# impossibility theorem

yes

at last

Many voting paradoxes (e.g. Arrow’s theorem) ultimately stem from the fact that there is no deterministic way to map `[0,1]` to `{0,1}` in any “homomorphic” manner, but this becomes possible once some randomness is permitted.
—  Terry Tao
Things a reasonable voter would want in a voting system
• If every voter prefers alternative X over alternative Y, then the group prefers X over Y.
• If every voter’s preference between X and Y remains unchanged, then the group’s preference between X and Y will also remain unchanged (even if voters’ preferences between other pairs like X and Z, Y and Z, or Z and W change).
• There is no “dictator”: no single voter possesses the power to always determine the group’s preference.

And yet! In a system where you have more than two options, and your system involves ranking your politicians in order of your preference, these can’t all be true at the same time!

Voting systems are weird.

More here: http://en.wikipedia.org/wiki/Arrow’s_impossibility_theorem

Learning a language is one of the rare fields of study that has no real finish line, and has less of a chance for rivalry and competition.

Because in science, or math, or medicine there’s always something new to discover, some new element, some new impossible theorem, some new procedure to invent…

But language is its own field where you can’t “discover” something that people are doing naturally. A linguist can notice that a certain group of people are speaking a certain way or share certain linguistic characteristics, but you can’t “discover” it in the traditional sense because they speakers have to be doing it enough for it to be noticed and noticeable.

With actual language learning, it’s never really a competition because language is constantly changing; you don’t master a language, you “practice” a language.

And because people who practice languages are on a road without a finish line, it ultimately ends up becoming like climbing a mountain: where you judge your progress by distance but it never stops being difficult… and you can’t judge yourself as better than anyone because someone’s been there first or others are arriving to the peak at the same time as you are.

If you do brag about a language, you basically end up saying, “I took more steps than you” or “I got here before you”… which doesn’t mean anything because you weren’t first in line, and the other people can catch up.

So when I say, “there are no leagues” in language, I mean it. There’s no language sport. There’s no “winning the race” or “new discoveries”. You don’t get to “carve your mark”, unless you’re in the scientific aspect of language and linguistics.

There are no teams. There are no points. All goals are your own personal ones, and all the hurdles are specific to you.

All language really ends up being is a set of different roads, or a different mountain to climb, where no one “wins” or “loses”, it’s how you play the game.

Sometimes simple and bold ideas help us see more clearly a complex reality that requires nuanced approaches.  I have an “impossibility theorem” for the global economy that is like that. It says that democracy, national sovereignty and global economic integration are mutually incompatible: we can combine any two of the three, but never have all three simultaneously and in full.

Here is what the theorem looks like in a picture:

To see why this makes sense, note that deep economic integration requires that we eliminate all transaction costs traders and financiers face in their cross-border dealings. Nation-states are a fundamental source of such transaction costs. They generate sovereign risk, create regulatory discontinuities at the border, prevent global regulation and supervision of financial intermediaries, and render a global lender of last resort a hopeless dream. The malfunctioning of the global financial system is intimately linked with these specific transaction costs.

Rodrik goes on to suggest three ways out of the bind of his trilemma:

1. Global federalism, basically a United States of the World, but where the ‘states’ are nation states, not provinces. As he puts it, we would ‘expand the scope of (democratic) politics with the scope of global market’.
2. We can keep the nation state, but subordinate it to the forces and principles of global market integration. Sort of an economic colonization of the world’s nations.
3. Behind the third door is a decrease in international economic integration, a la the Bretton Woods, post WWII détente, with capital controls and limits on trade liberalization.

I think the second option – hyper-globalization – will gain the upper hand unless we actively stop it: the world is headed at present toward a dystopic kleptocracy

While I may – in my heart – be a one worlder, I doubt that we are ready for the shift of power and rise of localized democracy necessary to make a United States of Earth work. Not for a hundred years, or more. (Besides, I bet they way that unfolds is through local democracies – urban regions in particular – slowing wresting greater control from provincial and national governments. And then, one world of city states.)

The third door may be our only hope to stop hyper-globalization, where the nations (and extra- and infra-state regions) of the world opt to become less integrated, less connected, less open. This may slow hyper-globalization and its protagonists.

Rodrik ends with this:

So I maintain that any reform of the international economic system must face up to this trilemma. If we want more globalization, we must either give up some democracy or some national sovereignty. Pretending that we can have all three simultaneously leaves us in an unstable no-man’s land.

And in my view, Brexit has to be viewed through the lens of the trilemma, where the UK opting for the pain and costs of breaking with the EU may be a preamble to others’ efforts to counter hyper-globalization.