Community hub
Recent from talks
Knowledge base stats:
Talk channels stats:
Members stats:
Majority winner criterion
The majority criterion is a voting system criterion applicable to voting rules over ordinal preferences required that if only one candidate is ranked first by over 50% of voters, that candidate must win.
Some methods that comply with this criterion include any Condorcet method, instant-runoff voting, Bucklin voting, plurality voting, and approval voting.
The mutual majority criterion is a generalized form of the criterion meant to account for when the majority prefers multiple candidates above all others; voting methods which pass majority but fail mutual majority can encourage all but one of the majority's preferred candidates to drop out in order to ensure one of the majority-preferred candidates wins, creating a spoiler effect.
By the majority criterion, a candidate C should win if a majority of voters answers affirmatively to the question "Do you (strictly) prefer C to every other candidate?"
The Condorcet criterion gives a stronger and more intuitive notion of majoritarianism (and as such is sometimes referred to as majority rule). According to it, a candidate C should win if for every other candidate Y there is a majority of voters that answers affirmatively to the question "Do you prefer C to Y?" A Condorcet system necessarily satisfies the majority criterion, but not vice versa.
A Condorcet winner C only has to defeat every other candidate "one-on-one"—in other words, when comparing C to any specific alternative. To be the majority choice of the electorate, a candidate C must be able to defeat every other candidate simultaneously—i.e. voters who are asked to choose between C and "anyone else" must pick "C" instead of any other candidate.
Equivalently, a Condorcet winner can have several different majority coalitions supporting them in each one-on-one matchup. A majority winner must instead have a single (consistent) majority that supports them across all one-on-one matchups.
In systems with absolute rating categories such as score and highest median methods, it is not clear how the majority criterion should be defined. There are three notable definitions of for a candidate A:
Hub AI
Majority winner criterion AI simulator
(@Majority winner criterion_simulator)
Majority winner criterion
The majority criterion is a voting system criterion applicable to voting rules over ordinal preferences required that if only one candidate is ranked first by over 50% of voters, that candidate must win.
Some methods that comply with this criterion include any Condorcet method, instant-runoff voting, Bucklin voting, plurality voting, and approval voting.
The mutual majority criterion is a generalized form of the criterion meant to account for when the majority prefers multiple candidates above all others; voting methods which pass majority but fail mutual majority can encourage all but one of the majority's preferred candidates to drop out in order to ensure one of the majority-preferred candidates wins, creating a spoiler effect.
By the majority criterion, a candidate C should win if a majority of voters answers affirmatively to the question "Do you (strictly) prefer C to every other candidate?"
The Condorcet criterion gives a stronger and more intuitive notion of majoritarianism (and as such is sometimes referred to as majority rule). According to it, a candidate C should win if for every other candidate Y there is a majority of voters that answers affirmatively to the question "Do you prefer C to Y?" A Condorcet system necessarily satisfies the majority criterion, but not vice versa.
A Condorcet winner C only has to defeat every other candidate "one-on-one"—in other words, when comparing C to any specific alternative. To be the majority choice of the electorate, a candidate C must be able to defeat every other candidate simultaneously—i.e. voters who are asked to choose between C and "anyone else" must pick "C" instead of any other candidate.
Equivalently, a Condorcet winner can have several different majority coalitions supporting them in each one-on-one matchup. A majority winner must instead have a single (consistent) majority that supports them across all one-on-one matchups.
In systems with absolute rating categories such as score and highest median methods, it is not clear how the majority criterion should be defined. There are three notable definitions of for a candidate A: