikipedia.org/wiki/Majority_Judgmenthttp://en.wikipedia.org/wiki/Majority_Judgmenthttp://en.wikipedia.org/wiki/Voting_system#cite_note-mjbucklin-11%23cite_note-mjbucklin-11http://en.wikipedia.org/wiki/Voting_system#cite_note-mjbucklin-11%23cite_note-mjbucklin-11http://en.wikipedia.org/wiki/Majority_criterion#Majority_Judgmenthttp://en.wikipedia.org/wiki/Majority_criterion#Majority_Judgmenthttp://en.wikipedia.org/wiki/Voting_system#cite_note-mjmajority-12%23cite_note-mjmajority-12http://en.wikipedia.org/wiki/Voting_system#cite_note-mjmajority-12%23cite_note-mjmajority-12http://en.wikipedia.org/wiki/Voting_system#cite_note-mjmajority-12%23cite_note-mjmajority-12http://en.wikipedia.org/wiki/Voting_system#cite_note-mjconsistency-13%23cite_note-mjconsistency-13http://en.wikipedia.org/wiki/Voting_system#cite_note-approvalnash-6%23cite_note-approvalnash-6http://en.wikipedia.org/wiki/Voting_system#cite_note-mjcondloser-14%23cite_note-mjcondloser-14http://en.wikipedia.org/wiki/Voting_system#cite_note-mjcondloser-14%23cite_note-mjcondloser-14http://en.wikipedia.org/wiki/Voting_system#cite_note-mjreversal-15%23cite_note-mjreversal-15http://en.wikipedia.org/wiki/Voting_system#cite_note-16%23cite_note-16http://en.wikipedia.org/wiki/Later-no-harm_criterion#Noncomplying_methodshttp://en.wikipedia.org/wiki/Minimax_Condorcethttp://en.wikipedia.org/wiki/Minimax_Condorcethttp://en.wikipedia.org/wiki/Majority_criterion#Minimax_Condorcethttp://en.wikipedia.org/wiki/Condorcet_criterion#Minimax_Condorcethttp://en.wikipedia.org/wiki/Voting_system#cite_note-minimaxvariant-17%23cite_note-minimaxvariant-17http://en.wikipedia.org/wiki/Voting_system#cite_note-minimaxvariant-17%23cite_note-minimaxvariant-17http://en.wikipedia.org/wiki/Voting_system#cite_note-minimaxvariant-17%23cite_note-minimaxvariant-17http://en.wikipedia.org/wiki/Vote-splittinghttp://en.wikipedia.org/wiki/Vote-splittinghttp://en.wikipedia.org/wiki/Later-no-harm_criterion#Complying_methodshttp://en.wikipedia.org/wiki/Voting_system#cite_note-minimaxvariant-17%23cite_note-minimaxvariant-17http://en.wikipedia.org/wiki/Voting_system#cite_note-minimaxvariant-17%23cite_note-minimaxvariant-17http://en.wikipedia.org/wiki/Voting_system#cite_note-minimaxvariant-17%23cite_note-minimaxvariant-17http://en.wikipedia.org/wiki/Plurality_voting_systemhttp://en.wikipedia.org/wiki/Majority_criterion#Plurality_voting_systemhttp://en.wikipedia.org/wiki/Condorcet_criterion#Plurality_votinghttp://en.wikipedia.org/wiki/Vote-splittinghttp://en.wikipedia.org/wiki/Vote-splittinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-approvalLNH-8%23cite_note-approvalLNH-8http://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Voting_system#%23http://en.wikipedia.org/wiki/Preferential_votinghttp://en.wikipedia.org/wiki/Later-no-harm_criterionhttp://en.wikipedia.org/wiki/Voting_system#cite_note-4%23cite_note-4http://en.wikipedia.org/w/index.php?title=Voting_system&action=edit§ion=17http://en.wikipedia.org/wiki/Majority_criterionhttp://en.wikipedia.org/wiki/Majority_criterionhttp://en.wikipedia.org/wiki/Mutual_majority_criterionhttp://en.wikipedia.org/wiki/Mutual_majority_criterionhttp://en.wikipedia.org/wiki/Monotonicity_criterionhttp://en.wikipedia.org/wiki/Monotonicity_criterionhttp://en.wikipedia.org/wiki/Monotonicity_criterionhttp://en.wikipedia.org/wiki/Consistency_criterionhttp://en.wikipedia.org/wiki/Consistency