Nominally is exactly right! The treaties have been violated many times.

You're missing the 1959-61 famine in China! Sure, famines have happened for other causes. Typically 100+ years ago before technology advanced. Now, famines largely come from poor governance.

Thanks for the background info!

Yes, I agree it is a patchwork system- and its probably quite difficulty to analyze! I'm arguing that a private ownership model with trading would lead to better outcomes, and basically end for all practical purposes water shortages.

For example, the smaller mostly Hispanic farmers you described above wouldn't lose their water rights in a rights ownership system- they could hold them, rent them out, sell them etc. But they wouldn't lose them merely for being unable to farm. Of course, water rights are a resource rent and it might be desirable to tax them as well- effectively economically partially public ownership- but this doesn't change the core argument about the efficiency of tradable rights.

I am suggesting expanding their water right- instead of only the right to do X, Y, Z with the water, take whatever right to the water they do have, in terms of amount of water, and say "you can do whatever you want with this much water". How to allocate resource rents doesn't have much effect on the market structure itself.

A lot of vitriol against supply and demand without any evidence.

Food is life. Food is culture. Just as much as water. Which countries have had famine, those that allocate via some system of food rights, or those that had a free market in food? The largest examples of famine I am aware of, in the USSR and Maoist China, were driven by some central allocation of food rather than a market. Not a good record.

One of the great features of markets is that things don't need to be decided collectively. Perhaps 90% of people want to wear blue T shirts, but I want a red one. If we collectively decide, I get a blue T shirt. In the market, I buy a red T shirt- perhaps at a very slightly higher price due to less economy of scale.

We certainly know of areas where vanilla markets can fail- externalities etc, but these do not apply to the situation here. The existing system of water rights doesn't feel like a collective decision, but rather entrenched special interests and lobbyists.

If the Native Americans have water rights, they can also sell them. They can choose to use it inefficiently on subsistence farming, or they could sell at the going rate. A normal market itself doesn't imply any particular allocation of water rights, just that they should be as fungible and transferable as possible.

Why are the laws that govern the infrastructure particularly important? It only matters now because its a tangle of regulation. Yes, big users can often get bulk discounts or other special arrangements by committing to use. This happens in many areas.

There's no law governing what products my grocery store must carry. Yet, I can still choose a store with many things I like, at affordable prices. My store may (and frequently does) exclude all products containing some chemical considered harmful even if it isn't banned. Of course, water has more of a natural monopoly problem, but that's more for last mile infrastructure and not broader supply.

I don't understand the details of the riparian vs prior appropriation doctrine. How does this create an issue? If the water rights are defined somehow, in a usage-independent way, only in terms of the net water removal, to account for runoff from local use, and the water from them can be traded, then a market can work regardless of the specific nature of the right.

Any association holding the rights could allocate its water internally as it sees fit. Just like any other asset? Or it could decide to sell it and distribute the money instead- perhaps even better for fairness to it's members!

The problem is that water isn't traded on a normal market at all. Lots of people have historical water rights and pay nearly nothing for their water use. There's byzantine regulation and many have the right to use for some purpose on their land but not to resell, so the market cannot allocate to more efficient use.

If you just let the 101 level solution actually work, water prices will rise until inefficient uses like water-intensive agriculture (not even all crops!) are pushed out. Urban users easily outbid almost all agricultural use, even at what any person would consider dirt cheap prices. For example, desalinated water, which is considered expensive for agriculture, can be 40 cents per cubic meter of water. That's a lot of water! Usually the last mile of urban water delivery costs more than that.

The amount required to satisfy all urban use, including water hungry lawns etc, and datacenters, corresponds to a very minor reduction in agriculture. Perhaps even just changing which crop is grown or switching irrigation techniques.

Charging more to higher users, price discrimination, causes several problems. First, it creates an incentive to cheat. I'm not using all this water myself, its for this whole group of people who "live" here. Don't allow this kind of spreading (somehow...)? Now you actually screw any business or institution that serves a lot of people. A farm produces food for thousands- do they count as one user? A park uses much more water than a garden but serves many more people. Whatever framework you create will require another bureaucracy to run. Lobbyists will find or insert loopholes for their friends.

The heavy users actually improve the system robustness, in both electricity and water. Their higher demand pays for more supply infrastructure, which itself often benefits from economies of scale, and in a shortage they may even be more responsive to price increases due to their high use.

