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 18:57, 20 February 2021
, 3 years ago→Cardinalism and the "majority of consensus"
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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, that is, the ''mean distance'', which is also used to plot the dashed circles around the consensus for each candidate.
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. In reality things are not so simple, but the goal here is to show that in principle the information is there. Also, since cardinal voting contains total comparative information (candidates are not judged in isolation), the best and worst candidates define a "yardstick" voters use to measure distance. If voters are to be taken as equally worthy in opinion, the aggregation of cardinal ballots represents taking the ballot to represent the "mean yardstick" of voters.
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.)
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