User:Lucasvb/Majority and consensus under ordinal and cardinal perspectives: Difference between revisions
User:Lucasvb/Majority and consensus under ordinal and cardinal perspectives (view source)
Revision as of 09:16, 20 February 2021
, 3 years ago→Cardinalism and the "majority of consensus"
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In the diagram, the candidate closest to the consensus is being "magically" picked as the "winner", coloring the interior of the circle. There is no "voting" taking place! It is a completely geometric property being depicted, representing the candidate closest to the consensus. This candidate would be the closest to represent the "majority of consensus", by definition.
At the bottom, we have a distribution of distances from voters to the candidates, one distribution per candidate. This is what voters would be intuitively measuring during an election, and attempting to convey in their ballots. The vertical line is the mean of the distributions
This is analogous to voters voting in a continuous cardinal scale, from 0 (candidate has exactly the same beliefs as the voter) to infinity (candidate is completely incomprehensible to the voter), mapping distance perfectly to this scale.
Observe that the mean distances exactly match the coloring of the majority of consensus circle: if mean distance to the yellow candidate is lower than that of the purple candidate (the "voting"), the yellow dot is geometrically closer to the consensus ("magically" selected from the geometry of the problem). Note that the ''mean'' is used, not the median as one would naively expect. The median is inadequate under this scenario. (The reasons for this are a bit technical, so we omit it here.)
Under an actual cardinal voting scheme, the mapping of distances to the ballot scale are bounded by the limited ballot, confined to discrete steps, and may not be linear.
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