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The criterion known as Proportionality for Solid Coalitions (PSC) is specifically designed for electoral systems that employ official party lists.
Answer: False
Proportionality for Solid Coalitions (PSC) is designed for electoral systems that utilize ranked voting and do not rely on official party lists, adapting the quota rule principle for such contexts.
The fundamental concept underpinning PSC involves adapting the quota rule for ranked voting systems that lack official party lists.
Answer: True
PSC's core principle is indeed an adaptation of the quota rule, specifically tailored for ranked voting systems where voters express preferences for individual candidates rather than adhering to party lists.
Michael Dummett is credited with originating the Proportionality for Solid Coalitions (PSC) criterion.
Answer: True
The criterion of Proportionality for Solid Coalitions (PSC) was first proposed by Michael Dummett, a notable philosopher recognized for his contributions to logic and the study of voting systems.
The image in the sidebar, depicting interlocking gears, symbolizes the simplicity of electoral systems.
Answer: False
The interlocking gears image metaphorically represents the complexity and interconnected nature of electoral systems, rather than their simplicity.
The primary purpose of PSC is to ensure proportionality in systems where voters rank candidates directly, focusing on voter solidarity.
Answer: True
PSC aims to ensure proportionality within ranked voting systems by focusing on the solidarity of voter preferences, particularly in the absence of formal party lists.
Proportionality in electoral systems signifies that the composition of the elected body should accurately reflect the overall distribution of votes cast.
Answer: True
Proportionality in electoral systems is the principle that the legislative body's composition should mirror the electorate's overall voting preferences, ensuring representation aligns with vote share.
The phrase "no official party lists" in the context of PSC implies that proportionality is assessed based on party registration.
Answer: False
The phrase "no official party lists" signifies that proportionality is evaluated based on voter solidarity and preferences for candidates, rather than the formal registration or structure of political parties.
What is Proportionality for Solid Coalitions (PSC)?
Answer: A criterion to assess proportionality in ranked voting systems without official party lists.
PSC is a criterion designed to evaluate proportionality in electoral systems that utilize ranked voting and do not employ official party lists, adapting the quota rule principle.
Who is recognized as the originator of the PSC criterion?
Answer: Michael Dummett
Michael Dummett, a philosopher and logician, is credited with originating the Proportionality for Solid Coalitions (PSC) criterion.
Which electoral principle does PSC adapt for systems lacking official party lists?
Answer: The quota rule
PSC adapts the quota rule, a standard principle in proportional representation, for application in ranked voting systems that do not utilize official party lists.
What does the term "proportionality" mean in electoral systems?
Answer: The elected body's composition reflecting the overall vote distribution.
Proportionality in electoral systems refers to the principle wherein the composition of the elected body accurately mirrors the distribution of votes cast by the electorate.
What is the primary goal of the PSC criterion?
Answer: To ensure proportionality for cohesive voter groups in ranked systems.
The primary objective of the PSC criterion is to guarantee a measure of proportionality for cohesive voter groups within ranked-choice electoral systems.
What does the phrase "no official party lists" signify for PSC application?
Answer: Proportionality is assessed based on voter solidarity, not party structure.
The absence of official party lists indicates that PSC focuses on assessing proportionality through the lens of voter solidarity and preferences for candidates, independent of formal party affiliations.
What is the core function of the quota rule in proportional representation?
Answer: To establish a minimum threshold of votes needed for representation.
The quota rule in proportional representation serves to establish a minimum threshold of votes required for a party or coalition to achieve representation.
What is the primary purpose of Proportionality for Solid Coalitions (PSC)?
Answer: To guarantee representation for cohesive voter groups in ranked systems.
The primary objective of the PSC criterion is to ensure proportional representation for cohesive voter groups within electoral systems that utilize ranked voting.
What is the implication of the phrase "no official party lists" for PSC?
Answer: It highlights that proportionality is based on voter preferences, not party structures.