_criterionhttp://en.wikipedia.org/wiki/Participation_criterionhttp://en.wikipedia.org/wiki/Participation_criterionhttp://en.wikipedia.org/wiki/Participation_criterionhttp://en.wikipedia.org/wiki/Condorcet_criterionhttp://en.wikipedia.org/wiki/Condorcet_criterionhttp://en.wikipedia.org/wiki/Condorcet_loser_criterionhttp://en.wikipedia.org/wiki/Condorcet_loser_criterionhttp://en.wikipedia.org/wiki/Condorcet_loser_criterionhttp://en.wikipedia.org/wiki/Independence_of_irrelevant_alternativeshttp://en.wikipedia.org/wiki/Clone_independencehttp://en.wikipedia.org/wiki/Clone_independencehttp://en.wikipedia.org/wiki/Reversal_symmetryhttp://en.wikipedia.org/wiki/Reversal_symmetryhttp://en.wikipedia.org/wiki/Reversal_symmetryhttp://en.wikipedia.org/wiki/Polynomial_timehttp://en.wikipedia.org/wiki/Polynomial_timehttp://en.wikipedia.org/wiki/Polynomial_timehttp://en.wikipedia.org/wiki/Voting_machine#Vote-tabulation_Technologieshttp://en.wikipedia.org/wiki/Voting_machine#Vote-tabulation_Technologieshttp://en.wikipedia.org/wiki/Voting_machine#Vote-tabulation_Technologieshttp://en.wikipedia.org/wiki/Later-no-harmhttp://en.wikipedia.org/wiki/Later-no-harmhttp://en.wikipedia.org/wiki/Later-no-harmhttp://en.wikipedia.org/wiki/Approval_votinghttp://en.wikipedia.org/wiki/Approval_votinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-approvalrangecriteria-5%23cite_note-approvalrangecriteria-5http://en.wikipedia.org/wiki/Majority_criterion#Approval_votinghttp://en.wikipedia.org/wiki/Majority_criterion#Approval_votinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-approvalnash-6%23cite_note-approvalnash-6http://en.wikipedia.org/wiki/Voting_system#cite_note-approvalnash-6%23cite_note-approvalnash-6http://en.wikipedia.org/wiki/Condorcet_criterion#Approval_votinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-approvalnash-6%23cite_note-approvalnash-6http://en.wikipedia.org/wiki/Voting_system#cite_note-ambiguous-7%23cite_note-ambiguous-7http://en.wikipedia.org/wiki/Voting_system#cite_note-approvalLNH-8%23cite_note-approvalLNH-8http://en.wikipedia.org/wiki/Borda_counthttp://en.wikipedia.org/wiki/Borda_counthttp://en.wikipedia.org/wiki/Majority_criterion#Borda_counthttp://en.wikipedia.org/wiki/Condorcet_criterion#Borda_counthttp://en.wikipedia.org/wiki/Strategic_nominationhttp://en.wikipedia.org/wiki/Strategic_nominationhttp://en.wikipedia.org/wiki/Later-no-harm_criterion#Noncomplying_methodshttp://en.wikipedia.org/wiki/Instant-runoff_votinghttp://en.wikipedia.org/wiki/Majority_criterion#Instant-runoff_votinghttp://en.wikipedia.org/wiki/Monotonicity_criterion#Instant-runoff_votinghttp://en.wikipedia.org/wiki/Condorcet_criterion#Instant-runoff_votinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-9%23cite_note-9http://en.wikipedia.org/wiki/Later-no-harm_criterion#Complying_methodshttp://en.wikipedia.org/wiki/Kemeny-Young_methodhttp://en.wikipedia.org/wiki/Kemeny-Young_methodhttp://en.wikipedia.org/wiki/Majority_criterion#Kemeny-Young_methodhttp://en.wikipedia.org/wiki/Condorcet_criterion#Kemeny-Young_methodhttp://en.wikipedia.org/wiki/Independence_of_Smith-dominated_alternativeshttp://en.wikipedia.org/wiki/Strategic_nominationhttp://en.wikipedia.org/wiki/Strategic_nominationhttp://en.wikipedia.org/wiki/Voting_system#cite_note-10%23cite_note-10http://en.wikipedia.org/wiki/Kemeny-Young_method#Failed_criteria_for_all_Condorcet_methodshttp://en.wikipedia.org/wiki/Majority_Judgmenthttp://en.wikipedia.org/wiki/Majority_Judgmenthttp://en.wikipedia.org/wiki/Majority_Judgmenthttp://en.wikipedia.org/wiki/Voting_system#cite_note-mjbucklin-11%23cite_note-mjbucklin-11http://en.wikipedia.org/wiki/Majority_criterion#Majority_Judgmenthttp://en.wikipedia.org/wiki/Voting_system#cite_note-mjmajority-12%23cite_note-mjmajority-12http://en.wikipedia.org/wiki/Voting_system#cite_note-mjmajority-12%23cite_note-mjmajority-12http://en.wikipedia.org/wiki/Voting_system#cite_note-mjconsistency-13%23cite_note-mjconsistency-13http://en.wikipedia.org/wiki/Voting_system#cite_note-approvalnash-6%23cite_note-approvalnash-6http://en.wikipedia.org/wiki/Voting_system#cite_note-mjcondloser-14%23cite_note-mjcondloser-14http://en.wikipedia.org/wiki/Voting_system#cite_note-mjcondloser-14%23cite_note-mjcondloser-14http://en.wikipedia.org/wiki/Voting_system#cite_note-mjreversal-15%23cite_note-mjreversal-15http://en.wikipedia.org/wiki/Voting_system#cite_note-16%23cite_note-16http://en.wikipedia.org/wiki/Later-no-harm_criterion#Noncomplying_methodshttp://en.wikipedia.org/wiki/Minimax_Condorcethttp://en.wikipedia.org/wiki/Minimax_Condorcethttp://en.wikipedia.org/wiki/Majority_criterion#Minimax_Condorcethttp://en.wikipedia.org/wiki/Condorcet_criterion#Minimax_Condorcethttp://en.wikipedia.org/wiki/Voting_system#cite_note-minimaxvariant-17%23cite_note-minimaxvariant-17http://en.wikipedia.org/wiki/Voting_system#cite_note-minimaxvariant-17%23cite_note-minimaxvariant-17http://en.wikipedia.org/wiki/Vote-splittinghttp://en.wikipedia.org/wiki/Vote-splittinghttp://en.wikipedia.org/wiki/Later-no-harm_criterion#Complying_methodshttp://en.wikipedia.org/wiki/Voting_system#cite_note-minimaxvariant-17%23cite_note-minimaxvariant-17http://en.wikipedia.org/wiki/Voting_system#cite_note-minimaxvariant-17%23cite_note-minimaxvariant-17http://en.wikipedia.org/wiki/Plurality_voting_systemhttp://en.wikipedia.org/wiki/Majority_criterion#Plurality_voting_systemhttp://en.wikipedia.org/wiki/Condorcet_criterion#Plurality_votinghttp://en.wikipedia.org/wiki/Vote-splittinghttp://en.wikipedia.org/wiki/Vote-splittinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-approvalLNH-8%23cite_note-approvalLNH-88/2/2019 Bully Algorithm
18/22
Range
voting[nb1]
No YesYes[nb
2] No[nb 2] No
Yes[nb
14]
Ambig.-[nb 3] Yes Yes O(N) Yes Yes No
Ranked
pairsYes Yes No Yes Yes
No(but
ISDA)
Yes Yes YesO(N2
)Yes Yes No
Runoff
voting
Yes/
NoNo No No Yes No
No
(spoiler
s)
No YesO(N
)[nb 15]No
No[n
b 16]
Yes[nb17]
Schulze Yes Yes No Yes YesNo(but
ISDA)
Yes Yes YesO(N2
)Yes Yes No
Random
winner/
arbitrar
y
winner[nb
18]
No NA Yes No No Yes No NA Yes O(0) No No
Random
ballot[nb19]
No Yes Yes No No Yes Yes Yes Yes O(N) No No
"Yes/No", in a column which covers two related criteria, signifies that the given system passes the first
criterion and not the second one.
[edit] Experimental criteria
It is possible to simulate large numbers of virtual elections on a computer and see how
various voting systems compare in practical terms. Since such investigations are moredifficult than simply proving that a given system does or does not satisfy a givenmathematical criterion, results are not available for all systems. Also, these results are
sensitive to the parameters of the model used to generate virtual elections, which can be
biased either deliberately or accidentally.
