Some simple intuition how Non-Euclidean choice spaces work and how they affect our everyday lives, from the arenas where we have good data: politics and entertainment (music and movies).
In politics we know that most everything aligns on a single dimension, the "policy line" from left to right, progressive to conservative, with a second(ary) dimension (I call it establishment vs outsider) emerging in times of political realignment. Viz: Brexit.
The typical political economy model assumes a single dimension, left-to-right as [–1, +1], and single-peaked preferences. You have your ideological ideal point and are indifferent between equidistant shifts to the left or the right.

This model works out quite well empirically.
Some unease comes in when you observe political chatter, especially when you try to incorporate abstentions or protest votes in general elections. In particular when two candidates you perceive as clearly distinct are considered as "almost the same".
Typically observers indicate their own ideological ideal point by labeling the positions of others. All of this fits, with some squeezing, into a Euclidean line. The squeezing gets much harder to do when you also include those pairwise positions.
To express this a bit more intuitively: You're more likely to see the differences between, say AOC and Kamala Harris if you are ideologically close to them than if you are far away, in which case you probably subsume them into a "too left" bracket.
This is perspective bias, and this is an important and even "rational" process in the daily jungle of decisions we have to make, including which candidate to support. And indeed it's even hardwired into our brains.
Understanding this helps you understand certain micromotives like abstentions and protest votes and the resulting macrobehaviors like the collapse of the "Hotelling world" of moderate parties competing for the pivotal voter.

The problem is, how to map this formally.
As the saying goes, "Economics is about separating hyperplanes in the n-dimensional [Euclidean] vector world".

Which assumption do we need to relax in order to better understand a non-Euclidean choice space? Turns out, there's three.
For one, we can just ignore these distortions, stay in the Euclidean world with linear boundaries, and accept the cost of imprecision. This is very much the thrust of the neo-price theory movement.

This works if you ignore what happened in Silicon Valley over the last 25 years.
Understanding this process, from observed preferences (likes) to observed choices (purchases), and kicking the axiom of revealed preferences in the curb is big business for Silicon Valley, where imprecision kills.
Especially since the choice spaces where Silicon Valley makes money are aren't simply 1-plus dimensional. They tend to be high-dimensional even in quiet times. That's the world of recommender systems for music, movies, romance, or consumer goods.
The second approach is to relax the condition of linear boundaries (hyperplanes) and allow for Euclidean classifications with more complex boundaries. This is very roughly speaking the current thrust of modeling.
Or we can scrap the Euclidean assumption and model the subjective choice space with a Kohonen-type self-organizing map. Turns out that this is what our brain is doing already.
Where does this fit into the history of economic thought?

We can think of three revolutions: Marginalist from objective value to subjective utility, Knight/Bayesian from objective risk to subjective belief, which is still ongoing.
And the revolution from objective Euclidean to subjective perspective spaces which has its antecedents but hasn't really kicked off yet.

So any young researcher with "ML" and "behavioral" in their profile should head off in that direction, bc that's where future Nobels lie.
Or if you are an instructor who can put together a syllabus like that and bring together the people who have worked on these problems from all the different angles, you can start a new Carnegie School.
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