The phrase "no official party lists" signifies that PSC assesses proportionality based on voter preferences and solidarity, rather than relying on the formal structure or registration of political parties.
A group of voters constitutes a solid coalition for a set of candidates if they rank at least one candidate from that set higher than any candidate outside the set.
Answer: False
The definition of a solid coalition requires a stricter condition: every voter within the group must rank all candidates from the specified set ahead of any candidate not belonging to that set.
In electoral systems lacking official party lists, a solid coalition functions as an equivalent to a political party for the purpose of ensuring representation.
Answer: True
In the absence of formal party lists, solid coalitions serve as functional equivalents to political parties by representing cohesive groups of voters with aligned preferences, thereby facilitating proportional representation.
A voter is considered to be solidly supporting a set of candidates if they rank at least one candidate from that set as their first preference.
Answer: False
Solid support for a set of candidates requires a voter to rank all candidates within that set higher than any candidate outside the set, not merely to rank one candidate from the set first.
Moderate voter groups may fail to form a solid coalition if some members exhibit preferences for extreme candidates over centrist candidates from opposing factions.
Answer: True
A moderate group might not form a solid coalition if its members' preferences are not consistently aligned; for example, if some prefer candidates from opposing extreme factions over centrist candidates within their own broader group.
A set of voters V is defined as a solid coalition for candidates C if every voter in V ranks at least one candidate in C first.
Answer: False
The definition of a solid coalition requires that every voter in the set ranks all candidates within the specified group ahead of all candidates outside that group, not merely ranking one candidate first.
What defines a "solid coalition" in the context of PSC?
Answer: A group of voters who rank all candidates in a specific set ahead of any candidate outside that set.
A solid coalition is defined as a group of voters where every member consistently ranks all candidates within a particular set above any candidate not included in that set.
How does PSC function in electoral systems without official party lists?
Answer: It uses solid coalitions as an equivalent to political parties for representation.
In systems lacking official party lists, PSC leverages solid coalitions as functional equivalents to parties, ensuring representation for cohesive voter blocs based on their aligned preferences.
What is the most basic demonstration of solid support for a candidate under PSC?
Answer: Ranking the candidate first
The most fundamental way a voter demonstrates solid support for a candidate within the PSC framework is by ranking that candidate as their primary preference.
Why might moderate voter groups fail to form a solid coalition?
Answer: Because moderate voters might prefer candidates from opposing extreme factions over centrist candidates.
Moderate voter groups may not form a solid coalition if their members' preferences are not consistently aligned; for instance, if some prefer candidates from opposing extreme factions over centrist candidates.
What does the definition of a solid coalition emphasize?
Answer: Consistent preference for all candidates within a set over all outside candidates.
The definition of a solid coalition hinges on the consistent preference of voters for all candidates within a designated set over any candidates outside that set.
In the context of PSC calculations, the variable 'k' typically denotes the total number of voters.
Answer: False
In PSC calculations, 'n' represents the total number of voters, while 'k' conventionally denotes the number of seats to be filled.
The Hare-PSC criterion utilizes the Droop quota, defined as n/(k+1), to establish seat guarantees for solid coalitions.
Answer: False
Hare-PSC employs the Hare quota (n/k), whereas the Droop-PSC criterion uses the Droop quota (n/(k+1)).
The Hare quota is calculated by dividing the total number of voters by the number of seats to be filled.
Answer: True
The Hare quota is indeed calculated as the total number of voters (n) divided by the number of seats to be filled (k).
Michael Dummett also proposed the specific criterion known as Hare-PSC.
Answer: True
Michael Dummett, the originator of the general PSC criterion, also formulated the specific variant known as Hare-PSC.
Droop-PSC utilizes the Hare quota (n/k) for its calculations.
Answer: False
Droop-PSC is defined using the Droop quota, calculated as n/(k+1), not the Hare quota (n/k).
