Sunday, February 16, 2014

Deeper Understanding of Arrow's Impossibility

Collective preferences do exist, the problem is there's no way to honestly communicate them, because real voting must be zero sum but real preferences are not.

Also consciousness per se.

Riffing off this, via 1, via 2 Isegoria somewhere, revisited due to Nick Land. I referred to Wikipedia for logical diffraction, but I don't recommend doing so yourself in this case.

First, to make sure we're on the same page and so I can audit my thought processes...
"Andy likes sprinkles on his ice cream.  Andy walks into the ice-cream shop and seeing that they have chocolate, strawberry and vanilla chooses chocolate.  Before the vendor has a chance to scoop the ice cream she says "Today, chocolate comes with free sprinkles."  "In that case," Andy says, "I'll have vanilla.""
This happens in runoff voting systems. Proof by example:
First round, six for vanilla, seven for strawberry, seven for chocolate. Vanilla is eliminated, and four voters change to chocolate, for the win.
But, sprinkles.
First round, two strawberry voters are converted, so it's six, five, nine. Now strawberry is eliminated, and  everyone left changes to vanilla, which wins.

As per Arrow's theorem, eliminating this problem only introduces others. I ask myself, what's the nearest runoff like model that obeys positive association or monotonicity?

I think it's quicker to skip to idealism and work backward. If we could measure preferences directly like a voltmeter, it would work. However, voters would have different total voltages in this case. Converting to less-ideal self-reporting, it runs afoul of strategic voting. Everyone will self-report their voltage as infinite, vote infinitely for their first candidate, which either reduces to one-man-one-vote or is undefined. By contrast, any scheme to limit their voltages by external measurements will end up reintroducing the original problem when preferences change and the external corroborate doesn't.

Even if you don't buy my proof that consciousness is ontologically subjective, it is epistemically subjective for all practical purposes. It can't be measured, but nevertheless, a true well-behaved aggregate preference exists.

Arrow's Impossibility Theorem would be a consequence of ontological subjectivity, Aristotle could have worked out ontological subjectivity, then derived Arrow's theorem from it. My proof is therefore useful even if not exactly true. But usefulness is usually correlated with veracity...


Unknown said...

hello Alrenous.

My i talk to about AI?


Alrenous said...

I don't believe in the idea of 'off topic.'

Just, kindly distinguish between Artificial Intelligence and Artificial Consciousness. If possible, also respect that I define intelligence as the conflation of learning, logic, and creativity, or 'gather bits,' 'process bits,' and 'create bits.'

Unknown said...

Thank you.

I guess artificial intelligence for know. But i feel that
once AI become more mature it will lead to artificial consciousness.

I came across you on another forum, and it seems like
you may have a simular model of AI as mine.

Unknown said...

About the arrow's.
If i walk into an ice cream store very hungry, and
on a budget. I would pick the most calories for each
dollar. But sense i would have need for food i
would be in a ranking mood. I think the less we
crave for something then we are more inclined to
do permutation in are behavioral pattern, based less
on measurements.

Best regards,