Monday, April 1, 2019

Brexit has an odd algebra

An odd kind of cycle


The UK Parliament seems a mad place.
I used to teach micro theory - or at least when Seamus was on sabbatical. He understood the math better than I did, and would likely have corrected one or two things here.
Completeness was pretty easy. Nobody actually keeps the full set of preference relations in their heads. Most of the time, preference is only discovered in choice anyway. But it's conceptually easy.
Reflexivity - that's just like dotting the i in completing the requirements. Honestly, I've never thought hard about the reflexivity inequality. That an apple is at least as preferred as an apple seemed more like dotting the i in completing the axioms - not something of any particular consequence. Varian's text had the assumption as trivial. For all x in Xx is at least as preferred as x. Yawn.
It would be madness to imagine otherwise. How could something be less preferred than itself?
For my not-all-that-mathematical brain, identity meant this had to reduce to an equality rather than an inequality: if is x, then flipping the x to the other side of the inequality meant the only way it could hold was if it were actually an equality rather than an inequality 

The author has a bit of satire going on relative to Brexit voting.  Then he introduces transitive property, the ability to go in a cycle trying to allocate preferences, especially with respect to Brexit choices:

How MPs voted
ForAgainstDefeated by
Confirmatory referendum26829527
Customs union2642728
Labour's Brexit plan23730770
Common Market 2.018828395
Revoking Article 50 to avoid no deal184293109
No-deal exit on 12 April160400240
Malthouse Plan B139422283
EFTA and EEA membership65377312
No answer, or did all the votes imply a selection of default, no exit plan? Will they cycle? Does the algebra have a fixed point?

This list is the bid and ask board.  What the UK has now and didn't have before, was this board, the pending bid and ask.  The new property is a commutator, UK voters can re-vote on any one in any order, and measure its relative change to the board.  This means the Brexit has a market balancer, and a sort of velocity equation works where any individual can keep an account called (cost or gain from possible Brexit).  The loop cost is in the ledger, the hologram effect will now work for Brexit, it is a bound uncertainty, a known unknown.

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