The Droop quota is calculated as n/(k+1), where 'n' represents the number of voters and 'k' represents the number of seats.
Answer: True
The Droop quota is mathematically defined as the total number of voters (n) divided by the sum of the number of seats and one (k+1).
The Droop quota is generally larger than the Hare quota.
Answer: False
The Droop quota (n/(k+1)) is generally smaller than the Hare quota (n/k), meaning it typically requires fewer votes to meet the Droop quota.
What specific electoral quota is employed by the Hare-Proportionality for Solid Coalitions (Hare-PSC) criterion?
Answer: Hare quota (n/k)
The Hare-PSC criterion utilizes the Hare quota, which is calculated by dividing the total number of voters (n) by the number of seats to be filled (k).
How is the Droop-PSC criterion defined?
Answer: Using the Droop quota (n/(k+1)) and guaranteeing representation for 'j' candidates.
The Droop-PSC criterion is defined by employing the Droop quota (n/(k+1)) and providing guarantees for the election of 'j' candidates from a solid coalition that meets the quota threshold.
How does the Droop quota generally compare to the Hare quota?
Answer: The Droop quota is smaller.
The Droop quota (n/(k+1)) is typically smaller than the Hare quota (n/k), meaning it requires fewer votes to satisfy the Droop quota threshold.
Solid coalitions can be structured to span across distinct political factions if the overall preference structure remains consistent.
Answer: False
Solid coalitions cannot span across distinct political factions because the definition requires consistent preference for all candidates within the set over all candidates outside it; such consistency is unlikely across disparate factions.
Hare-PSC guarantees that if a solid coalition secures 'j' Hare quotas, at least 'j' candidates from that coalition must be elected.
Answer: True
The Hare-PSC criterion provides a guarantee that if a solid coalition achieves a threshold equivalent to 'j' Hare quotas, a minimum of 'j' candidates from that coalition will secure election.
In Hare-PSC, if a solid coalition comprises fewer than 'j' candidates, it is guaranteed that all of its candidates will be elected.
Answer: True
The Hare-PSC criterion ensures that if a solid coalition has a set of candidates smaller than the threshold 'j' (meaning they have fewer than 'j' candidates), then all candidates within that set must be elected.
In single-winner elections (k=1), Hare-PSC is equivalent to the unanimity criterion.
Answer: True
When only one seat is available (k=1), the Hare quota (n/k) becomes equal to the total number of voters (n). In this scenario, Hare-PSC aligns with the unanimity criterion, ensuring representation if all voters support a candidate.
Droop-PSC guarantees that a solid coalition commanding a majority of votes will invariably elect at least half of the available seats.
Answer: True
A key assurance provided by the Droop-PSC criterion is that any solid coalition achieving a majority of the total votes is guaranteed to secure representation for at least fifty percent of the allocated seats.
The Hare-PSC criterion guarantees representation for solid coalitions based on the Hare quota (n/k).
Answer: True
Hare-PSC ensures that solid coalitions meeting a threshold of Hare quotas (n/k) are guaranteed a minimum number of elected candidates proportional to those quotas.
What guarantee does Hare-PSC provide for a solid coalition meeting a quota threshold?
Answer: It guarantees at least 'j' candidates will be elected if 'j' Hare quotas are met.
The Hare-PSC criterion assures that if a solid coalition accumulates a number of votes equivalent to 'j' Hare quotas, then a minimum of 'j' candidates from that coalition must be elected.
In single-winner elections (k=1), what criterion does Hare-PSC become equivalent to?
Answer: The unanimity criterion
For single-winner elections (k=1), the Hare quota becomes equal to the total number of voters. Consequently, Hare-PSC aligns with the unanimity criterion in this specific context.
What is the relationship between the Hare-PSC and the unanimity criterion in single-winner elections?
Answer: They are equivalent when k=1.
