Cardinal voting systems: Difference between revisions
→Gradation and Range: Comment about the range and psychology.
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== Gradation and Range ==
The Range does not matter for aggregation by sum, average or median. This can be demonstrated by showing that there is always a mapping to the desired range which preserves the results. Simply put, voting in the range [0,1] or [0,100] or even [-42,7] is irrelevant. However, there could be psychological effect to the voter when voting.
However, the gradation or the number of choices within the range does matter. This is where [[Cardinal voting]] gets its name, the cardinality of a set of numbers is a measure of the number of elements of the set. For [[cardinal voting]] to contain more information than [[ordinal voting]], the number of gradations must be greater than the number of candidates. This is clear since this is the only way a clear ordering can be determined from a cardinal value. Further gradation would result in better discernment of the amount to which each candidate is preferred. However, it becomes increasingly difficult to determine by the voter how different ratings would translate into winning candidates. Score voting, Cardinal aggregated by sum, is unbiased relative to polarization if the gradation is sufficiently large.
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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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