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 21:13, 20 February 2021
, 3 years ago→Final remarks
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As before, either the mean or median is capable of predicting which candidate is closer to the overall consensus. This is a property independent of the distribution, and thus, it always approximates the "majority of consensus". However, the mean will generally be more accurate to predict proximity to the consensus.
== Conclusion ==
* There is no such thing as "''the'' majority", as it is usually promoted in democracy and ranked method advocacy. It is not a property of the voters that we are "trying to find out" through the voting process.
* The existence of multiple issues implies the existence of multiple majorities and minorities, which will generally be incompatible. What is the legitimacy of giving power/representation to any one of them?
* A voting method cannot "guarantee a majority" in any meaningful or representative way.
* Ranking encourages factionalism and creates artificial polarization where there is none. This distorts our picture of the true ideological distribution of voters and factions, and voters will respond to this by becoming even more factionalist.
* If the goal of democracy is to represent the population as a whole, with all its agreements and disagreements, ranked methods are sub-optimal. If the goal of democracy is to promote the ideals of the dominant faction, established largely arbitrarily on the spot, then ranked methods suit this goal.
* More generally, forcing voters to take sides destroys consensus and agreements. The corollary of this is that [[Instant-Runoff Voting]] is anti-consensus.
== Final remarks ==
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* The "majority of consensus" reproduces the intuitive notion of majority, and it is well-captured by the median distance. However, the median is mathematically less capable of minimizing the distance to the consensus, as defined by the mean opinion as just explained. In the animations above, if one pays attention it can be seen that the smallest median distance does not correlate precisely with the color of the circle, "magically picked" by directly picking the candidate closer to the consensus. This is because the median still biases the results in favor of the dominant faction, as can be observed by how quickly the median lines move across the distance distributions in the polarized case. The median is in a sense more "neutral" to the underlying polarization structure.
* The cardinal method closest to applying this notion of "majority of consensus" is likely [[Majority Judgement]], but as per above, it will still bias towards majority factions, so even though it approximates the consensus, it ultimately sides with the dominant faction.
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