is the majority criterion satisfied

Full Answer

What is the majority criteria?

The majority criterion was originally defined in relation to methods which rely only on voted preference orders of the candidates. Thus, its application to methods which give weight to preference strength is in some cases disputed. Some such methods, such as the Borda count and range voting, fail the criterion under any definition.

Does the plural method satisfy the majority criteria?

Remember that if no majority candidate exists, then the criterion does not apply: it is neither satisfied nor violated. This election does not tell us anything about whether or not the plurality method satisfies the majority criterion. What if a majority candidate does exist? By definition, that candidate must have over 50% of the vote.

Is the majority criterion satisfied when it comes to elections?

The majority criterion is not satisfied because the winner by majority rule is Dairy Queen. Rogers, Browning, Hamilton, and Ross ran for a seat on the Central City commission. Head-to-head, Browning won the election. Hamilton got the fewest number of 1st place votes. When Hamilton was eliminated from the race, Ross had a majority.

What happens if there is no majority of first choice votes?

If no majority candidate exists, then the majority criterion does not apply. Example5.15 shows that the Borda Count violates the majority criterion: there is an election in which a candidate (Walnut Fudge) had a majority of first choice votes, but another candidate (Scarlet & Cream) won the election.

What satisfies the majority criterion?

The criterion states that "if one candidate is ranked first by a majority (more than 50%) of voters, then that candidate must win". Some methods that comply with this criterion include any Condorcet method, Instant-runoff voting, Bucklin voting, and Plurality voting.

What is a majority vote requirement?

For example, if a group consists of 20 individuals, a majority would be 11 or more individuals, while having 10 or fewer individuals would not constitute a majority. "Majority" can be used to specify the voting requirement, as in a "majority vote", which means more than half of the votes cast.

Does anti plurality voting pass the monotonicity criterion?

APV satisfies the monotonicity criterion, the participation criterion and the consistency criterion. It does not satisfy the Condorcet loser criterion, the independence of irrelevant alternatives criterion, the independence of clones criterion or reversal symmetry.

Is a majority candidate always a Condorcet candidate?

The candidate who wins a majority of the vote in every head-to-head election against each of the other candidates – that is, a candidate preferred by more voters than any others – is the Condorcet winner, although Condorcet winners do not exist in all cases.

Why is majority vote important?

As Rae argued and Taylor proved in 1969, majority rule is the rule that maximizes the likelihood that the issues a voter votes for will pass and that the issues a voter votes against will fail.

What is meant by majority government?

A majority government is a government by one or more governing parties that hold an absolute majority of seats in a legislature. This is as opposed to a minority government, where the largest party in a legislature only has a plurality of seats.

Which voting method may violate the monotonicity criterion?

Instant-runoff voting and the two-round system are not monotonic. Using an example that applies to instant-runoff voting (IRV) and to the two-round system, it is shown that these voting systems violate the mono-raise criterion.

Does plurality satisfy IIA?

Most ranked ballot methods and Plurality voting satisfy the Majority Criterion, and therefore fail IIA automatically by the example above.

What are the 4 voting methods?

When the House is operating in the Committee of the Whole, all of these methods of voting are available except for the yeas and nays.Voice vote. A voice vote occurs when Members call out "Aye" or "No" when a question is first put by the Speaker. ... Division vote. ... Yea and Nay Vote. ... Record Vote.

How do you tell if there is a Condorcet winner?

The number of votes for runner over opponent (runner, opponent) is compared with the number of votes for opponent over runner (opponent, runner) to find the Condorcet winner. In the sum matrix above, A is the Condorcet winner because A beats every other candidate.

In what type of ballot does the voter give each candidate a score on a predetermined scale?

Types. Score voting uses a ratings ballot; that is, each voter rates each candidate with a number within a specified score, such as 0 to 9 or 1 to 5. In the simplest system, all candidates must be rated. The scores for each candidate are then summed, and the candidate with the highest sum is the winner.

How does approval voting work?

Approval voting ballots show a list of the options of candidates running. Approval voting lets each voter indicate support for one or more candidates. Final tallies show how many votes each candidate received, and the winner is the candidate with the most support.

Is a 2/3 majority a vote?

Instead of the basis of a majority, a supermajority can be specified using any fraction or percentage which is greater than one-half. It can also be called a qualified majority. Common supermajorities include three-fifths (60%), two-thirds (66.66...

Is a quorum a majority?

The Open Meeting Law defines a quorum as a simple majority of the members of a public body, unless otherwise provided in a general or special law, executive order, or other authorizing provision.

What is an absolute majority vs simple majority?

A simple majority is when a majority of those who are present agree to the idea. Some ideas need to be agreed to by an absolute majority. An absolute majority is when more than half of the total membership of the Senate or House agree to the idea.