In single-winner elections (k=1), the Hare quota calculation results in Hare-PSC becoming equivalent to the unanimity criterion.
Aziz and Lee defined properties such as "inclusion PSC" to address electoral systems characterized by strict, complete voter rankings.
Answer: False
Aziz and Lee's generalized PSC properties, including inclusion PSC, were developed specifically to accommodate electoral systems where voters may express weak rankings, allowing for indifference between candidates.
Brill and Peters defined Rank-PJR+ to provide proportionality guarantees exclusively for perfectly solid coalitions.
Answer: False
Brill and Peters' Rank-PJR+ property extends proportionality guarantees beyond perfectly solid coalitions to include partially solid coalitions, accommodating weak rankings.
Justified Representation is primarily associated with electoral systems employing ranked-choice ballots.
Answer: False
The concept of Justified Representation is linked to electoral systems that utilize approval ballots, where voters can approve of multiple candidates.
What does "weak ranking" signify within the framework of generalized PSC criteria?
Answer: A situation where voters express indifference between certain candidates.
Weak rankings, within the context of generalized PSC properties, permit voters to express indifference between specific candidates, deviating from the strict ordering required in complete rankings.
The inclusion PSC property, defined by Aziz and Lee, ensures proportionality for coalitions that are subsets of larger cohesive groups.
Answer: True
Inclusion PSC, a property developed by Aziz and Lee, specifically addresses proportionality for coalitions that function as subsets within larger, unified voter groups, extending the concept of solid support.
The concept of Justified Representation is linked to approval ballots.
Answer: True
Justified Representation, a concept sharing similarities with PSC, is associated with electoral systems that utilize approval ballots, where voters can indicate approval for multiple candidates.
The Rank-PJR+ property, defined by Brill and Peters, extends proportionality guarantees to which type of coalitions?
Answer: Partially solid coalitions
The Rank-PJR+ property, formulated by Brill and Peters, broadens proportionality guarantees to encompass not only perfectly solid coalitions but also those that are only partially solid, accommodating weak rankings.
What is the core function of the quota rule in proportional representation?
Answer: To establish a minimum threshold of votes needed for representation.
The quota rule in proportional representation establishes a minimum threshold, typically calculated based on votes and seats, that parties or coalitions must meet to qualify for representation.
What do generalized PSC properties, defined by Aziz and Lee, allow for in voter rankings?
Answer: The expression of indifference between certain candidates (weak rankings).
Generalized PSC properties, as defined by Aziz and Lee, accommodate weak rankings, which permit voters to express indifference between specific candidates, thereby broadening the applicability of PSC.
What does Aziz and Lee's "inclusion PSC" property specifically address?
Answer: Proportionality for coalitions that are subsets of larger groups.
The inclusion PSC property, defined by Aziz and Lee, specifically addresses the proportionality guarantees for coalitions that are subsets of larger, cohesive voter groups.
Which statement about the Rank-PJR+ property is accurate?
Answer: It guarantees proportionality for partially solid coalitions.
The Rank-PJR+ property guarantees proportionality not only for perfectly solid coalitions but also for partially solid coalitions, accommodating weak rankings.
The single transferable vote (STV) is recognized as an example of a quota-proportional method.
Answer: True
The Single Transferable Vote (STV) system is indeed classified as a quota-proportional method, employing quotas to allocate seats based on voter preferences.
The expanding approvals rule satisfies the generalized PSC properties formulated by Aziz and Lee.
Answer: True
The expanding approvals rule is recognized for its compliance with generalized PSC properties, demonstrating its capacity to handle weak rankings within electoral systems.
The single transferable vote (STV) system violates the Rank-PJR+ property.
Answer: True
The Single Transferable Vote (STV) system has been identified as violating the Rank-PJR+ fairness property defined by Brill and Peters.
The expanding approvals rule is noted for its ability to accommodate weak rankings.
Answer: True
The expanding approvals rule is recognized for its capacity to effectively incorporate and manage weak rankings within electoral preference structures.
