Bucklin voting

The Bucklin - election is an election process from the family of preferred options, with which a single winner is determined.

Create voters according to their preferences, a ranking of the candidates. If a candidate has an absolute majority of Erstpräferenzen, he is elected. Otherwise, the second preferences of all voters are added to the Erstpräferenzen. Has now a candidate achieves an absolute majority, so he is the winner. Otherwise, one more rank is as long as evaluated on preferences until one candidate achieves an absolute majority.

Description of the selection method

The Bucklin - choice can be described as iterative application of the following two steps for each rank (starting with the first and then in ascending order ) the order of preference:

It should be noted that several candidates can achieve an absolute majority at the same time, since the absolute majority principle refers to the number of voters, whereas the -evaluated votes increases with each subsequent iteration. If there are several candidates with an absolute majority, the candidate has won with the higher number of votes.

Extension

When Bucklin - election is fixed, that exactly one candidate per " round " is introduced into the counting of each ballot. The voter must therefore specify on his ballot a strict total ordering of the candidates.

The Bucklin - choice can be generalized by choosing which candidates which round introduced in the count, is left to the voters, that is, the voter is allowed to assign multiple candidates the same rank and completely missing any ranks.

This generalization of Bucklin - election called Majority Judgment.

Example

Consider an election with four candidates A, B, C and D and the following preferences of the 14 voters:

With the first votes to the following result:

Since no candidate reaches an absolute majority ( 8 votes), the second preferences of voters to be added:

Still has no candidate on the votes of an absolute majority of voters (8 votes), so the third voter preferences are evaluated:

Now a candidate has an absolute majority of votes and the procedure terminates. In fact, even all four candidates have the same exceeded the absolute majority. The winner is candidate B because it has the highest vote value at this time.

Properties

In social choice theory, there are some criteria to determine the quality of the electoral system, under which the election Bucklin cuts as follows:

The Bucklin - choice satisfies the majority criterion, the mutual majority criterion and the monotonicity criterion.

The Bucklin - election violates the Condorcet criterion, the independence of clone alternatives, the later- no-harm criterion, the participation criterion, the consistency criterion that reversal symmetry criterion, the Condorcet loser criterion and the independence of irrelevant alternatives.

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