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If you define this too strictly then it becomes tautologically true but meaningless. One could never know whether one is an "oppressed minority" unless one first painstakingly computes this sum, find it less than zero and then, having done so, can generalize it no further than saying that the sum is less than zero.
This only matters if it affects things we care about. So heuristically I mostly agree with the general mathematical framing, provided we are careful to measure the "extent to which they're against you" by actions more than words. Words probably count a little bit since they affect social outcomes and psychological well-being, but things like violence or job opportunities matter much more. Here then is I think where the apparent "paradox unravels", in that the internal sentiment of people materializes at different rates in the realm of socially expressed sentiment and actual material outcomes. In a phrase: "talk is cheap". Zooming in on Example 3, we have a world where 90% of people say they support C, they get angry when B do terrible things to C. If they witness a discriminatory event in person they probably get upset at the B who did it, yell at them a bit, and then go make a social media post about how awful B are. The apparent social sentiment is overwhelming in favor of C, and thinks B are horrible ignorant scum. But if they don't actually do anything about it, then it's all just surface level talk and C continue to get discriminated against while B are fine as long as they make do a little bit of op-sec so they don't get witnessed discriminating too publicly.
If your model defines "oppressed minority" using apparent public sentiment in the equation, it will classify C here as "not oppressed", and fail to recognize a scenario which, while not a central example, shares a lot of the bad features associated with being an oppressed minority. At the very least, some new term needs to be used to describe this and a problem needs to be solved, rather than ignored because it's "not real oppression".
If instead your model defines "oppressed minority" using actual behaviors in the equation then you have a major legibility issue in that it's really really hard to measure. You can easily have a society in which apparent public sentiment is overwhelming in favor of one side but they're still an "oppressed minority" because the behaviors skew the other way.
In either case, the map is not the territory. Whatever word you use for it, it's entirely possible to have a society in which the majority of public sentiment skews one way and the majority of actionable offensive and defensive behaviors skew the other. It's rare, because public sentiment and behaviors are correlated, and I don't think it's the world we live in (in the U.S.) but it's logically possible.
It is meaningless, as nobody was ever interested in figuring out who was oppressed in the first place - they merely wanted to legitimize giving power and advantages to specific groups that they either identified with or felt sympathy for. This sympathy depends on the perceived strength and the perceived morality of the agent in question. There's little empathy when women attack men, since men are seen as stronger. There's no empathy when somebody accused of (insert social taboo) is attacked, because they're perceived as being evil. The judgement of evil is perceived as the lack of innocence, and the lack of innocence is proportional to the perceived free will of the doer (and to the extent to which they understand what they are doing). This is why we punish accidents and mentally unwell people less harshly. It also depends on the perceiver, as it gets harder to hate people and judge them as evil as you grow wiser and realize that we're just products of our circumstances (because this understanding of ours results in attributing less free will to others).
Some day I'd like to put human nature into equations, just simple, imperfect ones.
I personally just thought of it as (actual, not apparent) hostility. Actions and words are both downstream of that.
Yes, but again, situations like this arise because it's all a sham. A thing I've noticed is that most people who complained that X group is oppressing Y group hates group X more than they like group Y. So if somebody hurts a child, it envokes aggression towards the person who hurt the child, much more than it envokes the desire to protect the child. People rarely differentiate between the two when they think about such situations.
Many people also just want a socially acceptable victim to went their negative emotions at. Others want to think of themselves as being "good people". Others still want to show other people their values, and signal virtue or in-group membership. These selfish desires pretend to be altruistic, and the vast majority of people do not have enough self-awareness to notice themselves doing this.
So by "public sentiment" is mean the true sentiment, not the apparent one (which is misleading, which is why I find joy in exposing it like this)
People do not want this problem solved in general. They want to have their cake and eat it too. They want to be pro-freedom when it's to their advantage, but also to decrease the freedom of those who have different values. The public support for "colorblindness" on the political left disappeared because it was true neutrality, and that's not what they want, for that would disallow them from fighting racism with racism. They're opposed to freedom of expression too, also because it's neutral. If 90% of people hate the KKK, they will say "The will of the people have spoken, this is democracy, the majority is right". It was probably the same when a majority oppressed homosexuals in the past, it's just viewed differently in retrospect because, and only because, the majority is against it now. The majority can only disagree with the majority across time. The public could only start to agree that discrimination against homosexuals was bad when it stopped being much of an actual problem - for the two are one and the same thing. This is also why feminism is the most popular in the countries which need it the least - the more feminist a country is, the more power woman have, and the less women will be oppressed.
I think it's only possible in the map (the political consensus based on nonsense). In the territory, all of this is nonsense (meaning that it cannot be true in reality. My map of our social reality shows that our social reality is dishonest, and the "real" version which I claim to be true has a lot of tautologies, but I believe that speaks in its favor. Tautologies eat themselves, right? Like circular logic, I think they evaluate to nothing)
We have rules like "You're not allowed to discriminate against inherent traits" and yet we don't treat health, beauty, and intelligence like they're protected traits at all (which is why attacking these traits in opposing ideologies is so common). In fact, our set of "protected traits" is politically biased, and our enforcement of our own rules is biased as well. I'm curious what would happen if we made ideologies protected as well - they're not really different from cultures and religions anyway, they're all just worldviews with a set of values embedded in them. We didn't really improve anything when we changed from religious wars to culture wars, I don't even think the irrationality decreased much. Hell, to be against biases is impossible, as it's a bias in itself. One cannot have a strong preference for the equality of preferences.
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