Title: Theory / Unimportant / Math / Election
Tags: récupéré hasSeenConjDef

Name: The electorate
Definition: A set of voters
Page: 3
Chapter: 2

Name: Simple election
Definition: A set of candidates
Page: 3
Chapter: 2
Definition2: An electorates, having one vote each
Conjdef: An election with
Definition3: A unique winner, having the more vote

Name: Majority
Definition: A simple election whose candidate with more than 50% of voices wins
Page: 3
Chapter: 2
Context: Election
Name2: Absolute majority

Smaller0: 2
Greater0: is either a tie, or have a winner
Page: 3
Prefix Greater: a majority election
Prefix Smaller: the number of candidate is
Context: Election

Name: Majoritarian
Definition: with more than 2 candidates
Page: 3
Chapter: 2
Context: Election
Definition2: and a rule to choose the winner if no one have 50% of the voices
Conjdef: A simple election
Name2: Plurality system

Name: Plurality
Definition: where the candidate which the maximum of voices win
Page: 4
Chapter: 2
Context: Election
Conjdef: Plurality system
Name2: First-past-the-post

Name: Sequential voting
Definition: An election technique with multiple election. The result of an election modify the set of candidate of the next election
Page: 4
Chapter: 2
Section: 3
Context: Election

Name: Primary
Definition: The first election of a sequential voting
Page: 4
Chapter: 2
Section: 3
Context: Election

Name: Runoff method
Definition: primary: a simple majority vote, selecting two candidates
Page: 5
Chapter: 2
Section: 3
Context: Election
Definition2: an absolute majority vote
Conjdef: A sequential election with
Name2: Plurality runoff method

Name: A complete preference list
Definition: A total order of preference between the candidates that remains fixed throughout the voting process
Page: 5
Chapter: 2
Section: 3
Variables: \(A_1,\dots,A_n\) a list of candidates
\(E\) an elector
Context: Election
Name2: A ballot

Name: A preference list
Definition: An order of preference between the candidates that remains fixed throughout the voting process
Page: 5
Chapter: 2
Section: 3
Variables: \(A_1,\dots,A_n\) a list of candidates
\(E\) an elector
Context: Election
Name2: A ballot

Name: A preference profile
Definition: The set of all the voters preference lists
Page: 5
Chapter: 2
Section: 3
Variables: \(A_1,\dots,A_n\) a list of candidates
Context: Election

Name: A preferential voting
Definition: A method which require a voter to present a preference list
Page: 7
Chapter: 2
Section: 4
Context: Election
Definition2: Another name for Hare method
Conjdef: Either

Name: Ware/Hare method
Definition: preferential voting, sequential vote, at each turn, the candidate with the fewest first place is eliminated
Page: 7, 10
Chapter: 2
Section: 4
Context: Election
Definition2: sequential vote
Name2: Alternative vote
Example2: Instant runoff voting
Extra: Preferential voting is both the name of this method, and of the class of method
Applied to3: System which allow multiple similar candidates without penalizing them

Name: Generalized Hare system
Definition: A version of Hare system where some candidates can be removed from the list
Page: 9
Chapter: 2
Section: 4
Context: Election
Name2: Instant runoff systems

Name: A quota
Definition: A number, fixed before the election. If no candidate obtains this number of votes, the election is void.
Page: 9
Chapter: 2
Section: 4
Context: Election

Name: Coombs method
Definition: preferential voting, sequential vote, at each turn, the candidate with the most of last place is eliminated
Page: 11
Chapter: 2
Section: 5
Context: Election

Name: Point score method
Definition: A method allowing some score to each candidate.
Page: 12
Chapter: 2
Section: 6
Context: Election

Name: Borda count
Definition: A pointscore method in which the \(i\)-th candidate have \(n-i\) point
Page: 12
Chapter: 2
Section: 6
Variables: \(C_1,\dots,C_n\) candidates
Context: Election
Example: Olympic game, restricted to the three medals

Name: A Condorcet winner
Definition: A candidate which win against all other candidates
Page: 19
Chapter: 3
Section: 1
Variables: \(X\) a set of candidates

Name: A Condorcet extended method
Definition: Each elector put an order over each candidate
Page: 20
Chapter: 3
Section: 2
Variables: \(X\) a set of candidates
Definition2: start with an empty order relation. For each \(A\) which wins over \(B\) by \(n\) votes, with \(n\) decreasing, add \(A\ge B\) in the order relation if \(A\le B\) is not already in it. choose the greatest element of the relation.
Conjdef: in this order

Name: Sequential voting
Definition: a vote is taken, as a consequence a new set of candidates is selected; then a new vote is taken
Page: 4
Chapter: 2
Section: 3
Variables: \(X\) a set of candidates
Intuition: reduce the set of candidates to a manageable size often to size two

Name: Primary election
Definition: First election of a sequential voting
Page: 4
Chapter: 2
Section: 3

Name: Runoff election
Definition: Second election of sequential voting
Page: 4
Chapter: 2
Section: 3

Name: (Plurality) Runoff method
Definition: two top candidates are decided by plurality vote; all other candidates are eliminated; then a majority vote is taken
Page: 4
Chapter: 2
Section: 3

Name: The preference profile
Definition: The set of all voter preference list
Page: 4
Chapter: 2
Section: 3
Variables: \(E\) an election

Name: A ballot
Definition: A preference list which is a linear order
Page: 7
Chapter: 2
Section: 4
Variables: \(C\) a set of candidate
\(v\) a voter
Name2: A complete preference list

Name: \(v\)'s preference list
Definition: A order relation over the candidate
Page: 4
Chapter: 2
Section: 3
Variables: \(C\) a set of candidate
\(v\) a voter

Name: Preferential voting
Definition: Election requiring each voter to have a preference list
Page: 7
Chapter: 2
Section: 4
Variables: \(C\) a set of candidate
\(v\) a voter

Name: Hare method
Definition: A ballot from each elector
Page: 7
Chapter: 2
Section: 4
Variables: \(C\) a set of candidate
Definition2: Candidate with fewest first place vote is eliminated, and so on until there is a single candidate
Conjdef: A vote, wich
Name2: Alternative vote
Name3: instant runoff voting
Name4: preferential voting (ambiguous)

Name: Instant runoff system
Definition: A generalized Hare system.
Page: 9
Chapter: 2
Section: 4
Variables: \(C\) a set of candidate
Example: You can omit certain candidate from your ballot

Name: Quota
Definition: A number, such that to win the election, a candidate must have at least as much vote
Page: 9
Chapter: 2
Section: 4
Variables: \(C\) a set of candidate

Name: Coombs method
Definition: Each elector give a ballot
Page: 11
Chapter: 2
Section: 5
Variables: \(C\) a set of candidate
Definition2: The candidate with greatest number of last place vote is eliminated, and so on until there is a single candidate
Conjdef: the election where

Name: Point methods
Definition: Each elector order the candidates.
Each candidate get \(p_i\) points for each ballot where they is in \(i\)-th position
Points are added for a candidate. The one with most point win
Page: 12
Chapter: 2
Section: 6
Context: Election