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 08:59, 20 February 2021
, 3 years agotypos
m (typos) |
|||
Line 4:
== Deconstructing the majority ==
Majority rule is usually presented as a statement similar
While it feels intuitive that the "largest side should win", one aspect that is rarely addressed is ''what is a "side"''? Additionally, siding with '''what'''? How many "sides" are there? Does the 50% threshold
It should be clear that a majority, if to be sought and if to be considered legitimate at all, should ideally be an inherent property of the voters, based on some underlying degree of cohesion. After all, if it is ''not'' an inherent property of the voters (to sufficient degree), then in what sense is ''majority rule'' representative of the will of the voters?
Line 20:
So how is forcing voters to pick '''one''' side representative of their true beliefs and allegiances?
==
People can agree or
Considering the reality that there are hundreds if not thousands of potential
The most straightforward way to deal with this is to not
Let's imagine we pick one of these issues, and we do an opinion poll on it with all the voters, where they each evaluate their opinions on a scale of [completely disagree], to [neutral], to [completely agree]. In principle, this could be done for any issue we care about.
Line 34:
Note that this is distinct from the notion of a "center" or "moderate", which are perceived as relative.
If the issue we picked was something like "dogs should be outlawed as pets", we would find that the consensus is around [completely disagree]. This is an extremist and resolute position for most people, not a centrist or moderate opinion, and it is the overwhelming
The notion of a "center" or a "moderate" are rarely useful when one considers the mutual existence of other issues, especially
'''Polarization''' is when the distribution of opinions is concentrated in two separated groups. This could be between the [neutral] opinion and one of the extremes, or it could be between opposite extremes. Between polarization and consensus there is a continuum of possible distributions.
Line 50:
One form of expressing such opinions is through '''ranked ballots''', which express ''preference''. Ranked preferences are inherently comparative, so a ranking is always between two options, such as "I prefer A to B" (or simply A>B). If more options exist, the ranking has to, somehow, work for all of them simultaneously. But fundamentally, a preference refers to a choice between exactly two alternatives.
The alternative are ''rated ballots'', which express ''evaluations''. The context of voting inherently makes the evaluations comparative, so rated ballots may still carry the same preference information as ranked ballots. But rated ballots do something more: they '''evaluate''' all options under the same comparative scale. The information is not strictly pairwise, but instead considers the relative assessment with respect to all other options,
These are two competing traditions to deal with democracy: ordinalism (rankings) and cardinalism (with evaluations).
== Ordinalism and the "majority of preference" ==
Line 70:
In this 2D opinion space, in which there is a true consensus over both issues, taking into account only ranked preferences between two candidates (darker moving circles) leads to distortions, due to the creation of "artificial factions" between the two. (If there were no candidates, there would be only one big consensus faction in which everyone belongs.)
Note that while there is plenty of consensus, the ranked preferences "slices" the population in various ways (here, we assume a voter sides with whatever candidate is ideologically closer). Thus, rankings are inherently factionalist, and any "majority" created (shaded background)
Thus, under ordinalism or ranked preferences, "majoritary" is a property of the '''candidates''' more than that of the
Notice how fringe candidates (when the dots move towards the edge) can easily radicalize their minority faction, creating a highly distorted faction consensus near the fringe.
Line 80:
In real life, complete allegiance to a faction, and support for political candidates, usually creates an echo chamber effect. These people will be more likely to side and engage with other "like-minded people", according to this faction that was established.
But as we can see from the above diagram, even if the population as a whole shares a lot of
What if we had a mixture of polarization and consensus?
Line 110:
Can we recover the spirit of this "majority of consensus"? It turns out yes, we can.
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
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 (not the median, as one would expect), that is, the mean distance.
| |||