The method of equal shares is mentioned as a system that violates the Rank-PJR+ property.
Answer: False
The provided information does not explicitly state that the method of equal shares violates the Rank-PJR+ property; rather, the Single Transferable Vote (STV) system is cited as doing so.
Which electoral system is mentioned as satisfying generalized PSC properties and accommodating weak rankings?
Answer: Expanding Approvals Rule
The expanding approvals rule is cited as an electoral method that successfully satisfies generalized PSC properties, including its capacity to manage weak rankings.
Which electoral system is noted for violating the Rank-PJR+ property as defined by Brill and Peters?
Answer: Single Transferable Vote (STV)
The Single Transferable Vote (STV) system is identified as an electoral method that fails to satisfy the Rank-PJR+ property.
Which of the following is NOT listed as an example of a quota-proportional method?
Answer: Hare-PSC
While Hare-PSC utilizes a quota, it is presented as a criterion for evaluating proportionality rather than a complete electoral method like STV or the expanding approvals rule, which are explicitly listed as quota-proportional methods.
Which electoral system is cited as satisfying Rank-PJR+?
Answer: Expanding Approvals Rule
The expanding approvals rule is cited as an electoral system that satisfies the Rank-PJR+ property.
What is the core difference between PSC's application and party-list proportional representation?
Answer: PSC focuses on individual candidate rankings and voter solidarity, not party lists.
Party-list proportional representation allocates seats based on party vote share, whereas PSC emphasizes individual candidate rankings and voter solidarity, particularly in systems without formal party lists.
Which of the following electoral systems is mentioned as an example of a quota-proportional method?
Answer: Single Transferable Vote (STV)
The Single Transferable Vote (STV) system is cited as an example of an electoral method that employs quota-proportional principles.
A significant drawback of Droop proportionality is its tendency to favor smaller parties.
Answer: False
Droop proportionality is generally associated with seat bias that favors larger parties, rather than smaller ones.
Seat bias in Droop proportionality implies that smaller parties may fail to obtain a proportional share of seats, even when they command a majority of the votes.
Answer: True
Seat bias in Droop proportionality means that the distribution of seats may not accurately reflect vote shares, potentially disadvantaging smaller parties even if they achieve a majority of votes.
Determining whether a committee satisfies the Rank-PJR+ criterion is computationally infeasible (i.e., not solvable in polynomial time).
Answer: False
It has been established that adherence to the Rank-PJR+ criterion can be determined efficiently within polynomial time, rendering it computationally feasible.
Seat bias can result in larger parties receiving fewer seats than their vote share warrants.
Answer: False
Seat bias typically favors larger parties, meaning it can lead to them receiving *more* seats than their vote share warrants, or smaller parties receiving fewer seats than their vote share suggests.
What is a major drawback associated with Droop proportionality?
Answer: It leads to significant seat bias, favoring larger parties.
A primary disadvantage of Droop proportionality is its tendency to introduce substantial seat bias, which disproportionately benefits larger political parties in the allocation of legislative seats.
What is the computational feasibility of determining adherence to the Rank-PJR+ criterion?
Answer: It can be determined efficiently in polynomial time.
The determination of whether a committee satisfies the Rank-PJR+ criterion is computationally feasible, solvable within polynomial time complexity.
What does "seat bias" in electoral systems typically imply?
Answer: Disproportionate advantage for larger parties.
Seat bias refers to the phenomenon where the distribution of seats in an electoral system does not perfectly mirror vote shares, often resulting in a disproportionate advantage for larger parties.
What potential issue arises from the Droop quota's calculation (n/(k+1)) compared to the Hare quota (n/k)?
Answer: It is generally smaller, potentially favoring larger parties due to seat bias.
The Droop quota, being smaller than the Hare quota, can contribute to seat bias, potentially offering an advantage to larger parties in the allocation of seats.