Cardinal voting systems: Difference between revisions

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'''Cardinal voting systems''', aka '''evaluative''', '''rated''', '''graded''', or '''range''' systems, are one of the major classes of voting. They are ones in which the voter can evaluate each candidate independently on the same scale. 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, Arrow's Impossibility Theorem does not apply to cardinal methods. Furthermore, all cardinal methods satisfy the participation criterion. Additionally, Cardinal methods partially dodge the Gibbard–Satterthwaite theorem making strategic voting much less of an issue than with Ordinal or Plurality voting.

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. Additionally, Cardinal methods partially dodge the [[Gibbard–Satterthwaite theorem]], making strategic voting much less of an issue than with Ordinal or Plurality voting.

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.

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It is worth noting why [[Approval Voting]] does not lead to a tyranny of a centrist majority situation. There is difference between a tendency towards a moderate or compromise candidate and a majority candidate. For example, if there is a small group in desire of representation then the candidates would gain approval if they could add the desires of this group to their platform. This means issues that are neutral to the centrist majority and highly relevant to a small group are important for candidates to understand. Additionally, if the overlap of votes is released then the candidates can study the results to determine which candidates represented an isolated group. For example, if there were a candidate who only received votes because of a particular issue, then all candidates would be wise to integrate this issue into their platform for the next election to be more competitive. However, a case can be made that candidates are incentivized to make promised to special interest groups which benefit the few a lot but do not hurt the majority enough for them to get mobilized. In many instances, like with tax code, this effect lowers the total prosperity of the society at large. This effect certainly exists in other systems and it has not been empirically shown that it is more problematic in Approval Voting.

== [[Single Member systems]] ==

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| [[Majority Approval Voting]]|| Median || [[Approval Voting | Binary]]

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== [[Multi-Member Systems]]==