One desirable feature that can be explored in this way is maximum voter satisfaction,called in this context minimum Bayesian regret. Such simulations are sensitive to their
assumptions, particularly with regard to voter strategy, but by varying the assumptions they
can give repeatable measures that bracket the best and worst cases for a voting system. [6] Todate, the only such simulation to compare a wide variety of voting systems was run by a
range-voting advocate and has not been peer-reviewed.[7][8] It found that Range votingconsistently scored as either the best system or among the best across the variousconditions studied.[9]
Another aspect which can be compared through such Monte Carlo simulations is strategic
vulnerability. According to the Gibbard-Satterthwaite theorem, no voting system can be
immune tostrategic manipulation in all cases, but certainly some systems will have thisproblem more often than others. M. Badinski and R. Laraki, the inventors of the majority
http://en.wikipedia.org/wiki/Range_votinghttp://en.wikipedia.org/wiki/Range_votinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-approvalrangecriteria-5%23cite_note-approvalrangecriteria-5http://en.wikipedia.org/wiki/Voting_system#cite_note-approvalrangecriteria-5%23cite_note-approvalrangecriteria-5http://en.wikipedia.org/wiki/Voting_system#cite_note-approvalrangecriteria-5%23cite_note-approvalrangecriteria-5http://en.wikipedia.org/wiki/Majority_criterion#Range_votinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-approvalnash-6%23cite_note-approvalnash-6http://en.wikipedia.org/wiki/Voting_system#cite_note-approvalnash-6%23cite_note-approvalnash-6http://en.wikipedia.org/wiki/Condorcet_criterion#Range_votinghttp://en.wikipedia.org/wiki/Condorcet_criterion#Range_votinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-approvalnash-6%23cite_note-approvalnash-6http://en.wikipedia.org/wiki/Condorcet_criterion#Range_votinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-rangeIIA-18%23cite_note-rangeIIA-18http://en.wikipedia.org/wiki/Voting_system#cite_note-rangeIIA-18%23cite_note-rangeIIA-18http://en.wikipedia.org/wiki/Voting_system#cite_note-ambiguous-7%23cite_note-ambiguous-7http://en.wikipedia.org/wiki/Later-no-harm_criterion#Noncomplying_methodshttp://en.wikipedia.org/wiki/Ranked_pairshttp://en.wikipedia.org/wiki/Ranked_pairshttp://en.wikipedia.org/wiki/Majority_criterion#Ranked_Pairshttp://en.wikipedia.org/wiki/Condorcet_criterion#Ranked_Pairshttp://en.wikipedia.org/wiki/Independence_of_Smith-dominated_alternativeshttp://en.wikipedia.org/wiki/Later-no-harm_criterion#Noncomplying_methodshttp://en.wikipedia.org/wiki/Two-round_systemhttp://en.wikipedia.org/wiki/Two-round_systemhttp://en.wikipedia.org/wiki/Majority_criterion#Two-round_systemhttp://en.wikipedia.org/wiki/Condorcet_criterion#Two-round_systemhttp://en.wikipedia.org/wiki/Vote-splittinghttp://en.wikipedia.org/wiki/Vote-splittinghttp://en.wikipedia.org/wiki/Voting_system#cite_note-19%23cite_note-19http://en.wikipedia.org/wiki/Voting_system#cite_note-20%23cite_note-20http://en.wikipedia.org/wiki/Voting_system#cite_note-20%23cite_note-20http://en.wikipedia.org/wiki/Later-no-harm_criterion#Complying_methodshttp://en.wikipedia.org/wiki/Voting_system#cite_note-21%23cite_note-21http://en.wikipedia.org/wiki/Voting_system#cite_note-21%23cite_note-21http://en.wikipedia.org/wiki/Voting_system#cite_note-21%23cite_note-21http://en.wikipedia.org/wiki/Schulze_methodhttp://en.wikipedia.org/wiki/Majority_criterion#Schulze_methodhttp://en.wikipedia.org/wiki/Condorcet_criterion#Schulze_methodhttp://en.wikipedia.org/wiki/Independence_of_Smith-dominated_alternativeshttp://en.wikipedia.org/wiki/Later-no-harm_criterion#Noncomplying_methodshttp://en.wikipedia.org/wiki/Sortitionhttp://en.wikipedia.org/wiki/Sortitionhttp://en.wikipedia.org/wiki/Voting_system#cite_note-22%23cite_note-22http://en.wikipedia.org/wiki/Voting_system#cite_note-22%23cite_note-22http://en.wikipedia.org/wiki/Random_ballothttp://en.wikipedia.org/wiki/Random_ballothttp://en.wikipedia.org/wiki/Voting_system#cite_note-23%23cite_note-23http://en.wikipedia.org/wiki/Voting_system#cite_note-23%23cite_note-23http://en.wikipedia.org/wiki/Voting_system#cite_note-23%23cite_note-23http://en.wikipedia.org/w/index.php?title=Voting_system&action=edit§ion=18http://en.wikipedia.org/wiki/Bayesian_regrethttp://en.wikipedia.org/wiki/Voting_system#cite_note-24%23cite_note-24http://en.wikipedia.org/wiki/Voting_system#cite_note-25%23cite_note-25http://en.wikipedia.org/wiki/Voting_system#cite_note-25%23cite_note-25http://en.wikipedia.org/wiki/Voting_system#cite_note-26%23cite_note-26http://en.wikipedia.org/wiki/Voting_system#cite_note-27%23cite_note-27http://en.wikipedia.org/wiki/Monte_Carlo_methodhttp://en.wikipedia.org/wiki/Gibbard-Satterthwaite_theoremhttp://en.wikipedia.org/wiki/Tactical_votinghttp://en.wikipedia.org/wiki/Tactical_votinghttp://en.wikipedia.org/wiki/Range_votinghttp://en.wikipedia.org/wiki/Range_votinghttp://en.wikipedia.org/wiki/Voting_sys