bully algorithm

8/2/2019 Bully Algorithm

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Bully algorithm

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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:Politics


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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_representation


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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_ballot


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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/Mathematics


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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&section=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&section=1http://en.wikipedia.org/wiki/Ballothttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Legislative_bodyhttp://en.wikipedia.org/wiki/Constituency


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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&section=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&section=3http://en.wikipedia.org/wiki/Primary_electionhttp://en.wikipedia.org/w/index.php?title=Voting_system&action=edit&section=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&section=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&section=3http://en.wikipedia.org/wiki/Primary_electionhttp://en.wikipedia.org/w/index.php?title=Voting_system&action=edit&section=4http://en.wikipedia.org/wiki/Weighted_voting


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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&section=15http://en.wikipedia.org/w/index.php?title=Voting_system&action=edit&section=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&section=15http://en.wikipedia.org/w/index.php?title=Voting_system&action=edit&section=16http://en.wikipedia.org/wiki/Kenneth_Arrowhttp://en.wikipedia.org/wiki/Arrow's_impossibility_theorem


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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_voting


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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&section=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&section=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-8


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&section=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

bully algorithm

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