What is difference between majority and plurality?

Pie charts illustrating the difference between a mere plurality (where the green/bottom area is less than 50% of the total area) and a majority (where the green/bottom area is greater than 50% of the total area of the pie chart).

What is the majority criterion?

The majority criterion is a single-winner voting system criterion, used to compare such systems . The criterion states that "if one candidate is ranked first by a majority (more than 50%) of voters, then that candidate must win".

What is satisfaction of the Condorcet criterion?

Satisfaction of the Condorcet criterion implies that of the majority criterion, but not vice versa. With the Condorcet criterion the individuals comprising the majorities of voters answering affirmatively may vary according to Y, but the majority criterion requires a single majority which has X as their first choice, preferred to every other candidate.

What is non preferential voting?

In the strict sense, where a majority of voters consider one candidate better than all others, approval voting empowers those voters to elect their favorite candidate, but it does not force them to.

Which is stronger, the Condorcet criterion or the Condorcet criterion?

The Condorcet criterion is stronger. According to it, a candidate X should win if for every other candidate Y there is a plurality of voters that answers affirmatively to the question 'Do you prefer X to Y?'.

What is the difficulty of approval voting?

For approval voting, the difficulty is that the criterion refers to an exclusive preference, and it is unstated whether this preference is actually indicated on the ballot or not. The common simple statement of the criterion, as given in the introduction to this article, does not resolve this, for the word "prefer" can refer to a mental state or to an action; a complete statement of the criterion would either refer to actual marks on the ballot showing the required preference, or it could refer to the mental state of the voters.

Why is a candidate rated higher than a candidate?

Because candidate A is rated higher than candidate B by a (substantial) majority of the voters, but B is declared winner, this voting system fails to satisfy the criterion due to using additional information about the voters' opinion. Conversely, if the bloc of voters who rate A highest know they are in the majority, such as from pre-election polls, they can strategically give a maximal rating to A, a minimal rating to all others, and thereby guarantee the election of their favorite candidate. In this regard, score voting gives a majority the power to elect their favorite, but just as with approval voting, it does not force them to.

Which criterion does Borda count not meet?

Systems that meet the majority criterion (plurality, Condorcet, and IRV) elect the Red candidate when they receive a majority of the vote. Borda count does not meet the majority criterion and does not select Red.

What is the majority criterion?

The majority criterion states that if a candidate has a majority of first choice votes, then that candidate should be the winner of the election. If no majority candidate exists, then the majority criterion does not apply. Example5.15 shows that the Borda Count violates the majority criterion: there is an election in which ...

What if a majority candidate does exist?

What if a majority candidate does exist? By definition, that candidate must have over 50% of the vote. Therefore, all other candidates combined must have less than 50%. No matter what, no other candidate can have as many votes as the majority candidate. Hence, any candidate with a majority must necessarily be the plurality winner, so the plurality method satisfies the majority criterion. This is the kind of explanation we use to show that a method satisfies a criterion: we've demonstrated why it must be true in any election.

What was the Borda count rejected in favor of?

The Borda Count rejected it in favor of Scarlet & Cream, which had less first choice votes but was not the last choice of anyone. Some people see this as a positive feature of the Borda Count, since it rejects polarizing candidates. Others see its violation of the majority criterion as a drawback.

How many points does a 3rd choice vote get?

First notice how the number of points assigned to each ranking has changed. The rules for the Borda count state that every last choice vote gets 1 point, and then we count going up. Hence, when there are three candidates, a 3rd choice vote gets 1 point, a 2nd choice vote gets 2 points, and a 1st choice vote gets 3 points. Comparing this to the example with four candidates, note that the number of points awarded for a first choice vote will always be the same as the number of candidates.

What is the first method of ranked voting?

Our first method of ranked voting is called the Borda Count. Its rules are fairly easy to state. The Borda Count is named for Jean-Charles de Borda, a French mathematician, scientist, and naval engineer who developed this system in 1770.

When we can show that a voting method is guaranteed to fulfill a given fairness criterion in any?

When we can show that a voting method is guaranteed to fulfill a given fairness criterion in any possible election, we say that the method satisfies the criterion.

What happens when you don't rank every candidate?

Note: When voters do not rank every candidate, we will treat them as if the candidates who they didn't rank are all in last place. Thus, for example, the 20 voters who ranked only G first will give 3 points each to G, but also give 1 point each to B and M, as if both those candidates were simultaneously ranked last.

Overview

The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is ranked first by a majority (more than 50%) of voters, then that candidate must win".
Some methods that comply with this criterion include any Condorcet method, Instant-runoff voting, Bucklin voting, and Plurality voting.

Comparison with the Condorcet criterion

Application of the majority criterion: controversy

Examples

See also