Cardinal voting systems: Difference between revisions

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'''Cardinal voting methods''', aka '''evaluative''', '''rated''', '''graded''', or '''range''' methods, are one of the major classes of voting. They are ones in which the voter can evaluate each candidate independently on the same scale to cast a Cardinal ballot. Unlike ranked systems, a voter can give two candidates the same rating or not use some ratings at all if they desire, and skipped ratings can affect the result.

Cardinal voting is when each voter can assign a numerical score to each candidate. Strictly speaking, cardinal voting can pass more information than the ordinal (rank) voting. This can clearly be seen by the fact that a rank can be derived from a set of numbers provided there are more possible numbers than candidates. Unlike ordinal voting, [[W:Arrow's Impossibility Theorem|Arrow's Impossibility Theorem]] does not apply to cardinal methods. Furthermore, all cardinal methods satisfy the participation criterion.

Cardinal voting is when each voter can assign a numerical score to each candidate. Strictly speaking, cardinal voting can pass more information than the ordinal (rank) voting. This can clearly be seen by the fact that a rank can be derived from a set of numbers provided there are more possible numbers than candidates. A distinction should be made between the "pure" cardinal methods Approval Voting and Score Voting, and "semi-cardinal" methods, such as STAR Voting and all other cardinal methods. Most of this article discusses the properties that pure cardinal methods pass. Unlike ordinal voting, [[W:Arrow's Impossibility Theorem|Arrow's Impossibility Theorem]] does not apply to pure cardinal methods. Furthermore, all pure cardinal methods satisfy the participation criterion.

In Cardinal voting, if any set of voters increase a candidate's score, it obviously can help him, but cannot hurt him. That is a restatement of monotonicity. It is a stricter requirement than Independence of Irrelevant Alternatives so it is satisfied as well. As such, a voter’s score for candidate C in no way affects the battle between A vs. B. Hence, a voter can give their honest opinion of C without fear of a wasted vote or hurting A. There is never incentive for favorite betrayal by giving a higher score to a candidate who is liked less.

In pure Cardinal voting, if any set of voters increase a candidate's score, it obviously can help him, but cannot hurt him. That is a restatement of monotonicity. It is a stricter requirement than Independence of Irrelevant Alternatives so it is satisfied as well. As such, a voter’s score for candidate C in no way affects the battle between A vs. B. Hence, a voter can give their honest opinion of C without fear of a wasted vote or hurting A. There is never incentive for favorite betrayal by giving a higher score to a candidate who is liked less.

While in all systems all votes are actually counted, there is a psychological effect to the feeling that the vote “does not count” in a wasted vote situation. ~~Cardinal~~ voting ~~maximizes~~ the number of people who vote for a candidate to become the representative. This is expected to have a knock-on effect of better acceptance of results and higher voter turnout.

While in all systems all votes are actually counted, there is a psychological effect to the feeling that the vote “does not count” in a wasted vote situation. Pure cardinal voting is likely to maximize the number of people who vote for a candidate to become the representative. This is expected to have a knock-on effect of better acceptance of results and higher voter turnout.

==Vote Aggregation and Tallying Methods==