Building a little reduces prices a little. Building a lot reduces prices a lot. If the prices are very high, then it's very profitable to build, so unless stopped by regulation, you will get a lot of building. Even if building merely keeps the price from going up as density increases, the value provided by living in an area goes up from agglomeration effects as it grows.

You'd set the congestion charge, by law (at least on public roads), to the minimum required for efficient road use- not the revenue maximizing price, which would likely be much higher due to monopoly.

But say this does happen a lot-this means rich people pay enormous road use fees, which can then be used for road maintenance, construction, and improvement, as well as other transit infrastructure!

So, the rich willingly subsidize infrastructure for everyone? Seems like a win-win!

Due to the effects described in the article, entering a road that's close to congested imposes negative externalities due to the delay on everyone behind you, even higher if you are pushing the road below optimal throughput. Push that externality into the price, and suddenly drivers will change their behavior in the desired fashion:

1. People will move their travel to less expensive times. Even if no other change occurs than people waiting for prices to fall, the roads operate at much higher throughput due to never getting into the region of diminishing throughput.

2. People will carpool/vanpool/mass transit- no need for any special treatment for transit, a bus with 50+ people can simply outbid most cars on the road for space, even accounting for the difference in road space taken by the bus. With the economic incentive in place, you'd even expect private buses/etc to pop up spontaneously. Right now, its rarely worth it to pool/bus- it adds extra time for you, but the benefit to the road you never see. With proper pricing, its still faster to take a car, but a lot more expensive- and the carpool/bus/etc is still probably faster than driving would be with congested roads.

3. Similarly, the high prices will incentivize alternatives such as biking, subways, etc, and give very good information on exactly what routes are in high demand when, estimates of how much an improvement would be worth, etc.

There's a formal equivalence between Markov chains and literally any system. The entire world can be viewed as a Markov chain. This doesn't tell you anything of interest, just that if you expand state without bound you eventually get the Markov property.

Why can't an LLM do backtracking? Not only within its multiple layers but across token models as reasoning models already do.

You are a probabilistic generative model (If you object, all of quantum mechanics is). I guess that means you can't do any reasoning!

Let H(z) = (z- exp(i theta)) (z - exp(i phi))

H(z) is zero only for our two points. We'll now take the norm^2, to get something that's minimized on only our two chosen points.

|H(exp(i x))|^2 = H(z) x conj(H(z)) = sum from -2 to 2 of c_j x exp(i j x)

For some c_j (just multiply it out). Note that this is just a Fourier series with highest harmonic 2 (or k in general), so in fact our c_j tell us the four coefficients to use.

For a simpler, but numerically nastier construction, instead use (t, t^2, t^3, ...), the real moment curve. Then given k points, take the degree k poly with those zeros. Square it, negate, and we get a degree 2k polynomial that's maximized only on our selected k points. The coefficients of this poly are the coefficients of our query vector, as once expanded onto the moment curve we can evaluate polynomials by dot product with the coefficients.

The complex version is exactly the same idea but with z^k and z ranging on the unit circle instead.

In fact, I think we can do it in d=2k dimensions, if we're willing to have arbitrarily precise query vectors.

Embed our points as (sin(theta), cos(theta), sin(2 x theta), cos(2 x theta)..., sin(k x theta), cos(k x theta)), with theta uniformly spaced around the circle, and we should be able to select any k of them.

Using a few more dimensions we can then ease the precision requirements on the query.

https://www.frbsf.org/wp-content/uploads/wp2017-25.pdf

Although developments of the land do improve the value, and thus land ownership has significant utility economically by incentivizing this, there isn't really an economic justification for the owner receiving value for the land itself- why should someone have exclusive rights to a piece of land they didn't create? They bought it, sure, but why did the previous owner have perpetual exclusive rights?

I'd advocate for a small property tax as a replacement for other taxes, because the component that does tax "land value" won't cause economic harm, but all of income tax causes deadweight loss. (Note, Land Value Tax is great in theory, but impossible to define practically- property tax good enough, much harder to game!)

Note that in practice, the biggest abuser of land hoarding is local governments with extremely restrictive zoning that stops productive development of the land- from an economic perspective they own the land, and have sold (or in reality, seized) some but not all of the rights from the 'landowner'. Although this can have advantages to help with coordination problems, in practice it's caused enormous economic damage to many cities by preventing development. At its heart, it's a problem with land hoarding.